Quanta Magazine

Neutrinos From Deep Inside Earth Provide a New Picture of the Mantle

Fri, 07 Aug 2026 01:55:32 GMT

The JUNO experiment, located outside the city of Guangzhou in China, is expected to report its first geoneutrino detections this year.

JUNO Collaboration

In a laboratory 2 kilometers underground, a crane lowers Matt Depatie, a detector technologist, through a hatch into a white-walled cavern filled with about 7,000 tons of ultrapure water that glows as blue as wiper fluid in the light. “Splashdown,” Depatie says over a radio as he steps into an inflatable raft waiting below.

Normally, the cavern is one of the darkest places on Earth, but today, it is lit up for maintenance, offering us a rare chance to see inside. I peer through the hatch at Depatie as he paddles over to examine the submerged experiment. He’s inspecting a house-size detector built to catch some of the most elusive particles known to physics: neutrinos.

This is the SNO+ neutrino experiment, buried deep within the Creighton mine at Snolab, an underground physics laboratory in Sudbury, Canada. SNO+ consists of an acrylic sphere lined with nearly 10,000 sensitive light detectors and filled with 780 tons of oily liquid scintillator, which flashes when lit up by energetic particles. The water around the device and the rock above it shield the detector from the glare of cosmic radiation, allowing the flickers of less common particle interactions to shine through.

Our whole journey down has been part of the crusade to maintain absolute darkness, even beyond the visible spectrum of light. As we descended the main shaft and walked through a rocky tunnel to the lab, our bodies and clothes collected minute amounts of radioactive radon dust. Before entering the main laboratory space, we tossed our mine clothes, showered, and changed into electric blue jumpsuits and hairnets to minimize the contamination we carried in with us. “The showers aren’t for you,” Depatie said as we changed, “they’re for the science.”

Matt Depatie, left, helps maintain the SNO+ detector, which reuses components of the SNO experiment that ran from 1999 to 2006.

James Dinneen

Such extremes are necessary when you’re trying to catch ghosts — in this case, ghosts that may help reveal the secrets of inaccessible regions deep within the Earth.

Radioactive Planet

Neutrinos are the most abundant of all the particles that have mass. But that mass is tiny: just a millionth the mass of an electron. With such little heft and a neutral electromagnetic charge, the particles hardly ever interact with other matter. Trillions of neutrinos — mostly those produced in the sun — pass through our bodies every second, yet after years of hunting them with detectors such as SNO+, researchers have captured only a few hundred thousand of their precious flashes.

Even more elusive — so much so that after decades of searching, scientists have detected only a few hundred of them — are geoneutrinos.

Geoneutrinos are produced in processes that heat the interior of the planet. This heat plays a major role in powering the flow of rocks in the mantle, which shapes everything from plate tectonics to Earth’s magnetic field. It comes from two main sources: heat left over from the planet’s formation, and heat produced by the decay of uranium, thorium, and potassium in the rocks of the mantle and crust. Without this second source, Earth would have long since cooled off and become a tectonically dead planet.

The SNO+ experiment sits deep underground, shielded from cosmic rays beneath 2 kilometers of rock.

Courtesy of Leo Duquette/SNOLAB

In counting geoneutrinos, physicists can get a direct measure of Earth’s vital heat-producing elements. “It’s the one thing we do that focuses on the Earth,” said Ryan Bayes, a particle astrophysicist at Queen’s University in Ontario who works on SNO+. “Everything else we do is more focused on what we receive from other places in the universe.”

The first detection of geoneutrinos, by an instrument in Japan called Kamland, was reported in 2005. In 2009, the Borexino detector in Italy reported catching several dozen more. In November 2025, SNO+ reported its first detection, bumping up the number of observed geoneutrinos by about 50.

What makes the detections at SNO+ special is the experiment’s location: These are the first geoneutrinos measured in the western hemisphere, offering a new perspective on Earth’s radioactive interior.

Major uncertainties remain in interpreting the results from these experiments, but researchers’ best estimates suggest that each site is measuring a different flux. “It could be that that’s the first hint that the mantle is not uniform,” said Mark Chen, a particle astrophysicist at Queen’s University and director of the SNO+ collaboration.

Geochemists have conventionally assumed that radioactive elements are distributed evenly throughout the mantle, because the flowing rock should mix everything together. But the measurements of geoneutrinos in different locations could hint that this is not the case.

The regions that seem to be producing the most geoneutrinos sit roughly above continent-size blobs of anomalously hot, dense material, known as large low-shear-velocity provinces, or LLSVPs, which seismologists have mapped on either side of the core. One is under Africa, the other under the Pacific Ocean. “There may be deep Earth structures in the mantle that are not understood,” Chen said. “It could be that [they] concentrate some kinds of elements.”

Neutrinos could one day offer new insight into the still mysterious origin of these deep structures and, more broadly, the patterns in the mantle that underlie many aspects of the Earth system. “It really would be a way to make a chemical map of the Earth’s interior,” said William McDonough, a geochemist at the Chinese Academy of Sciences who has long been a leading voice in the search for geoneutrinos.

Catching Geoneutrinos

The outstanding question is whether the geoneutrino measurements reveal differences between the areas of mantle below each experiment, or if the imbalance originates in the way the different experiments count their geoneutrinos. Researchers across the board say there’s still so much uncertainty that it’s impossible to say.

“If we take it at face value, we could say maybe the western hemisphere has a lot more radioactive material in it than the eastern hemisphere,” McDonough said. But there are reasons to be wary of these estimates. “Are the Italians right? Are the Japanese right? Are they both right? Or is something wrong?” he said.

The Borexino experiment, located at Gran Sasso National Laboratory in Italy, was designed primarily to study neutrinos from the sun.

Volker Steger/LNGS-INFN

The uncertainties associated with each detector’s results come from the sorting process that physicists go through to identify geoneutrinos, Bayes said. “They don’t just show up and say, ‘Hi, I’m a geoneutrino.’”

Scientists must eliminate signals from particles with too much energy, particles with the wrong measure of a property called helicity, and particles that they expect to see flowing from nuclear reactors. They must also eliminate geoneutrinos coming from Earth’s crust, with the largest contribution coming from the area within a few hundred kilometers of the detector. When those other detections are subtracted from the total count, the geoneutrino signal from the mantle should be all that’s left.

In general terms, the geoneutrino flux from the mantle seems to be very high at Borexino and very low at Kamland, though the uncertainties are great. A detailed geological interpretation of the SNO+ results is still in the works, Chen said, but so far scientists see a “pretty in-between” mantle below Canada.

A particular challenge for SNO+ scientists is understanding the neutrinos coming from the detector’s surroundings, including a basin formed 1.8 billion years ago by a giant impactor. “There are lots of unknowns in this geological area,” said Virginia Strati, a researcher at the University of Ferrara in Italy who helped develop a local model of radioactivity for Snolab.

The 20-kiloton JUNO detector began operation in August 2025. In addition to catching geoneutrinos, it studies particles that stream from the Taishan and Yangjiang nuclear power plants.

JUNO Collaboration

Uncertainty also comes from estimates of the total amount of radioactive material heating the mantle. The flux of geoneutrinos suggests that these elements could contribute anywhere from just a small percentage of its heat to half of it — a discrepancy equivalent to the output of tens of thousands of nuclear power plants.

Both sources of uncertainty make it even more difficult to detect any differences between the chemical makeup of particular sections of the mantle. The difference in the geoneutrino flux expected from various distributions of radioactive elements “is very small, and is hidden in these uncertainties,” Strati said.

Future Flux

The detection at SNO+ comes at an exciting moment for geoneutrino research: JUNO, another huge neutrino experiment currently collecting data in China, is expected to report its first geoneutrino flux later this year, adding a fourth and notably richer view. With more than 20,000 tons of scintillator, the experiment — buried under a mountain outside the city of Guangzhou — is so large that it is expected to detect more geoneutrinos in its first year than the combined output of Kamland, Borexino, and SNO+ over decades.

Clearer estimates of the geoneutrino flux at each experiment could come from more detailed geological data, as well as further geoneutrino counts at each site. However, McDonough says the best thing would be to build a neutrino detector at the bottom of the ocean. It’s an idea McDonough has championed for decades.

Such a detector would be far from continental rocks, which are rich in radioactive elements; oceanic crust is also thinner and more uniform. Crust-related uncertainties go down so much that “you are in mantle-only territory,” he said.

The idea of an ocean-bottom detector, estimated to cost hundreds of millions of dollars, has seen little take-up from government funders to date. But McDonough is hoping he can make something happen in China, which has given the green light to other big geoscience projects. “It’s very possible,” he said. Until then, physicists will keep paddling around for answers deep underground.

How Does Touch Lead To Pain Or Pleasure?

Thu, 06 Aug 2026 01:37:48 GMT

Chanelle Nibbelink for Quanta Magazine

Pain and pleasure seem like simple facts of life, however they are anything but that. Neuroscientists still cannot say why physical pain differs from psychological pain, for instance, or why a loved one’s touch soothes while a stranger’s touch repels.

To explore the science behind these sensations, Janna Levin talked to Ishmail Abdus-Saboor, a neuroscientist at Columbia University’s Zuckerman Institute. Their conversation covers how pain serves an evolutionary purpose, how researchers measure pain and pleasure in the lab despite the absence of any objective biomarker, and how touch functions as a social and emotional signal, not just a sensory one. Abdus-Saboor also describes his work with naked mole rats — a species that barely feels pain, shows no signs of aging, and lives in colonies built almost entirely on touch — and the ethical trade-offs when studying sensations in animals that cannot describe what they feel.

Listen on Apple Podcasts, Spotify, TuneIn or your favorite podcasting app, or you can stream it from Quanta.

Transcript

[Music plays]

JANNA LEVIN: Hello. Hello out there, I’m Janna Levin.

STEVE STROGATZ: And I’m Steve Strogatz.

LEVIN: And this is The Joy of Why.

STROGATZ: A podcast from Quanta Magazine in which we explore some of the biggest unanswered questions in math and science today.

LEVIN: So Steve, we’ve been talking with Ishmail Abdus-Saboor who’s a professor here at Columbia [University], not a few blocks from me, about skin as an organ and as a vehicle for transmitting both pleasure and pain.

STROGATZ: Mm-hmm. That sounds very interesting.

LEVIN: Yeah. I think it’s interesting that very little is known about pain. I mean, if you think about your own experience, it’s kind of strange when you start to meditate on it. What is it exactly, right? It’s very unpleasant, but other than that, what is it?

STROGATZ: It’s really mysterious, especially when you have pain that doesn’t really relate to tissue damage. Like, sometimes I’ll just be washing something at the sink in the kitchen, and then suddenly I have pain, and I think, “Come on, that’s ridiculous. I didn’t do anything to my back.” And, you know, people will tell you pain is mental. You can sort of talk yourself out of certain pain, which raises the point that pain is not as simple as it might seem at first.

LEVIN: Yeah, and in particular, he studies this at the level of animals. But it’s one of these things that’s very hard for animals to tell you reliably what they’re experiencing. So, a lot of his work is really trying to interpret the animal’s interiority, the animal’s experience of different sensations.

STROGATZ: Yeah, I wondered as you were describing this work, is it touch as a means to learn about interiority, or is touch the primary object of interest here?

LEVIN: I mean, I think that that’s an interesting question. Like, with many scientific ambitions, sure, maybe the big goal is consciousness, right? But no, the big goal is always very far off. That’s not the language in which they’re operating.

The language in which they’re operating is data, observations. You know, it’s more immediate to their experiments.

STROGATZ: Well, right. They say science is the art of the solvable, and so we’re trying to restrict ourselves to things where we can make advances, make real progress.

But I have to say, I got a little bit of a queasy feeling when you mentioned pleasure and pain, especially as a person with an animal at home. My dog, Murray, that I love so much.

LEVIN: Yes, I’ve heard about Murray.

STROGATZ: I know. I’m sure everyone has.

LEVIN: I’ve seen pictures of Murray.

STROGATZ: Okay. Okay. But still, I mean, the thought of pain, you know, and I know there’s a lot of animal rights people among our listeners. So I hope in listening to this episode, I don’t know, what’s the pain part of this gonna be about?

LEVIN: We did talk about this. I mean, this is a very gentle animal lover. It’s really interesting to talk to Ishmail. His experiments, they’re gentle. Maybe, they’ll notice if a paw is retracted, so if it’s uncomfortable, but they’re not torturing these animals.

But even then, I think animal experimentation, even in the most benign sense, is called into question. And he thinks about the ethics of that.

Well, let me introduce our guest. His name is Ishmail Abdus-Saboor. He’s a neuroscientist just down the road at Columbia University Zuckerman Institute, and he studies the skin-brain axis, and in particular, our sense of touch, including gentle touch and soothing touch.

STROGATZ: Fantastic.

[Music plays]

LEVIN: Welcome to The Joy of Why, Ishmail. I’m so glad to speak to you.

ISHMAIL ABDUS-SABOOR: It’s an honor to be here with you as well.

LEVIN: It is a pleasure to get to know colleagues on the same larger campus. I’m very interested in starting with your journey. You grew up in Philadelphia. I read some of your other interviews where you discussed your love of animals, and how at one point you converted the third floor of your home into a year-long science experiment. And maybe I’m exaggerating, but tell me about your initial relationship with animals as a child.

ABDUS-SABOOR: Yeah. Yeah, it’s really joy to be here and, I think, if you were to ask me when I was a kid, what I wanted to do with my life and career, I always said I wanted to become a scientist. You know, I didn’t know any scientists directly, but if I thought about the classes in school, that kept me very excited and energized, and I would watch Animal Planet a lot as a kid and I could just watch nature shows for hours on end.

I had many pets growing up, dogs and cats, but also like lizards and turtles and snakes. You know, I remember, like, as a kid having this subscription to this, like, Turtle Digest sort of a magazine. You know, I was very fascinated about biology and biological systems and how animals communicate and cooperate. I think my science career set in motion in earnest as a freshman in high school, as you alluded to, at Central High School in Philadelphia, as a part of an honors biology class. You know, actually, we didn’t get gym class because to sign up for this honors biology, we had to take two periods of biology. And for me, even as a 14-year-old kid, like, I just jumped at that opportunity. You know, who needs gym? Got teased a little bit.

But, you know, as part of that project, we were able to do this year-long science fair project, and many of the students worked at neighboring universities in Philadelphia, Temple or Drexel, or UPenn. But we also were able to do science at home. So this is what I did. You know, basic rudimentary equipment and things. And the project was actually looking at regeneration in crayfish.

So you know, my parents were very supportive of me and let me take over, you know, the third floor of our house there in the Germantown section of Philly. And, you know, there were hundreds of crayfish and I’m sure it didn’t smell so well up there. But at the time, you know, there was this really big push on, like, supplements and ginseng. And like ginseng was supposed to be like this magical supplement that, like, improved health and memory and all sorts of wonderful things.

So my idea was if I spiked the crayfish, their water with this ginseng herbal supplement, then this could, like, speed up the rate of regeneration because they do have the ability to regenerate lost appendages. So, you know, I got to become a scientist and I, like, trim parts of their appendages and measure the rates of it growing back. And, it was a very exciting time to keep a lab notebook and have hypotheses that I could test and to make graphs and plot my data and do statistical tests to see if there was anything here.

Unfortunately, I don’t quite remember the outcome of those.

LEVIN: You weren’t as diligent with your data analysis as you are now.

ABDUS-SABOOR: Yes, exactly. That’s exactly it.

LEVIN: We actually have something in common. My daughter is obsessed with animals, and at one point we had something like 23 animals in my New York City apartment. It looked like a Petco. There were snakes, lizards, tarantulas. It was insane. Only one time did one animal kill another animal. It’s a real calling, I feel, this interest in animals.

But you ended up studying smaller-scale biology, cellular, molecular. What led you to make that transition from this sort of love of animals to the actual smaller-level biology?

ABDUS-SABOOR: When I went to college, I thought, you know, again, this love of animals, maybe I wanna become a veterinarian.

So I worked in a number of veterinary clinics and hospitals, and there my experience was, like, helping the vet with spaying and neutering and, and it was very monotonous and, and frankly, quite boring. And I kinda missed, like, this kinda fast-paced nature of biological exploration. So I did another internship my junior year in college at University of Pennsylvania in the Cell and Developmental Biology department, and there we were working on, you know, cells in the hearts of mice, uh, um, proteins in the hearts of mice that are important for cardiac development and function.

And there I got exposed to molecular biology research and working at the bench, and just the culture of science, the whole ethos of the, you know, of scientific discipline at lab meetings and people presenting results and, and just talking about all the open questions and, and being able to, to look at life at the scale of molecules, DNA, RNA, you know, the molecules of life.

I thought that was just very exciting. It wasn’t until a few years later that I moved into, like, neuroscience and sensory neuroscience.

LEVIN: Yeah. There’s this interesting history, painful history — pardon the pun — of our relationship with animals and, sort of denial of the idea that animals are conscious or that they feel pain.

ABDUS-SABOOR: Yes.

LEVIN: Uh, and so going back to Descartes in the 17th century, he infamously performed vivisections when, you know, live animals howling. How could he possibly — and I’m not actually asking you to defend this point of view — but how could he possibly have suggested that the animals were not feeling pain?

What’s your understanding of how we transition from this physical detachment, you know, as our colleague of ours at Quanta said, “They don’t think, therefore they are not.” That was his attitude to accepting that animals feel pain.

ABDUS-SABOOR: This is a wonderful question, and it’s one that I’ve thought a lot about and keeps me and everyone in the lab awake at night. I mean, it’s a part of a broader question, the question of consciousness, right? Do animals have a level of consciousness that we would have?

So if we boil this down to the idea of pain and how it works and where do we draw the line on whether or not animals feel pain? It’s a debate that has raged for many years and I think the modern idea is that you need a brain, you need some central processing unit to have full function and cognition to be able to experience pain.

If you look at lower animals, perhaps, no one denies that they can sense nociception. Nociception, it’s a fancy term for receptors, neurons, out in the peripheral nervous system that can be activated by noxious stimuli. And those signals travel to some central processing units so that the animal knows to like move away. And I think this idea, everyone appreciates. Even simple, you know, bacteria, right, single cell organisms if you put them in an environment that’s not conducive, they’ll move away. They’ll recoil, because they have sensory neurons out in their peripheral nervous system.

Now, we would consider that nociception, but not quite pain. Encapsulate the experience of pain, you have to have a central processing unit whereby you can respond appropriately to subsequent noxious stimuli. There’s some sort of learning and memory. There’s higher level cognition. You understand that this particular stimulus that I’ve received, like, causes me pain, so now I’m going to avoid it.

So then the debate is, if that’s the case, then which animals have it and which animals do not? And I think, as a neuroscience community, by and large the idea has been that many animals, especially lower animals, perhaps do not have that level of higher cognition and consciousness.

You know, a question I get all the time, right, people, especially in the New England area, they ask about lobsters, right? Should I feel bad about throwing this lobster in this hot boiling pot while it’s still alive?

LEVIN: The classic example of slow boiling the lobster.

ABDUS-SABOOR: Exactly, but then people say, “Well, they tell me they can’t feel any pain, so I shouldn’t feel bad.” And they ask me, “Is that true?” Depends on who you ask, right? And perhaps you have to do the test.

So as a field, like the classical test that we do is like this conditioned place aversion. So does an animal have enough brain real estate to understand that this thing is noxious? They should be able to understand that the environment that they received this noxious stimulus is bad. Such that if you put them in that environment later, they can remember that something I received here was not good and I want to escape or avoid it.

Animals that don’t have that cognitive ability, even though they’ll recoil from something noxious. They don’t have the ability to form the memory, a conscious perception, the negative feeling that is attributed to pain, right?

So this is what people do, and if you can do this test and show that they can make these associations, then people say, “You know what? I think this animal can feel pain, and let’s add that animal to the list.”

LEVIN: This is interesting because the animals you work with specifically have to feel pain to be part of your study but also don’t. And that’s also part of your study. Why they don’t—we’ll come to the naked mole rats.

ABDUS-SABOOR: Yes. We mainly work with rodents, and I think it is accepted that rodents can experience pain or nociception. They will withdraw their paws, like we would withdraw our hands. There is some debate in our field about, again, these higher-level components of pain, the emotional negative valence that’s associated with pain. How much of that are rodents experiencing?

And this is part of, like, I think the importance of some of my work because we’ve taken really detailed behavioral mapping of animals as they experience different stimuli. And we can say actually they respond in ways that they can’t describe to us their ongoing emotional states, but if we can use behavior as a readout of their internal states, they are displaying behaviors very characteristic of negative emotional states of pain and we’re trying to, like, kind of map that in the brain.

LEVIN: It’s a very interesting question that you’re raising because while reading about your work, I was wondering about the ways in which psychological pain differs from physical pain. And beyond differing, how they’re interconnected, right? As you’re describing, if the animal doesn’t have the psychological component, we downgrade it in terms of severity.

ABDUS-SABOOR: That is very true. And you know, I think many times we downplay animal intelligence or cognition because we don’t know how to tap into it. We haven’t designed the right test.

You reminded me of some work from a colleague of mine, Professor Kay Tye at University of California San Diego and also the Salk Institute. In rodents, she’s asking this question, physical pain and emotional, psychological pain do they map or intersect anywhere in the brain? And she designed a really clever test, which she calls the FOMO task in mice, the fear of missing out, where she’ll have mice that are living together. And she puts a divider between them and the animal outside of the divider has to sit there and watch its friends get, like, this chocolate milkshake.

Okay, so the mouse is just watching its friends. The mouse is a little bit hungry, a little bit thirsty, and watching his friends take this milkshake. And her idea is that this is like a psychological form of pain. And then she’s doing recordings in the part of the brain called the insular cortex and asking the question like, does this interact with physical pain? And it appears that it does. Like it alters their threshold to respond to, like, physical pain after going through this emotional psychological pain. And maybe that there’s similar constructs in the brain, and we can even study this in a rodent.

LEVIN: Let’s discuss a little bit of the actual science that goes into this. So, your research in the somatosensory system deals with pain and touch and skin. Can you tell me about some of the brain pathways and the different receptors involved in the different types of sensations?

ABDUS-SABOOR: Sure. So right, as you mentioned, the somatosensory system is our sensory system that mediates touch, pain, itch, temperature, pressure.

LEVIN: And these are all very distinct experiences.

ABDUS-SABOOR: Yes, they are very distinct experiences. Really excitingly for us as a field, if you would look 30 years ago, for example, we didn’t have a lot of the molecular players to even have an entry point into thinking about how does this work.

We had a basic idea of the neuroanatomical pathways. So, you have these peripheral sensory neurons called, uh, they emanate from a structure called the dorsal root ganglia. And we have, like, 30 pairs of these that run alongside our spinal cord. They send one long process to the skin or other internal organs and one process to the spinal cord.

From the spinal cord, a different set of neurons kind of picks up the relay, goes to the brainstem, and then from the base of the brain to other areas throughout the brain.

So, the neuroanatomical pathways, we kind of have had this for quite some time. But as you mentioned, there’s touch, there’s hot, there’s cold, there’s itch, like these are quite distinct. So, it’s where the specificity resides that allows us to exquisitely detect these different sensations.

And you know, our field has had a really nice revolution in the last 15, 20 years where within these sensory neurons out in the peripheral nervous system, we have identified receptor proteins that confer specificity.

And two of the most famous ones I’ll just mention because they were the subject of a Nobel prize in 2021. So, one was the discovery of a receptor protein called, um, TRPV1. Transient Receptor Potential Vanilloid 1. This was discovered in the lab of David Julius, who’s set out to determine, like, how chili peppers, like why do we perceive them as hot? We had an idea of which neurons may do it, but like, how do you explain the “how” at a molecular level?

And so, he designed a really ingenious screen where he cloned receptors into a cell line and basically applied capsaicin, the active ingredient in chili peppers. And he wanted to find cells whereby once you add capsaicin, there can be like an intracellular response. They can be activated in the form of calcium entry into the cell, which is a proxy for, like, neuroactivity.

And this activity can be conferred by adding a certain receptor protein. So, he screened and basically found this channel that we now call TRPV1, that when it’s expressed on the surface of cells, confers the ability to respond to capsaicin.

We now know, and they showed in that paper, that this same receptor mediates the response to heat. So, this is why, like, capsaicin and chili peppers have this heat sensation because the heat sensing neurons that also respond to capsaicin expressed this one protein.

This paper came out like in 1999, I believe. And it really began a molecular age of pain research because now we had a receptor that we can say, okay, this is how you define a pain neuron or a heat sensing neuron if it expresses this TRPV1 receptor.

LEVIN: So, they’re actually physically specialized neurons. They’re physically different.

ABDUS-SABOOR: They’re physically different than other neurons, by their constitution of the genes and the proteins they express on their surface.

Now, this was in the late 1990s, and there was another pioneering study just a few years later by Ardem Patapoutian’s Lab, who was the co-winner with David Julius on that 2021 Nobel Prize. He did a similar sort of a screen in a different cell line looking for receptor proteins that confer mechanical sensation. Okay. And there they did a slightly different screen where they use RNAi to knock down the expression of receptor proteins in the cell line that they knew was mechanosensitive and could show that without this one protein or two proteins, then the cells no longer responded to mechanical force.

We now call those genes Piezo1 and Piezo2, and for the most part, almost every neuron that we know of that is mechanically sensitive, meaning can convert physical stimulus energy into the language of the nervous system, electrical activity. It’s conferred by this mechanical sensor Piezo. And it’s not just in neurons; it’s in non-neuronal cells.

So here’s another example. I just gave you two examples of they’re sensory neurons, but if this one has TRPV1, it’s gonna respond to heat, noxious heat. And if this one has Piezo, it’s gonna respond to pressure. And there are other sorts of receptors that confer itch or cold, et cetera.

Now as a field, if I jump ahead to 2026, there was just The Brain Prize, which is the biggest prize in neuroscience, was just awarded in our field again to David Ginty at Harvard and Professor Patrik Ernfors in Europe. They’ve done really pioneering work to show there are at least 15 different classes of these pain, touch, itch neurons that are defined by their expression of different genes, their physiological properties, their expression patterns within the skin. As a field, I think we’ve made, and are making, really great progress.

So you know, what’s left to do, and why am I still employed? You know, I think, as a field, we’ve learned a lot about detection in the periphery. One of the things that really drives me in the work we do in my lab is making a connection between the peripheral nervous system, all these mechanisms in the skin, and how does this connect to the brain where perception resides, right? Making the connection. This body, brain, physiology, and signaling. This is where I think the next wave of major discoveries we’re ripe for in this field.

LEVIN: So here the subject really has shifted from a kind of behavioral science to really hardcore molecular and genetic science. Your particular interest is very specifically skin, as you’re saying, and I know that you’ve quantified a pain scale to try to have a more quantitative way of discussing these things as opposed to just qualitative observations of behavior. Tell me about the pain scale and how that work ties in.

ABDUS-SABOOR: That’s a wonderful question. You know, it was like a side quest actually. So, I’m most at home in genetics and molecular biology. As I mentioned before, studying pain and rodents is challenging. They can’t talk to us, right? And I saw that for me to, like, have precision and understanding the genetic and molecular manipulations, I had to take a step backwards and understand the behavior. And that step backwards has been like 10 plus years of this, like plugging away of trying to make these rodent pain scales.

What we had in the field before some of our studies was just like, you poke an animal with something that you think is painful, and if they respond, they’re in pain. If they don’t, they’re not in pain.

Pain is so complex, right? Just think if someone, like, poked you and looked at whether you lifted your hand, would that be sufficient to explain your pain state? No. It’s so much richer. So, this is what we attempted to do with this rodent pain scale to put a number on their sensation.

LEVIN: Which, of course, doctors ask you to rate your pain scale, which is so fascinating. It’s not something you can measure.

ABDUS-SABOOR: Yes. That gets to another point that keeps us awake in the pain field is that we do not, to this day, you know, April 21, 2026, we do not have a biomarker for pain, alright? This drives us crazy. You cannot get a litmus test. There’s no, like, if this gene is up or if this brain area is on, that means you’re in pain. And if not, you don’t.

We don’t have that. We’re searching. We and everyone in the field is searching, but we don’t have it. In the clinic, we have to rely on self-reports. People largely telling us how they feel. There have been some advances in, like, fMRI and other brain-imaging approaches that looks promising, and maybe we will get to a day where there’s a signature that we can confidently say someone is in pain and not some other state. But we don’t have that yet.

LEVIN: Mm-hmm. As an animal lover and a person who has looked at the complex history of science in relationship to animals, how do you reckon with the ethics of continuing to work with animals?

ABDUS-SABOOR: It’s a tough question, you know. We have an institutional animal care and use committee that every single experiment we do with animals we have to justify, right? And we have to use the lowest amount of animals and do our best to induce the least amount of pain to study the biological process we’re interested in.

It’s a challenge for someone who’s studying pain because we have to like induce the pain to be able to study it, right? One of the benefits I think of our behavioral assays is that because we now get so much resolution, we can test less animals to reach our statistical observations and conclusions. So, this kind of helps with animal welfare.

We try our best to treat the animals humanely and with respect because we do understand that they are giving their lives oftentimes for human benefit. And this is just something that we have to appreciate. We need medicines, we need cures, we need treatments. And oftentimes animal research is a part of that pipeline. And I’m comfortable ethically with that understanding.

Now I know there’s some people who are not. And it’s not upon me to convince people to change their beliefs or thoughts. I respect those. And there have been people who say, “I love the research you do, but ethically this is not for me.” I understand those concerns as well.

But I think, you know, in 2026, we’re still at a point where we need animals to learn how the pain system works and how to design safe ways to relieve chronic pain. And we don’t have better models to do this, so we have to work responsibly and ethically in these animal models.

Now, will that change? Will there be a time where we can use computer models or stimulations or organoid models and learn just as much as we can in animal models? Maybe that day will come and we’ll have to revisit this. Maybe there won’t be a day where we can continue to justify using animals to study pain or in neuroscience research. But I don’t think that day has arrived and they’re still very important conduits to study.

LEVIN: Well, this opens up the question about this fundamental research that you’re doing in a laboratory in an academic setting, how does this transition to therapeutic treatments for human patients?

ABDUS-SABOOR: Yeah, I think the goal of any biomedical researcher such as myself where I’m a basic scientist, curiosity-driven scientist, and I think there is major value in this increasing knowledge for knowledge’s sake, even if it doesn’t have a direct application at the moment that we’ve made the discoveries.

However, in saying that, I do believe we have duty to the public and the taxpayers who fund our research to think about how the basic work we’re doing can translate into therapies and cures and especially for pain, right? There are millions of people who suffer with chronic pain.

The beauty of working in rodents is that many of the genes and molecules, the neuronal pathways I’ve talked about are highly conserved, right? The wiring and the neuroanatomy of the pain system is very much shared between rodents and humans, okay? We really do operate under the space that some of the things we discover can have direct application.

I’ll just mention an exciting example. Some papers in the early 2000s in humans showed that there was a family of patients who can’t feel any pain whatsoever. And there have been these rare cases throughout history of people who just don’t feel any pain. It’s actually, like, not a good thing because many of these patients don’t live long lives. They actually injure themselves. You know, pain is, from an evolutionary perspective, good for our bodies.

LEVIN: Good information.

ABDUS-SABOOR: It’s good information. And especially during development, you learn, like, to not touch that hot stove, right? To not do things that could hurt you.

Anyway, there was a family of people in Pakistan who didn’t feel any pain, so you could do genetic studies and kind of trace the pain and sensitivity. And the scientists went over there and did really heroic work where they sequenced their DNA and they found they all had mutations in a single gene. It’s called Nav1.7. It’s a voltage-gated sodium channel, okay? This channel, this protein, seems to be very specific to pain neurons in the periphery. So if people don’t have a functional version of this protein, they won’t feel pain.

And then conversely, there’s another class of patients that have the exact opposite. It’s called, like, Burning Man syndrome, where they just have spontaneous pain, mainly in their extremities throughout life. It turns out the mutation is in the same protein. This one protein, you don’t have it, no pain. Too much of it, lots of pain.

Same thing happens in rodents and many other mammals we’ve studied. This voltage gated sodium channel is very important for the activity of the neuron propagating an action potential and specifically in pain neurons. And in fact, they’re new drugs that have been improved that actually block this particular receptor and it seems to improve pain for many patients.

There’s another version of this protein called Nav1.8 that seems to have similar functions. So maybe some of the therapies in the future, we’ll kind of do a double block of both of these proteins.

And this work, a lot of it is going on in rodents, Here’s a one example of a lot of like back and forth and crosstalk between animal studies and actually direct translation.

One of the things we’re very excited about doing in my lab, I mentioned these behavioral tools. And with our behavioral tools we can delineate in rodents the sensory component of pain versus more emotional components of pain. And so there does appear to be an emotional network in the brain — areas like the amygdala, the anterior cingulate cortex, insular cortex, and some other areas that seem to confer an emotional component of pain. How that works, you know, we and others are hard at work.

But the point I wanna make, back to your question about translation. It would be very nice if we could have therapies of the future that don’t target the pain at the level of the peripheral nervous system, at the level of sensation, but alter it at the level of perception and maybe alter the negative emotional state of pain. Because maybe you don’t want a world where you can’t feel any pain, as we mentioned, it does serve some purpose, right?

But, if we can remove the hurting component but keep the sensory intact, then maybe this is how we want to tackle pain. But we have to know how that works at a deep level to be able to kind of target that. But I can envision a future where that’s possible.

LEVIN: It’s so interesting. I mean, I don’t even wanna know how they discovered that this family felt no pain. I don’t even wanna know what happened to them that brought that to the scientific community.

ABDUS-SABOOR: You know, in some countries there are a number of street performers actually who do things – you know, they’ll walk on hot coals or like, do things. And, you know, one of the kids in that family, he would do tricks. He would climb the second-floor building and jump off and just pop right up. And everyone would cheer. And so these sorts of things.

LEVIN: The ability psychologically to overcome pain or to mitigate pain is so fascinating to me because of course, we act like psychological is disconnected from the body. But what we really mean is what the neurons are doing in the brain. And I think that there is this kind of culture of magical thinking that we can transcend pain but there might be a sense in which that’s literally physiologically possible.

ABDUS-SABOOR: That is very true. And what you’re talking at too is one of the reasons I got into pain and pain research. There’s a really nice book called The Challenge of Pain, written by Melzack and Wall, two really pioneering scientists in our field who came up with one of the most important theories in the history of pain: the “gate theory” of pain. But anyway, in this book, they lay out, like, as you’re getting to all these cases where people should be experiencing lots of pain, but they don’t. You know, some people who you can hypnotize them and their pain goes away.

And there are too many anecdotes like this to think that it’s not a real phenomenon. A related phenomenon that we do know a little bit more about, and people are starting to model this in rodents, which I think is really cool, is the placebo effect, which is very strong for pain actually.

If they have a strong expectation and belief that this thing will alter my pain, it can actually work. And conversely, if you tell someone, “I’m gonna give you this treatment and it hasn’t worked for anybody, everyone says it’s crappy, but you’re outta options, and I just wanna try it anyway.” They’ll come back and say, “Doc, you’re right. It didn’t work.” And it could be the same medicine, right?

So this expectation and belief of pain relief is very strong. We now know it definitely taps into our endogenous opioid system, our endogenous system to kind of control pain. It taps into these things. If you block like opioid receptor signaling, you can block many of these effects.

It’s not magic, but it’s acting on defined neuro circuits in the brain. And there are many labs that are hard at work, Greg Corder and Matt Banghart and Greg Scherrer, amongst others to try to map how this is working.

LEVIN: Amazing. I did see that you had talked about the pain addiction connection. Particularly with opioids.

ABDUS-SABOOR: Correct.

LEVIN: And what you’re saying is there’s a biological substrate reason why there’s a connection between pain and addiction.

ABDUS-SABOOR: Yes, that’s very true. We have an endogenous opioid system that can be activated by many things, and we have these opioid receptors all throughout our body.

I mean, the discovery of the opioid receptors back in the late 1970s, in rodents, they could stimulate this one area in the brain, the periaqueductal gray. And you could get really strong pain relief. The rat tail would be on the hot plate, and you stimulate this area in the brain. Then they don’t respond, okay? And they found that this area is, like, flooded with opioid receptors. And this response was, like, dependent upon activation of the endogenous opioid system.

Opioids can be powerful relievers of pain and the receptors are everywhere. This is why they also have so many unwanted side effects because they act on the pain system, but they act in the periphery, they act in the bladder, in the gut, in the DRG neurons, the spinal cord. They’re loaded everywhere, so they come with so many unwanted side effects beyond just pain relief.

[Music plays]

STROGATZ: Wow. So many surprising and very immediate things to think about there. I think anyone listening to this can relate.

LEVIN: Mm-hmm. I didn’t really appreciate that the opioids… Of course, I knew they were pain relievers, I guess. I knew that was the story. People were originally going to seek pain relief, but I thought it was a external consequence, you know? I didn’t think it was targeting the same biology.

That was really surprising to me, and that we have this endogenous, natural mechanism that can do the same thing, which is why it suggests we can overcome pain psychologically to some extent, you know? I guess it also just shines a light. There’s a lot we don’t understand about how our own minds work and bodies work.

STROGATZ: I believe it. Watch any magic trick, and you’ll see that. But no, I mean, in something as corporeal as pain, I mean, right? That’s not an illusion. And yet maybe some aspects of it are an illusion. It’s confusing.

LEVIN: Yeah, I don’t know that it’s an illusion. I mean, things are triggered. There are signals, right? But you can flood the receptors with other chemicals. I mean, that’s really what it sounded like to me. And it has an interesting evolutionary role, right, pain in terms of survival. It’s important that we don’t go running if our foot’s broken, and it is very disadvantageous to survival to have no pain receptors, and they know that there are certain people who don’t feel pain. So just appreciate when your back hurts at the sink, Steve.

STROGATZ: Yes, I see. I should be grateful for my pain receptors.

LEVIN: Exactly. Well, after the break, we’re gonna leave pain behind, and we’re gonna talk about something a little more pleasant, and that is the wonderful naked mole rat.

[Music plays]

LEVIN: Welcome back to The Joy of Why. We’re speaking with neuroscientist Ishmail Abdus-Saboor, who studies the brain and our sense of touch.

I do want to turn to your important work in antithesis to pain, which is about gentle touch and social touch and pleasing touch. So, I’m both curious what drew you in this other direction, and of course how the receptors involved in gentle touch or stroking touch are different from pain receptors and why this is so important in the social fabric of possibly both animals and humans.

ABDUS-SABOOR: Great question. You know, as I was ending my postdoctoral studies at UPenn and opening my lab about eight years ago, I started to think about, okay, who would want to come work in my research lab? And if I only have projects studying pain, maybe that could be off-putting. Could be some people who would prefer to study, you know, social touch, appetitive, something good. And that was the case, yeah.

I wanna pay homage to a colleague of mine, David Anderson, at Caltech. He published this paper that I read as a postdoc, and it was just so fascinating and exciting because what they had discovered was that there was a population of neurons that seemed to be activated by stroking touch on the mouse’s skin, consistent with these being pleasurable social touch detectors.

And that paper, they didn’t look in the brain, and they hadn’t linked it to like any behavior. So, I thought this was right for someone with my background and genetics and molecular manipulations, really careful analysis of behavior and also linking that with brain imaging. So, the thing that differs between these neurons and this pathway and pain is that it’s a different molecular population. These neurons happen to express, at least in a mouse, this gene called MRGPRB4. It’s a tongue twister. They do express Piezo channels, this other mechano sensor I told you that’s important. So, they’re definitely mechanosensory neurons.

What makes them special is their constellation of genes they express that’s different than some of the other classes that mediate other types of somatosensation. Their wiring where they’re, that they innervate the hairy skin areas that are, like, normally touched. The neurons that they’re connected to in the spinal cord and from spinal cord to the brain. Basically, the whole pathway from skin to brain is gonna be different than a pathway for like hot or cold or pain, okay. So, the whole, like, circuit, the anatomy, the wiring is totally different.

LEVIN: Wow. So highly specialized again.

ABDUS-SABOOR: Highly specialized again. For example, if you stimulate, like, a pain pathway to animals, like, quickly they give you signs that this is painful and they don’t like it, they avoid it. But with this pathway, they give us signs that they actually like it. They want to spend time in environments where this pathway is stimulated. And if we look at, for example, dopamine release in the brain’s reward center, we can see that stimulating this pathway in the skin leads to like this dopamine release or if we genetically ablated these neurons, we see social touch behaviors are greatly kind of diminished.

Now, some of our ongoing studies where we’re really excited, because this gets to your question again about, like, why it’s important and translational impact in humans. You know, we think this pathway is also important for the ability of touch to relieve stress and anxiety and depression.

When you’re down or going through some negative emotion, just think about a hug from a loved one, a parent, a friend. It can really calm you down, and make you feel better. We appreciate this phenomenon, but how it works at a molecular, cellular and neuronal level is almost completely unknown. The skin to brain pathway for social touch that we’ve been discovering and elucidating, we think could be important for that. And we have really strong evidence. It’s unpublished, but hopefully, you know, maybe later in this year we’ll submit this paper showing that activating this pathway can relieve negative states, which is really exciting. And we do think it has direct therapeutic potential. Maybe we can even think about treating diseases of the brain, chronic stress, not in the brain but by targeting neurons in the skin.

LEVIN: Wow. Fascinating. Now there’s this research that you’ve done where you have genetically altered mice to become sensitive to blue light so that instead of physically stroking them, you can illuminate them with this blue light, and they have the experience of being gently touched. So, I have many aspects to this question.

One is, what a crazy thing to do. That’s not a question. And the other is, you know, are we going to genetically alter human beings so that they can do blue light therapy as part of this, you know, attempt to heal certain disorders of the mind?

ABDUS-SABOOR: Yeah, it would be nice if we could get there one day. So, this technology is called optogenetics and I think it is one of the most important technologies in all of neuroscience. And hopefully there’s a Nobel prize on its way for some of our colleagues.

But anyway, this shows that the beauty of, like, evolutionary biology and looking across diverse species, there’s this protein and algae that allows the algae to propel through these muddy ponds to blue light. It’s an ion channel, a non-selective cation channel, which just basically means there’s a part of the protein that when blue light hits it, the channel opens, it allows positive ions to flood into the cell that expresses this protein.

This is, like, perfect for neurons. Neurons are electrically excitable cells that fire to positive ionic current flowing into the neuron. So, if you can put this special protein on the surface of your neuron through some sort of viral genetic engineering, you can confer the ability to directly activate these neurons in this way.

So, part of this project that we did some genetic engineering crossing mice together to put this blue light sensitive protein only in these neurons. And we can just shine light directly to the skin, as you mentioned to confer behavior.

Now, to do this in humans, one would have to get to a point where you could do, like, gene engineering to add this protein to cell types of interest.

People are doing this now to treat – this is not our work – but to treat like forms of retinal degeneration and blindness actually. It’s really incredible. So maybe there is a pathway for using this technology to treat people.

LEVIN: You were discussing similarities in how certain neural networks are working for mice and for human beings in some of these complex systems. But you famously work with naked mole rats and who doesn’t love a great naked mole rat colony? Please, for those who are not in the know of the extraordinary naked mole rat, can you describe them a little bit for us and, why their colonies are so unusual in the rodent kingdom.

ABDUS-SABOOR: Yeah, they’re amongst the most fascinating animals I’ve ever encountered. Some days we’re just like, “What are we studying?” Some days we literally just sit there and just stare at them.

LEVIN: Watch them?

ABDUS-SABOOR: Yes, yes, yes. Because their biology is so fascinating, but some of the things that really excite us about them.

So for one, they don’t feel many forms of pain, for reasons that are not fully clear. They seem to be immune or recalcitrant, unable to get cancer. They’re long lived for rodents, so they live about 30 to 40 years.

LEVIN: Wow, that’s a long lived rodent.

ABDUS-SABOOR: Yeah, yeah. Most mice and rats, they only live one to two years. Yeah. Yeah. And they don’t really have traditional signs of aging. So, when they die, they just die. You can’t look at ’em and age them. They don’t seem to have any like cognitive or physical decline. They just die.

And they’re highly social. And this is the thing that we really keyed in on my lab to date. In the last three plus years or so, we’ve been working with them. They’re actually the most social animals in the entire mammalian kingdom. So, one colony can contain dozens or hundreds of animals all living together and a really tight-knit colony. And they’re driven by this really single dominant queen, who’s the matriarch that kind of guides the whole society. And all the other animals are essentially workers and drones and are reproductively suppressed in the presence of the queen. She’s the only one who mates with one or two like breeding males in a colony. And she continues to give birth her entire life. So, no menopause or signs of slowing down. And so, as she has a litter, they never leave. The colony just gets bigger and bigger and bigger, okay. They’ve decided that it’s best for their survival of their colony to do everything together, okay.

They chiefly come from East Africa, Kenya, Ethiopia. They live completely underground as well. And the leading hypothesis is that, you know, maybe in this dry, arid desert climate, where food and resources are not plentiful, that it was easier to have a communal form of living such that some animals are foraging and hoping to stumble upon a tuber, like a sweet potato. And if they do, like the whole colony is alerted and they all can feed off that together.

LEVIN: It’s insect-like.

ABDUS-SABOOR: It’s very insect-like or bee-like, but they’re mammals, which is very interesting.

So, you know, we want to know like, how does this pain insensitivity work? How does you know this highly social life, like how is it set up? How is it maintained? How do they even recognize one another, especially because they’re essentially blind?

LEVIN: And they’re hairless, so there’s a lot of skin-to-skin contact.

ABDUS-SABOOR: There’s a lot of skin-to-skin contact. They crawl right over each other. They’re always touching. Even if you make the colony really big and you go to look at ’em, they’re always on top of each other. They just are always touching, you know?

And from our early studies and observations, it appears that, not saying other senses are not important, but touch is certainly outsized. You know, most of their sensory cortex seems to be dedicated to touch. So, they’ve lost the visual parts of their sensory cortex because they’re blind. But the somatosensory cortex, the touch cortex, has like encroached upon it.

So, we think they’re like touch specialists and they might be able to do things with touch that other seeing animals do with vision. Like communicate and recognize one another and know who it is that they’re interacting with.

LEVIN: Wow. Fascinating. And so, is there a sense in which we’re trying to understand human social interactions through touch by studying the naked mole rat? Or are these just two disparate fields of study?

ABDUS-SABOOR: I hope they’re not disparate fields of study. One could even make the case that their long-term stable relationships are more akin to human societies than a mouse, which is the predominant model system used to study these things, right?

We have long-term stable relationships. You know, people for 10 or 20 years, or you see a friend from college or whatever, you remember them. And these sorts of dynamic relationships that we see in their colonies we don’t see like in other animals. So, I think there are principles that we hope are very similar and could teach us about societies.

You know, I think one very exciting idea is that if we can learn like the principles, the genes, the molecules, the neural circuits, the neural networks that they use to like cooperate with one another and use shared resources like maybe some of that can be used to like inform human societies and how we can better cooperate given limited resources, for example.

LEVIN: In human societies, touch is a sensitive issue. Pardon the pun. But there’s an important role, obviously, that social touch plays, both aversion and appeal. Are you thinking about this in human society or is that kind of a meta level that you dream about maybe when you’re walking down the street, but isn’t really part of your actual research?

ABDUS-SABOOR: No, we do think about that. That question we’re actually trying to address on the mouse side of the lab, not in the naked mole rats. Maybe in the naked mole rats one day. But right now, we are working on this.

It’s really fascinating as you mentioned, right. If you’re in the comfort of your home and a loved one strokes you on the back or arm, it may feel good, but if you know you’re on the 1 train or something and someone touches you like that, right? You wanna recoil, and you know it’s not gonna feel good. But it could be the same touch to the skin. So then how does your brain know that this touch is in a good context and this is a bad context?

There must be some sort of gating in the brain that allows you to quickly approximate how you should respond. And how does that all work? It’s unclear, but I think we have good approaches to kind of study this.

Back to the mouse, I talked about those neurons we discovered as part of like that positive balance, social reward pathway. Now if we give animals mice that same stimulation, but we pair it, they’ve learned to associate with something negative like a shock. And now we do that optogenetic stimulation to activate the neurons. The animals don’t have a positive response; they have a negative response. So, we can easily dial in, like, good touch, bad touch in the animals and read this out.

So now we’re saying, “Well, how does this look in the brain?”, okay. There’s one area in the brain that we’ve become very excited about called the orbital frontal cortex, a frontal area, the front of the brain that appears to integrate sensory components and high level like learning and planning. And we think there might be neuro ensembles that are talking to other areas of the brain to let the animal know, like if the animal’s in a good state for a touch to be perceived as good, or if the animal’s somewhere where they’re afraid or anxious or have had a bad experience with it, such that now this gate to like the positive violence networks won’t be activated. So early days of this project, but we’re trying to figure out how this works at the level of the brain.

LEVIN: A lot of what you’re raising taps into, going back to metaphysics. So we began with Descartes, “I think therefore I am,” you know, consciousness is all important. Going down deep into genetics, molecular biology, neuroscience, and now it’s kind of to my mind, the questions start to come back again of how these neurons translate into this mental world, this interiority, this experience.

And I guess I just wonder how much at this scientific level you feel we can approach this really difficult question of why does it feel like something?

ABDUS-SABOOR: It is a wonderful question. And one of the things I’ll say is that I also have to appreciate my limitations as a molecular biologist, neuroscientist, right? Some of these questions may be slightly outside of the realm of where we can approach, you know, especially using a mouse model, right? I think there are mechanistic studies we can do in animals, but I do not think we can reach the highest levels of these high-level cognition and consciousness in a rodent model.

And this is where I think folks like me, we need to be interacting with cognitive scientists, people in psychology, people in other spaces. There’s too much of a disconnect between neuroscience and psychology. We’re not talking to one another, you know, but we’re both studying the brain and the mind, right. The neuroscientists tend to use animal models and are doing the work I talked about very mechanistic. Whereas the psychologists are doing really beautiful work, but they’re more tapped into, you know, the human experience.

The more we can talk to one another, I think we’ll be able to address these higher-level problems. And this is part of the institute I’m in, the Zuckerman Mind Brain Behavior Institute. Maybe this is a plug for our institute, but you know, this is something that we try to do because this is the only way we’re gonna solve the brain and the mind by bringing people together who think across skills.

LEVIN: Fascinating. I think you’ve portrayed this very well in your responses and in this conversation, which has just been so intriguing. But there’s a question we’d like to ask here at The Joy of Why, and that is what brings you the most joy or fulfillment in your work?

ABDUS-SABOOR: Yeah, I think I would answer that in two ways.

So one is just discovery, okay? When we have that kinda aha moment, that moment of insight where we say, “Oh my goodness, this is it.” For example, something we’re very excited about that we all can relate to is lactation, nursing that occurs in mammals, right? Now, we’ve known for a long time that, for example, with nursing, there’s a suckling stimulus on the skin from the child to the mom or the pup to the mom, and that physical suckling stimulus is enough to mediate milk release.

There’s like this neuroendocrine reflex that goes from the skin up to the brain back to the tissue. The milk comes down. The baby, the pup gets it. It all is initiated by, in part by touch, okay? But we had no idea, like what are the touch neurons that mediate that? In the last few months, we’ve been able to discover and put in a molecular handle. We found the neurons that mediate this. When we made this discovery, it was just like jumping for joy. It’s like the thing that we and others have been looking for for a very long time, like we cracked it, and the data looks so beautiful and convincing. Like, those are the moments that I really live for, where we can go from just not knowing to – at least at that moment – we might be the only people in the world who, like, have appreciated something.

Those are the moments that we live for. So, discovery is the thing that really drives me and brings joy to my life. And mentorship, right? Helping people achieve their dreams and goals in life and kinda working alongside them, I also live for that, too, and sometimes that’s just as like exciting for me as discovery.

LEVIN: Thank you so much for taking the time to bring those ideas out of the lab and share them with us and with our audience. It’s just been a pleasure, Ishmail. Thank you.

ABDUS-SABOOR: Thank you. You’ve been great. you’ve really pulled a lot out of me today. Thank you.

STROGATZ: I’m smiling at that, and so are you, Janna. We can see each other here, and I just, I had a feeling that he would say something about, “At that moment, I’m the only person,” or, “My team is the only team in the world.” There is something about that. It’s not exactly vanity, but I think every scientist feels that, every mathematician, right?

I mean, is that why you were smiling when he said that?

LEVIN: Oh, yeah. Well, also he was such a lovely person, you know? And you just, you enjoyed that he enjoyed it. You know that he had this wonderful moment of discovery and I also thought it was incredibly fascinating how he was talking about the speciation of the actual neurons. Like, they’re specialized, and they’re not these generic neurons, but they’re intended for these purposes. I mean, I just thought that was also really fascinating, and you can imagine that moment of discovery was just tremendous for them.

Anyway, wonderful stuff. I’ll give you a hug next time I see you.

STROGATZ: Very good. I might recoil. Touch is a big thing for me. So don’t take it personally.

LEVIN: Oh my God. That’s hilarious. I’m gonna come at you with such a bear hug next time.

STROGATZ: Come at me!

[Music plays]

STROGATZ: If you’re enjoying The Joy of Why and you’re not already subscribed, hit the subscribe or follow button wherever you’re listening. You can also leave a review for the show. It helps people find this podcast. Find articles, newsletters, videos and more at QuantaMagazine.org.

LEVIN: The Joy of Why is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests or other editorial decisions in this podcast or in Quanta Magazine.

The Joy of Why is produced by PRX Productions. The production team is Caitlin Faulds, Jade Abdul-Malik, Genevieve Sponsler, and Merritt Jacob. The Executive Producer of PRX Productions is Jocelyn Gonzales. Edwin Ochoa is our project manager.

From Quanta Magazine, Simon Frantz and Samir Patel provided editorial guidance, with support from Samuel Velasco, Simone Barr, and Michael Kanyongolo. Samir Patel is Quanta’s Editor-in-Chief.

The episode art is by Chanelle Nibbelink and our logo is by Jaki King and Kristina Armitage. Special thanks to Garth Avery at the Cornell Broadcast Studio.

I’m your host, Janna Levin. If you have any questions or comments, please email us at [email protected]. Thanks for listening!

[Music fades]

Corals Spin Tiny Vortices to Get Oxygen, but Not if It’s Too Hot

Wed, 05 Aug 2026 03:40:41 GMT

Fluorescent, oxygen-reactive nanoparticles are caught in swirls of water created by a coral’s cilia.

Cesar Pacharres/colored by Quanta Magazine

At first glance, corals present as little more than colorful rocks — piles of lobes, stalagmites, and branches poking out from the seafloor.

They are anything but. Corals are complex creatures that form enduring colonies, and just like other animals they need oxygen to live. Across the living surface of coral, a frantic dance of survival takes place, invisible to our eyes and unknown to science before 2014. The tiny dancers are hairlike cilia, and new research into these microscopic structures is revealing just how active corals are in determining their own fate.

Corals aren’t fortunate enough to have a consistent supply of oxygen, and they can’t change location to seek it out. During the day, the tiny polyps that make up a coral colony get plenty of oxygen from the symbiotic algae that photosynthesize within their tissues. But at night that process stops, and a coral polyp’s only source of oxygen is the water around it. Then it’s do or die for the cilia. Using mechanisms scientists are still trying to understand, the cilia wave around to generate fast-moving vortices of water that circulate oxygen to the coral’s outer tissues, in addition to helping keep the colonies free of sediment.

A study published in Science in May 2026 provides new insight into how organisms with no brain or musculoskeletal system can generate and regulate this process — and what happens when the water around them warms up. Warmer water naturally carries less oxygen, which prompts corals to move their cilia faster and faster, as if gasping for breath. Above a certain temperature, the system starts to work against itself; the furious beating of cilia uses up any oxygen the coral’s tissues can absorb, and then the polyps can suffocate in the less oxygenated water. Biophysicists, marine biologists, mathematicians, and modelers are now collaborating to better understand the physiological and hydrodynamic forces at work, and how they correlate with bleaching patterns, coral disease, and mass die-offs.

This dynamic picture is somewhat new to scientists, who have long used corals’ symbiotic algal partners as indicators of their health. Cilia may serve as a more direct signal, said Rachel Alderdice, a marine biologist who studies coral stress biomarkers and genomics at the University of Konstanz in Germany and was not involved in the research. “It’s these finer details that could help us understand why some corals bleach and others don’t, [even when] they sit right beside each other.”

Swirling To Survive

Every coral colony is cushioned by a thin boundary layer of water whose movement is slowed by friction at the coral’s surface. Researchers assumed that corals were passive with respect to the slow-moving boundary layer, simply relying on natural diffusion through it to provide nutrients and oxygen.

A colony of Porites lutea, a stony coral, continues to grow slowly in waters off the Samoan Islands.

National Marine Sanctuaries

Then, in 2014, a team from the Massachusetts Institute of Technology and the Weizmann Institute of Science published a groundbreaking study showing that coral cilia interact with the boundary layer by rapidly whipping about to generate swirls of fresh, oxygenated seawater. Until a decade ago, scientists thought of these cilia merely as brooms that move mucus and sweep away waste particles and other debris. The research not only modeled the tiny vortices created by the cilia for the first time, but also revealed the cilia’s importance for survival and metabolism.

At first, the microbiologist and environmental engineer Orr Shapiro, who led the 2014 work at MIT as a postdoctoral fellow, was interested in how microbes that infect corals and cause disease follow concentration gradients, a process called chemotaxis. Under the microscope, he noticed something weird: In the boundary layer, particles were swirling around and mixing together — not at all like the passive diffusion he had been expecting.

“That was to me, and I think later on to the entire field, sort of a paradigm shift,” said Shapiro, now a researcher at the Volcani Institute in Israel. It became clear that the boundary layer wasn’t static, but rather a dynamic zone, and one where cilia were creating their own turbulence. The realization inspired Shapiro’s team to go off on a tangent, mapping the flow of oxygen to coral tissues via cilia. “It really transformed how we understand this [micro]environment, because suddenly the diffusion is no longer really important,” Shapiro said.

Diffusion is the default route for nutrients traveling through water, but it’s painfully slow. It can take as long as four minutes for oxygen to travel just 1 millimeter. That’s why the fast-moving flows created by cilia are so important: because naturally flowing water slows down near the coral’s surface, and corals consume oxygen faster than diffusion can supply it.

It is a system that delivers enough oxygen, despite the cilia’s energy consumption. But there’s a downside: Oxygen dwindles as temperature climbs. That’s when corals run into trouble.

Hyperventilating Under Water

Scientists have a clear understanding of one thing that happens to corals when water gets too hot: bleaching. As water temperatures rise, a coral’s symbiotic algae become stressed and release molecules that are toxic to the coral in large quantities. To protect itself, the coral expels its own algae — a primary food, energy, and oxygen source — and soon loses its color. It’s a slow death and an increasingly common occurrence as heat waves sweep across the world’s reefs.

But sometimes, some corals on a reef bleach while others don’t, and in other cases corals under heat stress die without expelling their algae.

An international team of microbiologists, engineers, and physiologists was eager to understand how heat affects cilia, and whether this could explain different types of coral death.

In the experiment, researchers exposed stony coral to various water temperatures. Fluorescent nanoparticles revealed the flow of oxygenated water.

Courtesy of Cesar Pacherres

“We’re living in a world right now of extreme scenarios,” said Cesar Pacherres, a co-author of the new study and a marine biologist at the University of Copenhagen who studies fluid dynamics. As marine heat waves become more common, and as a particularly strong El Niño year threatens to catalyze a fifth global bleaching event in late 2026, “corals can experience an increase in temperature of several degrees in a time frame of a few hours,” Pacherres said.

To explore heat’s impact on cilia, the team ran a series of 24-hour experiments. They exposed aquarium-raised stony coral called Porites lutea to incrementally higher water temperatures up to 39 degrees Celsius (more than 102 degrees Fahrenheit) — an extreme scenario, but one that could occur. They kept the tanks dark to better observe how cilia transport oxygen when algae aren’t producing any.

Every hour, the researchers recorded the microscopic cilia with a high-speed camera to capture how frequently they moved as they were exposed to warmer and warmer water. The team also used a technology called SensPIV to track oxygen flow. Fluorescent, oxygen-reactive nanoparticles “traced” the water swirls, creating a vivid map of how oxygen concentrations corresponded to the cilia’s vortices.

Visualizing the movement of oxygen was key to the team’s findings. In warmer water, corals burned energy faster, which increased their demand for oxygen — prompting the cilia to dance faster. But there’s only so much dissolved oxygen available in the surrounding water, and as temperatures climbed, the cilia started to send oxygen-deficient water toward the coral in their frenzy. “The oxygen demand of the coral increased faster than the increased swirling of the water,” said co-author Michael Kühl, a marine microbiologist at the University of Copenhagen.

When the water approached 37 degrees Celsius (the temperature of the human body), the cilia started to slow down. Past 39 degrees Celsius, they shut down altogether, and the coral died. These were the findings they reported in Science in May 2026.

Coral cilia move normally in water heated to 27 degrees Celsius (left). At 39 degrees Celsius (right), cilia motion slowed and eventually stopped.

Courtesy of Cesar Pacherres

Pacherres cautioned against interpreting these temperature limits as a standard threshold; each species of coral is adapted to its own range of daily temperature fluctuations. Even so, climate change has started to push many corals toward their respective limits, with record-high surface water temperatures nearing 38 degrees Celsius in places such as Florida.

Why the cilia move faster in hotter water remains a mystery. Perhaps seawater’s viscosity — which decreases as temperature increases, making the water thinner —affects ciliary movements, Shapiro said. Corals lack a central nervous system and brain, but they do have neurons — inside what’s called a nerve net — to process sensory information. Perhaps the coral senses heat or lack of oxygen, and some biological mechanism then triggers the faster beating. “It’s physics, biology, engineering, all mixed up together, which is what makes it really interesting,” he said.

A Polyp Puzzle

Scientists are now investigating cilia physiology and the boundary layer as a whole. “It’s much more complex than we thought,” Shapiro said.

In another paper co-authored by Pacherres and Kühl in May 2026, they found that cilia’s vortices resemble corkscrews. The turbulence pushes unwanted particles away from the coral’s surface while redirecting nutrients toward polyps’ mouths.

Under a microscope it’s possible to see the density and arrangement of cilia on a coral surface.

Courtesy of Cesar Pacherres

The cilia on each polyp, they found, are arranged in hexagonal units that keep ciliary movement streamlined, which helps explain how cilia can coordinate their movement to produce predictable swirls. “It demonstrates that coral skeletal architecture and living tissue are functionally integrated,” Pacherres said.

Combined, the studies recontextualize how ciliary movement, previously overlooked, gives corals some stability and buffers them against environmental change, he said.

The relationship between cilia and bleaching remains ambiguous, said Alderdice, who was not involved in the studies. But testing cilia under bleaching conditions without heat — by using red light, for example, which can also trigger bleaching — would help answer this question.

Playing Catch-Up

Scientists knew from the 2014 work that cilia help corals self-ventilate when water flow is low, said David Suggett, a marine biologist at King Abdullah University of Science and Technology who wasn’t involved in the research. “But until this point, we had been focusing on molecular and metabolic machinery” to understand how corals evolved to deal with low-oxygen conditions, he said. “We hadn’t really appreciated that there are these behavioral-physiological mechanisms at play.”

For Suggett, the research raises a critical question: What does this say about how corals will deal with future climates?

Sometimes, corals of a single reef don’t bleach evenly, with some individuals dying off while their neighbors persist. In new research led by Suggett’s colleague Tadd Truscott, marine biologists are finding that these patchy bleaching patterns are correlated with areas of reduced water flow — areas therefore receiving less oxygen.

Next, Kühl and Pacherres’ team wants to test corals under different conditions — especially under normal light-dark cycles — and to better understand the mechanism driving ciliary beating. Is it a molecular process that activates their movement? The physics of warmer seawater? A bit of both, or something else?

It’s only in the past decade that scientists have realized the role of deoxygenation in coral health, Suggett said. Ocean acidification took center stage as the primary concern for corals in the early 2000s. In hindsight, deoxygenation was a much bigger issue, he said. The new research suggests that deoxygenation, not just bleaching, is a fatal threat to corals resulting from a hotter climate.

“We’re playing massive catch-up,” Suggett said. “The amount of information we’re gathering quickly is demonstrating just what a problem for corals it is — so much so that we’re starting to really revisit long-standing paradigms of the role of other environmental factors, like temperature and light, where in fact, it could be oxygen that’s been the smoking gun all along.”

Why the Legendary Erdős Problems Are Falling to AI

Mon, 03 Aug 2026 03:05:20 GMT

DVDP for Quanta Magazine

On May 20, 2026, OpenAI made an announcement that shook the mathematical world. An internal AI model — one not available to the public — had come up with a counterexample to the “unit distance” problem, a conjecture made in 1946 by Paul Erdős, the prolific, itinerant Hungarian mathematician.

Erdős posed thousands of questions, but this one was special: It was both simple to explain and mathematically deep. It was the first historically significant proof to come from an AI model. Though the model’s result wasn’t definitive — human mathematicians would substantially improve on it within weeks — it was innovative, bringing in ideas from a distant branch of math that no one had successfully applied to this problem before. And it was influential: Within a few days, related techniques were used to solve other important problems.

Then on August 1, OpenAI announced that an unreleased model named Astra made 10 additional mathematical advances, including finding solutions to three more problems posed by Erdős.

Many mathematicians have hailed developments such as these as a phase transition in the mathematical capability of AI models. These models are “changing dramatically the way mathematical research is being done,” said Noga Alon of Princeton University, who has solved dozens of Erdős problems over his decades-long career.

Erdős and his conjectures have long fascinated mathematicians. He traveled constantly — living out of a suitcase for years at a time, staying with friends, owning almost nothing. He rattled off problems in published papers and letters to mathematicians around the world, often attaching prize money that he would pay out of pocket to the first person to come up with a solution. The reward might be a token $10 or $25, or, for problems he considered important or difficult, it could range into the thousands. Erdős died of a heart attack in 1996 while attending a math conference in Warsaw, but a nonprofit foundation based in Iowa has promised to make good on his bounties.

He was a beloved figure, but also a downright weird one. He only wore silk, and he avoided the touch of other people. Deeply cynical about authority, he gave away most of the money he earned and relied on a friend to manage his finances and other practical affairs. He referred to God as the “Supreme Fascist” and fueled his incessant output of mathematical ideas with a steady diet of amphetamines. It is a strange irony of history that the problems he suggested have now become a central proving ground — and, in effect, a series of PR coups — for the world’s biggest and most powerful technology companies.

But in all likelihood none of this would have happened had it not been for an English mathematician named Thomas Bloom.

Many Meetings

Like Erdős, Bloom was interested in both number theory and combinatorics. His focus has been an area called arithmetic combinatorics, which lies at the intersection of the two. After getting his doctorate in 2014, Bloom established himself as a rising star in the field, landing a prestigious fellowship from Britain’s Royal Society, which let him work at almost any university he wanted to. (He’s now at the University of Manchester.)

Bloom has liked Erdős’ style for as long as he can remember. But he always found it hard to keep track of which problems had been solved and which had been forgotten entirely. So in early 2023, he decided to gather as many problems as he could into a list.

He intended it for his own use. But “I thought it would be easier if I could access it wherever I was,” he said; he figured he “might as well make a website, kind of with the expectation that maybe nobody would use it.” He gathered a couple hundred problems and launched erdosproblems.com. Bloom used ChatGPT to write the Python code that ran the website, which was, at the time, a remarkable thing for a large language model to be able to do. Using one to collaborate on the math itself still seemed like only a distant possibility.

His goal was not just to cross items off a list. He wondered if “modern day mathematics, often using techniques unknown by Erdős, could clear up many of these more obscure problems,” he wrote in a blog post. “We will then be left with a core of interesting, difficult problems, which can serve to demonstrate the limits of our knowledge.”

Bloom did crucial work in curating the list: Sometimes Erdős stated problems in ambiguous or unclear ways, and Bloom figured out what the most sensible version of each problem should be. He kept adding problems to the site, and gradually its audience grew. Over the course of 2024 and the first eight months of 2025, the statuses of 111 problems on the list were changed from “open” to “solved” (although some of these had been solved years earlier, and their status change reflected the rediscovery or verification of a proof).

Then, in August 2025, some colleagues suggested that Bloom add a commenting function, so that people could talk about problems they were interested in. He was able to do so quickly, using ChatGPT to write the code. By now he’d cataloged nearly 1,000 problems.

Bloom’s timing was good. He made it possible for like-minded people to talk to one another, and that “really let a community build up,” he said. For the most part, comments were sporadic — a problem might attract a single comment pointing out an example or noting how hard the problem looked. But activity steadily grew, and some problems catalyzed nuanced mathematical discussions between strangers.

“Tom probably never really realized this, but for me it’s honestly changed my life,” said Wouter van Doorn, the fourth-most-prolific commenter on Bloom’s website. Like many people who became active on the site in the autumn of 2025, van Doorn isn’t exactly a professional mathematician. He works “for a company that gets hired by other companies to do customer service support,” as he put it. But he isn’t exactly an amateur either — a decade prior, he almost completed a master’s degree in math at KU Leuven in Belgium. In 2024, spurred in part by how capable he saw LLMs getting, he took a six-month leave of absence from work to focus on math. At the time, while he didn’t particularly want to use AI, he remembers thinking, “Right now I’m still better at mathematics than an AI is, but who knows what it’ll be in a year, two years, five years? If I want to finish these projects, and I want them to be mine, now is the time.”

And so, in October 2025, van Doorn, now back at his day job, left the first comment on the page for Problem 1102. The problem, which Erdős posed in 1981, asks about properties of sets of “square-free” integers — that is, integers that have no repeated prime factors. (For instance, 30 is square-free because it is equal to 2 × 3 × 5, but 18 is not, because it is equal to 2 × 3 × 3; the 3 repeats.)

In early November, van Doorn shared progress toward an answer — which he’d figured out without relying on AI — as a comment on the problem page.

Later that day, another commenter on the site replied, claiming he had found a flaw in van Doorn’s argument. The two traded remarks in rapid succession, and van Doorn convinced his interlocutor that his argument was correct. “I see how your argument works now. Nice!” the other mathematician replied. That other mathematician was Terence Tao, a professor at the University of California, Los Angeles who is arguably the best-known mathematician alive today, and inarguably one of the most influential. (Not incidentally, when Tao was just 10 years old, he crossed paths with Erdős.)

Bloom’s website, which has the look and feel of an earlier time, was becoming an example of the internet at its democratic best. “This entire collaboration would not have been possible without Tom’s website and the comments section there,” van Doorn said. It didn’t matter if you had tenure or not, if you were young or old, if you were at a fancy university or even at a university at all. If you wanted to work on math and had good ideas, you could find people to collaborate with.

But as the winter set in — around the same time that van Doorn found himself collaborating with Terry Tao — things started to change.

Journey to the Cross-Roads

Kevin Barreto and Liam Price, both in their early 20s, became friends in the summer of 2025 on a Discord server dedicated to AI. Barreto is currently an undergraduate at the University of Cambridge; Price studied some math in college but left before finishing. In December, convinced that the newest AI models might succeed in resolving some Erdős problems, the pair started throwing batches of problems at them. They realized early on that if they told GPT-5.2 that a problem’s answer wasn’t known, it wouldn’t make much headway, so as Barreto put it, they learned how to “prompt it in a very particular way, gaslighting it into thinking the problem is easier than it actually is.”

They had what they thought was their first triumph on Erdős Problem 333. Early on Christmas morning, Barreto posted a proof to Bloom’s website, writing, “We believe, to the best of our knowledge, this is the first case of an LLM fully autonomously resolving an Erdős problem, not previously resolved by humans.” Even though 333, which dealt with the sums of sets of integers, was not a particularly important problem, solving it with AI still felt important.

But a few hours later, another user pointed out that Erdős himself had provided a resolution to 333 in a paper published in 1977. Barreto owned up to the mistake. “My formal request to all members of the website is to put greater focus on literature search on the problems currently marked as open,” he wrote. “As someone who has fallen for this twice now, it’s quite gut-wrenching.”

Undeterred, he and Price kept at it, and by January 4, 2026, they’d used GPT-5.2 Pro to find a solution to Erdős 728, a problem about when certain numbers are divisible by other numbers. This time nobody could find prior work already proving it. Barreto used another AI tool called Aristotle (developed by a startup called Harmonic) to certify that the proof held together logically. Nat Sothanaphan, a software engineer and the only forum participant more prolific than Bloom, Tao, and van Doorn, had ChatGPT write up the formalized result and posted it online.

Price developed a methodology for how to ask LLMs to solve open questions. First, he would ask a chatbot for a solution. Then he would feed that solution into a fresh instance of the chatbot, asking it to check the previous chatbot’s work. He’d repeat this process until he had what looked like a workable solution. (This echoes some of the work that companies have been doing internally to create what they call harnesses or scaffolds, which automate the sort of iteration that Price does by hand.)

Barreto and Price’s papers represent just a fraction of the many Erdős problems solved at least in part by AI over the past few months. There are multiple reasons why these problems in particular have become such a fertile test bed for LLMs. The primary one is that, by and large, Erdős problems are in number theory, combinatorics, and graph theory, all areas of math that have proved more accessible than others to large language models. The problems also vary widely in difficulty and mathematical significance. This variation makes them appropriate for a nascent technology whose abilities also vary widely.

Many of Erdős’ problems had a monetary value attached to them from their moment of inception, a playful incentive from a wandering eccentric. But now, as the problems have become an informal benchmark for AI, their solutions are being discussed in terms of their “per-problem cost” — the price of the tokens needed to solve them.

“A lot of my recent papers should be mostly credited to AI,” van Doorn said. “The ideas involved were ideas I did not come up with myself.” Like many people active on the Erdős site, van Doorn is excited about the way LLMs are allowing him to do more things more quickly. “If I read an idea by an LLM, I digest it, try to understand it, simplify it, and generalize it,” he said. He uses AI to better understand the math.

Not everyone holds themselves to this standard. “A big problem is AI is being used a lot by people who aren’t mathematicians, who don’t have a huge mathematical background and are not capable of verifying the output,” Bloom said. “They like to move fast, ask their AI to check it, it grows and grows. We’re seeing a lot more of these 100- to 200-page papers that people are posting. ‘I solved this theorem; I got AI to generate the proof and check the proof and write the paper.’ But no human has read it, and no human is going to read it. It’s a huge challenge now.”

By Price’s own assessment, he doesn’t have enough mathematical understanding to verify the solutions he ultimately coaxes from the LLMs. But with Barreto’s help, he’s been able to find mathematicians knowledgeable and willing enough to check the results. Both Price and Barreto are co-authors with Tao, Jared Duker Lichtman of Stanford University, and other accomplished mathematicians on a May 2026 paper resolving Erdős Problem 1196, one of their more significant results. (1196 asks about the possible size of so-called primitive sets — collections of integers, such as {2, 5, 9, 21}, in which no number divides any other.)

Bloom was surprised that despite lots of attention from OpenAI, Google DeepMind, and several startups, most of the new results had come from hobbyists and undergraduates using publicly available LLMs, not from corporate labs using more advanced internal models.

But that would change a few weeks later, on May 20, 2026, when OpenAI announced that they had solved one of the most well known Erdős problems of all, the unit distance problem.

Many Partings

In the first months of 2026, the major tech companies began to see opportunity in erdosproblems.com. As Lichtman explained, “Erdős had over 1,000 papers. They were scattered.” An institute in Hungary had collected scanned images of many of the papers, but nobody had collected all the problems. “This kind of single repository that anyone can access — labs realized that this could effectively be a benchmark.”

In January, a team of 24 researchers led by Google DeepMind shared a paper solving four problems and finding old, forgotten solutions to nine more, after “using Gemini to systematically evaluate 700 conjectures labeled ‘Open’ in Bloom’s Erdős Problems database.” In May, a separate DeepMind team of 21 researchers announced that “our most capable agent autonomously resolved 9 of 353 open Erdős problems at the per-problem cost of a few hundred dollars.” (As of this article’s publication, Bloom’s database contains 565 solved problems and 652 open ones, but the DeepMind team narrowed their search to problems that have been written in formal logic.)

And, on May 20, OpenAI shared a solution to the unit distance problem, along with a blog post explaining the work and a companion paper that featured nine world-class mathematicians commenting on the correctness of the proof and the importance of what had been done (as well as presenting a streamlined human version of the result). Mathematicians had generally believed that Erdős’ conjecture — about how many evenly spaced points can be placed on a plane — was correct. To general surprise, OpenAI’s internal model found a counterexample. To do so, it had found a sophisticated way to use tools from an area of math called algebraic number theory. As Jacob Tsimerman of the University of Toronto wrote in the companion article, “This is a really impressive piece of work. … It is definitely an intimidating construction.”

In the same article, Tim Gowers of Cambridge and the Collège de France wrote that “if a human had written the paper and submitted it to the Annals of Mathematics and I had been asked for a quick opinion, I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that.”

The author on the paper that presented the original solution was given simply as “OpenAI.”

Terence Tao was 10 years old when he met Erdős.

Billy Grace Tao

Later, using techniques related to the ones the AI model had applied to the unit distance problem, a group of four mathematicians, including Bloom, disproved a version of another long-standing Erdős conjecture. The “sum-product” conjecture proposed that if you have sets of numbers, either their sum or their product must grow quickly. The mathematicians found a set of real numbers for which both the sum and the product grow more slowly than expected. The conjecture for integers remains open.

Figuring out what impact AI will have on math and mathematicians means not only looking to its most important results, but also examining how it changes the everyday practice of solving quotidian problems. Noga Alon, the Princeton mathematician, estimates that he has solved a few dozen Erdős problems over his career. He has now stopped trying. “Once AI started to solve them, there is no point anymore,” he said. Terry Tao has stepped away from the Erdős problem community to focus on getting work done.

Van Doorn, who for now still has his day job at a customer service company, said that LLMs “are clearly better at thinking and doing math than I am. I don’t hold a candle to current AI systems.” However, he added, “the eventual proofs that I write are simpler, more general, and easier to read for other people than the thing that ChatGPT came up with.” AI has indisputably boosted his productivity, and he’s still having fun. “If you want to play piano, you aren’t going to hire a piano-playing machine that does it better than you. You will play the piano because you like playing the piano. I enjoy thinking about numbers, doing math, writing papers. I’m not going to hire a paper-making machine that does it for me.”

For van Doorn, there is joy to be found in digesting the responses he gets from LLMs. “I’ve been doing a lot of math recently thanks to the Erdős-problems community. It used to be the case I just did everything all by myself, struggled alone in my room. I don’t know how it happened, but nowadays people contact me saying, ‘I have this idea. Do you want to join me thinking about this?’”

The increasing capability of AI has made it easier for people like Price or van Doorn, with less mathematical training, to solve puzzles, while making those puzzles less interesting to people like Alon who have devoted a lifetime to understanding them.

Nonetheless, “many and maybe most good mathematicians will use AI,” Alon said. He notes that a number of first-rate mathematicians have left academia to work at AI companies, not only because they are well paid to do so but because “maybe this is where the action now is.” In July 2026, on the same day that Tsimerman was awarded the Fields Medal, the highest honor in math, he announced that he was leaving academia for a job at OpenAI.

Is AI Reasoning Right for the Wrong Reasons?

Fri, 31 Jul 2026 02:50:11 GMT

Celsius Pictor for Quanta Magazine

I’ll just say it: What the hell is going on with AI “reasoning”?

Sorry for the air quotes. That punctuational side-eye was more common in 2024, when the specially trained cousins of LLMs now known as “large reasoning models,” or LRMs, were still new. Nowadays it may seem downright churlish, though, given that a “general-purpose reasoning model” from OpenAI solved a famous open mathematical research problem in one shot in May 2026. Still, I’m not sure how else to acknowledge my intellectual whiplash over the scientific interpretation of what these AI systems are actually doing.

Reasoning comes in many technically defined forms, but the basic procedure is easily recognizable: arriving at a sound conclusion by linking together intermediate steps that logically follow from each other. We do this with thoughts; LRMs use so-called chains of thought, a term of art for the streams of synthetic text that the models emit before arriving at an answer to a complex query. One minute, the idea that AI could reason via these chains was being prominently and credibly critiqued (by a team of researchers from Apple) as an “Illusion of Thinking” subject to “complete accuracy collapse” under surprisingly simple conditions. The next minute, LRMs were bagging gold medals at the International Mathematical Olympiad, a feat so challenging that “even very successful mathematicians and scientists may well highlight [it] on their CVs all their lives,” as the scientist and AI critic Gary Marcus and Ernest Davis wrote in 2025. If that’s not a sign of “real” reasoning, what is?

But wait — soon after, more research, from the Santa Fe Institute, showed that LRMs can crush even carefully designed benchmarks for reasoning (like a collection of analogy-like visual puzzles) using mere “surface-level ‘shortcuts.’” What they were doing looked less like generalizable reasoning than just gaming the system. Then, as if on cue, another “hold my beer” moment: Google DeepMind and the mathematician Terence Tao (the GOAT!) used AI to rediscover or improve the solutions to 67 problems “spanning mathematical analysis, combinatorics, geometry, and number theory.” Deal with it, haters!

What about additional evidence that LRMs can’t reason reliably, even when they possess the necessary algorithm and computational budget to do so, and suffer from a list of scientifically documented failure states long enough to use as a Slip ’N Slide? Whatever — I guess that’s just “jagged intelligence” for you (AI-speak for “when it works, it works”).

And so it went from late 2025 into 2026. I’ve been a science journalist for 20 years and an AI journalist for half of that, so I know better than to expect tidy consistency out of rapidly advancing research. But even for me, this back-and-forth has been a bit much. To quote Al Pacino in The Insider, “I’m getting two things: pissed off, and curious.” I don’t believe there’s fraud to be found here. I just want to know which way is up. Can AI reasoning somehow be both BS and not at the same time? And if so, how on Earth does that work?

I knew just who to call first.

Melanie Mitchell’s career in AI stretches back to the 1980s, but lately she’s earned a reputation as an au courant AI truth teller, penning lucid explainers for Science and her widely read newsletter, as well as conducting research at the Santa Fe Institute. (The study about “surface-level ‘shortcuts’” is hers.) When I asked her what we actually know about AI reasoning, her answer was brief enough to fit on an index card.

“Number one: It works. It improves things,” she said, referring to LRMs’ superior accuracy on reasoning tasks compared to LLMs. “Number two: The actual text that’s generated” — i.e., the chain of thought that every LRM is trained to produce to improve its performance — “isn’t necessarily faithful to what’s going on [inside the model]. And number three: A lot of that text isn’t even useful. You can actually take it out.”

Let’s unpack numbers two and three, because that’s where the superposition of “BS and not” actually lives. Chains of thought were half-discovered, half-devised in 2022 as a prompting hack for LLMs: Provide them with examples of written-out reasoning (or, famously, just ask them to “think step by step”), and they’ll suddenly give less boneheaded answers to simple logic and math problems. LRMs, starting with OpenAI’s o1 model in 2024, are trained to automate this trick by generating such prompts — also called reasoning traces or thinking tokens — and then feeding them back to themselves. Because LRMs are essentially just language models, those extra bits of text create what looks convincingly like a paper trail of the model’s “thought process.”

Except it’s not that simple. A growing body of academic and industry research has cast doubt on whether these “intermediate tokens” are a faithful representation of an LRM’s inner workings. Instead of being auditable receipts or accurate reports, they can appear more like what the Arizona State University researcher Subbarao Kambhampati calls “mumblings” — bits of language, yes, but ones whose meaning may be entirely incidental to any reasoning that might have occurred. Kambhampati’s lab showed in 2025 that fully replacing a model’s correct “traces” with incorrect or irrelevant ones didn’t degrade its performance on a formal reasoning task. Meanwhile, training the model only on correct trace data still led it to occasionally generate invalid records of its reasoning — even when it produced a correct solution to the original problem it was given. A 2024 paper from researchers at New York University showed that “meaningless filler tokens” — literally, strings of dots — could function effectively in place of a human-readable “chain of thought.”

William Merrill, one of the authors on that paper and currently a professor at the Toyota Technological Institute at Chicago, put the matter plainly: “There’s no guarantee the chain of thought has to be meaningful in any sense.” Pavel Izmailov, a researcher at NYU who also works for Anthropic (and was part of its original reasoning-model team), said he doubts that reinforcement learning — a typical training method for LRMs — even incentivizes models to produce faithful chains of thought in the first place. “I mean, maybe it will,” he told me. “But I would say the chances are not very high.”

OK, so the linguistic content of reasoning traces may be dubious. But surely the tokens themselves must play a role in producing the model’s outputs? (Think of a pinball machine: It runs on coins, not the words “In God We Trust.”)

Not so fast. A 2025 paper from Northeastern University and the University of California, Berkeley on frontier open-source LRMs showed that between 30% and 60% of their “thinking steps” had “minimal causal impact” on the answers the models produced to benchmark math questions. Chop half of them out, and a model’s performance barely suffers. “We want to be careful when we review these chain-of-thought prompts because they may not be linked to the final output,” said Weiyan Shi, one of the study’s authors.

So reasoning traces, the very things that supposedly distinguish LRMs from the mere next-word-predicting LLMs, are not necessarily either meaningful or causal to a model’s … reasoning? I’m no philosopher, but this seems to stretch the meaning of “reasoning” beyond its tensile strength. Kambhampati’s research group sounded frankly fed up in the title of their position paper on the subject (presented at the 2026 International Conference on Machine Learning, one of the field’s most prestigious academic gatherings): “Stop Anthropomorphizing Intermediate Tokens as Reasoning/Thinking Traces!”

To be clear, Kambhampati, a former president of the Association for the Advancement of Artificial Intelligence, with a background in AI planning algorithms, doesn’t deny that LRMs can work (when they work). “We are in wondrous times,” he told me, when I asked what he thought of OpenAI’s 2026 victory in solving the famous unit distance problem in math. If he has a bone to pick, it’s with what he sees as a rush in both academia and industry to embrace overly convenient explanations.

“Many ideas that have been proposed [about] the sources of strength [of these models] have been misunderstood or mischaracterized,” he said. “There’s this general mindset that says, ‘Let’s go ahead and claim certain abilities, because eventually that might become true anyway.’ And my sense is: That’s not science. That is investment.”

On the other side of the AI-reasoning fence, the disdain seems to be mutual. “These ‘scientific’ papers from last summer — I would put this in big, big air quotes,” said Sébastien Bubeck, a member of OpenAI’s technical staff (and a prominent evangelist for the company’s reasoning models among scientists and mathematicians). He called earlier Apple results critiquing AI reasoning “wrong,” claiming that they were due to a training quirk in models that are now obsolete. “Modern models starting with GPT-5.5 do not suffer from this issue,” he said. “It would be interesting to revisit those results.” (Apple did not make its researchers available for interviews.)

Here’s the thing: Nobody denies that AI reasoning models can, indeed, produce significant and accurate results. Furthermore, every researcher I spoke to acknowledged that negative findings about the models’ capabilities on certain reasoning tasks (especially those of smaller, open-source LRMs) may not always generalize to the latest-and-greatest AI products. Their inner workings remain trade secrets. But if we’re disinclined (as I am) to simply dismiss contradictory evidence about the mechanisms driving AI reasoning, the question remains: How do we account for it?

Kambhampati, as it turns out, is interested in doing exactly that. “I’m not negative. I just sound negative because everybody else is way too positive,” he said. “In science, you have to actually understand what the current thing does and what it cannot do.”

One straightforward reason state-of-the-art LRMs work, he told me (a point also echoed by Mitchell), is that they’re often surrounded by “normal” software that guides and verifies their outputs. Agentic AI systems, which have transformed software engineering since the fall of 2025, work this way. So does Google DeepMind’s AlphaProof Nexus, which relies on Lean, an automated theorem-proving tool. But Kambhampati is more interested in making sense of stand-alone reasoning models that rely solely on their self-generated reasoning traces — “the ‘think’ part,” he said.

The “think” part is what OpenAI, for one, is doubling down on. When I asked Bubeck if the splashy unit distance proof was produced with methods outside the LRM’s own chain of thought — perhaps with Lean verifying its results — he seemed to find the question almost nonsensical.

“It’s not like we’re making a mystery of it,” he said. “We have released the chain of thought. You can just go and look at it. The whole point is that the model is reasoning like a human would. And when humans reason, we don’t use Lean.” Technically, OpenAI released a “rewritten summary” of the model’s chain of thought produced by two human experts using Codex, another OpenAI model. Since 2024, the company has not publicly revealed “raw” chains of thought from its reasoning models, a policy also adopted by Google DeepMind and Anthropic.

Kambhampati’s analysis begins in a surprisingly similar place: with the idea that LRMs are just LLMs with more specific training. “There is no extra magic,” he said. But he diverges sharply from there. “It doesn’t make sense to me that an LLM would actually do a step-by-step description of what it is [reasoning] before giving the solution — because that’s a much harder task than just guessing the solution, given the way that LLMs are trained.”

His working hypothesis is that an LRM, like its LLM precursors, performs what he calls “approximate retrieval” across its vast training corpus: “somewhere in the middle” between pattern matching and reasoning, he said, but closer to the former. The role of “thinking tokens,” then, isn’t to narrate an actual chain of thought (because there isn’t one). Instead, it’s to load up the model’s context window in a way that makes it more likely to predict, or “approximately retrieve,” reasoning-shaped strings of text.

Kambhampati compared this process to mumbling words to yourself to jog your memory: It barely matters what the words are (though related ones may help), as long as they knock loose something useful. An LRM’s vast “memory” includes all the call-and-response-like examples of written reasoning it was trained on, mulched into numerical “embeddings” that encode their similarities and differences (plus other inscrutable associations) as geometric relationships in a high-dimensional space. Probabilistically arriving at an answer within that space may involve intermediate tokens whose embeddings map to coherent-looking “thoughts” in plain English, but not necessarily. They could be bits of other languages. They could be fake exclamations like “aha.” Under the right conditions, they could just be dots.

“Whether the [embedding] actually corresponds to a single word or not” — much less a faithful reasoning process — “is beside the point,” Kambhampati said.

This framing could help explain both the odd “BS”-ness of some chains of thought and the fact that they can elicit accurate outputs anyway. It would also neatly account for LRMs’ steady improvement in coding and math — what AI researchers call “verifiable domains.” Code runs, or it doesn’t; proofs are either correct or not. These binary conditions and the written steps associated with them can create convenient training signals for LRMs. The model doesn’t have to learn or reliably apply a general reasoning process, Kambhampati said; it just has to absorb enough examples of what the steps look like to predictively mimic them on its way to “stitching together” a plausible result that can then be verified.

The limit of a reasoning model’s training and step-following capability, known as the “inference horizon,” Kambhampati added, was what Apple researchers exposed with their “Illusion of Thinking” paper in 2025. Newer models have appeared to push this horizon further, albeit jaggedly. “Most of the time they probably are not learning the algorithm” associated with a reasoning process, he said. It’s much likelier that they are leveraging an ever-enlarging set of examples and clever reward signals.

Kambhampati hardly considers his case closed, and neither do I. But it’s a start — and one I find plausible, given that other researchers have also used similar “it’s the training, stupid” approaches to demystify AI behavior. Still, there was an elephant left in the room: How much does it matter whether or not we can accurately observe, characterize, and validate the processes at work inside large reasoning models?

The honest answer, according to Mitchell, is that it depends. “Think of AlphaFold,” she said, referring to Google’s AI tool for predicting protein structures. “It’s doing some kind of incredibly complex statistical associations. We don’t know what they are, but they seem to work. These things are [already] black boxes, even without a ‘reasoning trace.’” If LRMs can supercharge mathematics research the way AlphaFold did for computational biology, this line of thinking goes, why not embrace them, idiosyncrasies and all, and just verify the results? “My perspective is: We’re trying to be useful. We’re trying to build these models so that they can solve problems that matter, so that we actually accelerate scientific research,” said Bubeck. “It’s more interesting and more productive to talk about what they can do, rather than, ‘Oh, but they can only do that because of X [reasons].’”

But as Mitchell also points out, the possibility that an LRM could be “right for the wrong reasons” has an obvious relevance to the future of doing research. “You want the right answer for the right reason, so you can trust these things,” she said, and not just in verifiable domains.

Tal Linzen, a researcher at NYU and Google whose Computation and Psycholinguistics Lab published results similar to Apple’s “Illusion of Thinking” paper, said that “you want an AI system to be able to apply an algorithm reliably, regardless of whether you call [it] reasoning or not.” Treating chains of thought too reverently — even when their results are verifiable — could also prevent scientists from discovering even better ways of biasing LRMs toward accurate outputs. “We may be leaving some opportunities unexplored,” said Pradeep Dasigi, a researcher who helped train open LRMs at the Allen Institute for Artificial Intelligence. Kambhampati, unsurprisingly, puts it in even starker terms: Taking the meaning of AI reasoning traces seriously, he said, was a scientific “rabbit hole,” akin to believing in geocentrism or the ether.

Harsh, perhaps, but he has a point. Those incorrect mental models made intuitive sense at the time, just as chains of thought do now. When an LRM produces a correct answer — along with pages of “thoughts” showing how it got the result — intuition tells us that the two must be linked. It’s hard to imagine that process and outcome may have little to do with each other. But in the 1990s (in an episode Mitchell and Izmailov both brought up), it was hard to imagine how brute-force search could beat world champ Garry Kasparov at chess. And in 2023, it was hard to intuit how a giant pile of matrix multiplications could write in iambic pentameter. For most of us, these just weren’t thinkable thoughts. Until, suddenly, they were.

In summer 2024, just months before the first LRM appeared, Mitchell turned me on to a concept that I keep returning to in my AI reporting: “wishful mnemonics.” The phrase was first used all the way back in 1976 by the computer scientist Drew McDermott, in a paper with the epically grouchy title “Artificial Intelligence Meets Natural Stupidity.” I’ll quote the same passage Mitchell did:

A major source of simple-mindedness in AI programs is the use of mnemonics like “UNDERSTAND” or “GOAL” to refer to programs and data structures. … If a researcher … calls the main loop of his program “UNDERSTAND,” he is (until proven innocent) merely begging the question. He may mislead a lot of people, most prominently himself. … What he should do instead is refer to this main loop as “G0034,” and see if he can convince himself or anyone else that G0034 implements some part of understanding. … Many instructive examples of wishful mnemonics by AI researchers come to mind once you see the point.

This is how I make sense of AI reasoning. LRMs, chains of thought, thinking tokens: It’s wishful mnemonics all the way down — a heady mix of shorthand and suspended disbelief, like Oprah-style “manifesting” with a computer science spin. This isn’t necessarily a dig; all novel research likely requires some version of this mindset just to get off the ground. It certainly doesn’t mean AI reasoning can’t or doesn’t work. But the “wishful” part seems to be as powerful as ever.

“We react to language in a way that is very anthropomorphizing. That’s just the way that we humans work,” Mitchell told me. Much of the contentious research activity around AI reasoning, she said, “is par for the course. But in other ways, there’s a lot of very unscientific aspects to it.” Or, as Kambhampati put it, “A fake theory is worse than admitting that we don’t have a theory.”

In any case, we have to call it something while we figure out what it is. I don’t foresee always reaching for the air quotes around AI reasoning, any more than I’d put them around the “horse” in horsepower. LRMs are like engines: They require fuel, emit exhaust, and go fast. Still, when I describe the oomph my Toyota can deliver when I step on the gas, it’s not because I believe there are little hooves pounding away under the hood. Until a clearer scientific account emerges of what’s going on under the hood of AI reasoning models, I’ll regard their horsepower in a similar spirit — even as the engines roar.

Physicists Solve a Big Quantum Mystery. Now, Old Results Don’t Add Up.

Wed, 29 Jul 2026 02:53:08 GMT

Years after physicists at Fermi National Accelerator Laboratory in Illinois used a giant magnetic ring to measure precisely how much the muon wobbles, researchers are still puzzling over the result.

Reidar Hahn/Fermilab

For 25 years, physicists have been puzzled by an apparent one-part-in-a-million problem. Their expectations of the way that certain particles should wobble in a magnetic field were clashing with what they saw in experiments. The discrepancy was an electrifying hint that they might be seeing evidence of unknown particles.

Then in 2021, that hint seemed to evaporate. When researchers updated the way they did their theoretical calculations, they found that their predictions matched the experimental results much more precisely than before, to one part in 100 billion.

But that, in turn, has created another puzzle: The old calculations seem perfectly valid. So why don’t they match the new calculations? Those older predictions were not purely based on theory; they were also inferred from other experiments. If the older calculations conflicted with newer results, and the older calculations were based on experimental data, was something strange going on in those old experiments?

One promising clue comes from a particle collider in Siberia, which has recently started seeing its experiments dramatically diverge from what it and other colliders saw in the past. Its results have sparked a flurry of activity as physicists try to determine whether the conflicting measurements are a side effect of different experimental procedures, or a sign that new particles are popping up after all.

Weird Wobbles

The particle at the center of the mystery is the muon, a heavier cousin of the electron. A muon behaves a bit like a tiny bar magnet. Spin one in a circle inside a magnetic field and the magnetism will make it wobble, tracing out its own, smaller circles. The sizes of these circles are determined by a number called a “g-factor.”

If the muon sat isolated from other particles, its g-factor would be exactly 2. But quantum theory requires that all other particles influence the g-factor. As the muon wobbles, it releases particles such as photons, which are too short-lived to show up in detectors. These can release other particles, which can release still more particles. The muon quickly reabsorbs all these fleeting particles, and the only trace they leave behind is that the muon wobbles a little bit more. Through these intricate chains of emission and reabsorption, every particle in existence has some small effect on the movement of the muon.

Samuel Velasco, Mark Belan/Quanta Magazine

That makes the precise size of the excess wobble, the muon’s “g–2,” invaluable as a window into the quantum world. “The measurement of muon g–2 is a proxy for saying how many particles exist in the universe,” said Alex Keshavarzi, a senior research fellow at University College London.

So when an experiment at Brookhaven National Laboratory on Long Island measured the muon’s g-factor in 2001, physicists were thrilled that it came out larger than expected. To some, it hinted that new particles — perhaps even particles that could account for dark matter — were at work.

Physicists set out to check the result with an even more precise measurement. In 2013, Brookhaven’s 50-foot-wide magnetic ring was moved via an elaborate series of barges and trucks to Fermi National Accelerator Laboratory (Fermilab) in Illinois, where an upgraded version of the experiment would take even more data.

To prepare for that new experiment, physicists also made a huge effort to understand the theoretical prediction that disagreed with the data. Their challenge was to understand the muon’s chains of emission and reabsorption in extreme detail. In particular, how much do the particles associated with each of nature’s four fundamental forces participate in these chains?

The calculation is straightforward for three of nature’s four forces. Gravity is so weak that physicists can ignore it outright. And both the electromagnetic force and the weak nuclear force can be deduced using a standard technique.

The strong force, however, is not so easy to deal with. That force tightly binds particles known as quarks into composite particles such as protons and neutrons. Standard theoretical techniques don’t work on the strong force. So physicists have to get creative.

In his doctoral thesis in 2018, Keshavarzi helped hone an alternative way of understanding the strong force, called the data-driven method. In this method, physicists don’t try to predict how often muons will emit and absorb groups of quarks. They go out and measure it.

The main way that happens is by colliding electrons and their antimatter partners, positrons. The matter and antimatter annihilate each other, creating other particles, including bundles of quarks. If lots of quarks appear, physicists know they have a tight quantum link to particles such as electrons and positrons. In short, the more quarks appear in electron-positron collisions, the more strongly they will affect the muon.

Using the data-driven method, physicists set out to calculate the expected size of the muon’s magnetic wobble. That prediction, which was released in June 2020, sharply differed from Fermilab’s precise experimental measurement, which came out in April 2021. The discrepancy was so strong that it nearly crossed the stringent threshold required for physicists to claim they had discovered new particles.

But a different theoretical calculation would tell a different story.

Wrangling Lattices

Not all physicists pursued the data-driven method to calculate the muon’s wobble. Some were working on a more purely theoretical technique to make their prediction.

The approach resembles what happens in weather forecasting. While it is possible, in principle, to understand the weather by keeping track of the precise contour of every breeze in the atmosphere, in practice that task is absurd. Instead, meteorologists divide the atmosphere into big boxes — a 3D grid — and calculate how each box changes on average over time.

Likewise, it’s too hard for physicists to keep track of every strong-force interaction between every pair of quarks. So physicists use a technique called lattice QCD (short for quantum chromodynamics, the theory of the strong force), to use a big grid to simulate the overall behavior of quarks.

In 2014, a collaboration among researchers in Budapest, Hungary; Marseille, France; and Wuppertal, Germany — the BMW group — started on a project to use lattice QCD to calculate the muon g-factor.

In 2013, researchers carefully transported Brookhaven’s magnetic ring from New York to Illinois by sea, river, and road.

Brookhaven National Laboratory

At first, their predictions were 10 times fuzzier than data-driven inferences. Low-energy particles tend to spread out, so capturing their possible positions requires using a huge lattice. High-energy particles need a comparatively smaller grid, but one with an extremely fine mesh. “Back then, it was unimaginable that one day lattice would reach the same precision” as the data-driven method, said Kalman Szabo, a professor at Wuppertal who was involved in the effort.

It took a decade of developing clever computational techniques — and waiting for increased computing power — for the BMW group to wrangle grids that were both sufficiently big and sufficiently detailed. But wrangle them they did. In 2021, on the same day that Fermilab released its updated muon g–2 measurement, the BMW group’s result appeared in the journal Nature.

According to the BMW group’s lattice calculation, Fermilab’s muons were wobbling exactly as they should. Since then, independent lattice groups have published matching calculations.

Today, many physicists believe the muon mystery is no more: According to the lattice simulations, the muon’s extra wobble can be explained entirely by the emission and reabsorption of known particles obeying the known laws of the known forces.

So why does the data-driven method indicate otherwise?

Inconsistent Experiments

To figure out what’s going on, physicists are drilling into the electron-positron collisions driving the data-driven method. These collisions are supposed to be a direct window into quark behavior, but calculations based on this data disagree with both the latest experimental results and BMW’s prediction. So what’s really going on in the aftermath of those collisions?

In the city of Novosibirsk in southern Siberia, the VEPP-2000 collider has been crashing electrons into positrons on and off since the turn of the millennium. It’s a relatively gentle collider, operating at 6,000 times lower energy than CERN’s Large Hadron Collider, near Geneva.

The VEPP-2000 features two detectors that precisely count how often certain bundles of quarks, known as pions, pop out of the electron-positron crashes — data that physicists have been using to infer how much the strong force was messing with muons.

In 2010, physicists installed a completely new detector. They then used it to more precisely measure this pion production rate, which they published in 2023. After the refresh, they found that the rate changed significantly.

Fedor Ignatov, a physicist at the University of Liverpool in the UK, was a member of the team that measured a mysterious new rate of pion production at the VEPP-2000 collider.

Courtesy of Fedor Ignatov

“It was a surprise. No one expected it to be like that,” said Fedor Ignatov, a physicist at the University of Liverpool in the UK and member of the team.

Physicists had seen faint hints that something strange was going on with the pion rate. They noticed that measurements of it from experiments in Italy and the United States were starting to drift apart. But the dramatic divergence of the new measurement from the detector’s own past results, along with the collaboration’s claim of high precision, made the situation hard to ignore.

Physicists have pored over the result. “No measurement has been scrutinized more,” Keshavarzi said. So far, no problems have been found.

Recent lattice-based simulations align with the newly measured rate. And preliminary data from the other detector at the VEPP-2000 collider also seem to match. Meanwhile, a 2023 analysis of data collected earlier at yet another experiment at a collider, BABAR in California, sits in striking agreement with the older rate.

All of this leaves physicists wondering what’s really going on in all these collider experiments. The discrepancies point either to signs of unknown particles meddling with the quarks, or to overlooked details generating the mistaken impression that quarks are misbehaving. Either way, particle physicists can’t rest until they have solved the new electron-positron mystery, and figured out whether the old pion rate, or the new pion rate, is the right one.

“There are four decades of measurements that preceded that, that were all done in different ways, that were all done by different people, that were all done by different experiments, that all paint a completely different picture,” Keshavarzi said. “There is so much still left to do.”

Correction: July 30, 2026
The original version of this article stated that the BMW group carried out simulations that directly predict the new pion rate. BMW’s calculations support the new rate, but only indirectly. Other lattice groups have more directly gone after the pion rate.

A New Way That a Cow’s Inner World Shapes Earth’s Atmosphere

Mon, 27 Jul 2026 02:40:59 GMT

Ada Zejun Shen/Quanta Magazine

Within every cow is a thriving ecosystem. Churning deep in its intestines, a massive fermentation chamber known as the rumen hosts a robust microbiome that can consume up to 100 pounds of feed daily. Inside this gut pouch, tens of millions of bacteria scavenge for scraps of fiber, starch, and other nutrients, and break down cellulose and proteins. They get a hand from microbial fungi, whose enzymes demolish stiff cell walls, and all are ruled by ciliates: large, predatory microbes that gorge themselves on bacteria.

This complex food web transforms a bounty of compounds to fuel the cow’s metabolism. Little goes to waste: Even hydrogen gas and carbon dioxide, the byproducts of fermentation, are scavenged by opportunists in this dark, warm, oxygen-free world. Those opportunists are rumen microbes called methanogens, and their waste product is methane, a notoriously powerful heat-trapping greenhouse gas.

In this way, the inner world of a cow has global significance. Ruminant livestock, including cows, goats, and sheep, have burped out about a third of all methane gas in the atmosphere. All told, when combined with more methane from landfills and fossil fuels, the gas is responsible for around 30% of the rise in global temperatures over the past 150 years. But it has a weak spot: It decays more quickly than carbon dioxide. That’s why cow gas has attracted interest from researchers across the globe. They are looking into livestock’s specialized stomachs to identify the biological mechanisms that produce methane, which could be targeted to slow global warming within our lifetimes.

A recent study published in Science has revealed a clue wrapped in a membrane. Amid new genome sequences for 450 ciliates — the rumen’s apex predators — researchers followed a trail that led them to an organelle, new to science, that is essential to the biochemical process of rebuilding atoms into compounds that are heating the planet. They named it the “hydrogenobody” because it produces hydrogen gas, which methanogens then turn into methane.

The findings offer new ideas for managing this pervasive source of warming, said Juan Tricarico, who researches enteric, or intestinal, methane at Dairy Management Inc., a nonprofit trade association for dairy farmers, and was not involved in the recent study. “Just targeting the methanogens is probably not enough.”

Understanding how microscopic organisms lead to changes at a planetary scale will require further disentangling of the rumen’s microbial food web and the specific mechanisms by which they produce methane, he added. “We want to understand the environment under which these microbes thrive.”

How the Methane Gets Made

Even though ciliates have been studied for over a century, their role in the cow-gut ecosystem has been neglected compared to the far more numerous bacteria. Microbiologists know they are the largest single-celled organisms in the rumen. Under a microscope, their hairlike cilia sweep the area outside the cell like wispy brooms, pulling bacteria into their mouths and pushing them around. Powering all those cilia takes a lot of energy, and making that energy releases hydrogen gas, which is then consumed by bacteria and archaea, including methanogens.

“The whole rumen system is highly evolved, it’s highly synergistic, it’s highly symbiotic, and it’s evolved to consume all of that hydrogen,” said Rod Mackie, a rumen microbiologist at University of Illinois, Urbana-Champaign, who was not involved in the new study. “And they [methanogenic archaea] do it by shunting that into mainly methanogenesis.”

To better understand the specific roles of rumen ciliates in methane emissions, microbiologists have turned to genomics. In 2021, Zhongtang Yu, a rumen microbiologist at Ohio State University, sequenced the very first rumen ciliate genome from a species called Entodinium caudatum; its genus includes roughly 90% of all ciliates in livestock rumens. A few years later, Yu assisted another team in sequencing the genomes of 52 additional rumen ciliates — a good start, but far from representative of the cow microbiome’s ciliate diversity.

So when the 2026 study in Science reported 450 new ciliate genome sequences, jaws dropped across the rumen microbiome community. (The study’s authors, most of whom are based at the Chinese Academy of Sciences or Nanjing Agricultural University, did not respond to interview requests from Quanta Magazine.) The genomes have been added to a database where any researcher can access and study the ciliate sequences.

The paper’s authors got a head start by searching the genomes for gene sequences of methane-making enzymes — including hydrogenases, the enzymes that catalyze the formation of hydrogen gas. They found that some of the ciliates’ hydrogenases were different from all known versions of the enzymes found across life. Experiments to locate these unusual enzymes found them in an unusual place, too: right at the edge of the cell membrane.

Electron microscope images of several prominent ciliate species revealed why. Lining the outer cell membrane, at the base of the cilia, were simple structures, each encircled by a single membrane. Inside was hydrogenase. The ciliates seemed to have organelles, the newly described hydrogenobodies, specially placed to provide energy to cilia.

Mark Belan/Quanta Magazine

At its most basic, an organelle is a membrane-bound structure with a specialized function that is “recognized as having a different molecular signature than anything else in the cell,” said Aaron Turkewitz, a cell biologist and emeritus professor at the University of Chicago who was not involved in the research. The hydrogenobody, like the nucleus and mitochondria, fits this description. “Finding a new organelle is pretty exciting,” he said.

When the study’s authors looked closer, they noticed that some ciliates had more hydrogenobodies than others. Isotrichs, one prominent type, are “huge,” Tricarico said, at least by microbial standards. They are covered in cilia that resemble fur and have far more hydrogenobodies on their cell membrane to fuel those cilia. Entodinomorphs, on the other hand, are smaller, with cilia and hydrogenobodies only in certain areas. Each type of ciliate occupies a different niche in the rumen, the same way that lions and cheetahs have different roles as predators on the savanna, Tricarico said.

Within the organelle, the hydrogenase enzyme isn’t just interesting for its role in hydrogen production; it also uses up oxygen. This action supports methanogens, too, since they are inhibited by oxygen. The hydrogenobodies therefore help keep the dark cave of the rumen oxygen-free enough for methanogens to thrive, in addition to providing them with a raw material.

It seemed plausible that these hydrogen-producing organelles were part of the methane puzzle, but to be certain, the researchers needed to know whether they noticeably affected methane production. To test this, they measured methane emissions from 100 dairy cows using a gas-measuring device called a head box, which is exactly what it sounds like: a box that surrounds a cow’s head to measure its methane burps. Then they analyzed the composition of isotrich and entodinomorph ciliates within the cows’ rumens. They found that cows with more isotrichs — and therefore more hydrogenobodies — had much higher methane readings than those whose microbiomes were dominated by entodinomorphs.

Scientists have long suspected that ciliates are associated with methane emissions, Yu said. The new study confirms the suspicion at a mechanistic level, presenting new ideas for how to tackle livestock’s methane emissions from the inside out.

From Organelle to Atmosphere

In the rumen microbiome, bacteria are essential to cow digestion, but ciliates may not be. If scientists and farmers could remove or reduce ciliates from the rumen without disrupting digestion too much, they can curb the burp, and with it, methane.

The basic idea goes back decades, Tricarico said, to when rumen microbiologists proposed removing all protozoans — the group of single-celled protists that includes ciliates — from livestock rumens as a potential methane mitigation strategy. But just like on a coral reef or savanna, eliminating predators threw the entire ecosystem out of whack. In experiments, wiping out protozoans allowed bacteria to grow exponentially, which generated more hydrogen and more methane, Mackie said. The new study helps identify which specific protozoans, such as isotrichs, are more problematic — producing more hydrogen — than others, he said, offering a more precise target.

Another possibility is to redirect the excess hydrogen away from methanogens. Indeed, other microbes in the rumen consume hydrogen without making methane, but methanogens put up stiff competition. By congregating on the ciliates’ surface, right next to the hydrogenobodies, they position themselves to get first dibs on any hydrogen that comes out of the organelles. Now that the new study has clarified the process, “scientists could actually start looking at these hydrogenobodies” themselves as additional targets, Tricarico said.

Take Bovaer, a popular feed additive that reduces cows’ methane emissions — or, in other words, minimizes the methane in their burps. The synthetic compound, 3-Nitrooxypropanol, interferes with enzymes that produce methane, but it doesn’t work consistently for all cows, diets, and environments. “This study could actually tell us why it’s not so effective in those other circumstances,” Tricarico said. By detailing the methane-making mechanisms, “you could create circumstances that allow probiotics [or feed additives such as Bovaer] to be more successful.”

While the study has been a leap forward for rumen microbiology, there are a few caveats. “This paper, important as it is, still has huge gaps connecting it to methane production,” Mackie said. While the head-box experiment is helpful, it doesn’t close the case on how different ciliate species, or the hydrogenobodies themselves, contribute to methane emissions. Importantly, he noted, the authors did not specify the cows’ diet — a primary factor in microbial methane-making, since different feed types result in different amounts of hydrogen gas.

Already, the study has inspired Mackie to explore new research questions. Instead of looking at hydrogen transfer between different species of bacteria and methanogens, “I think that now I should be looking at interkingdom hydrogen transfer,” he said, between bacteria, archaea, fungi, and protozoans.

By looking at the basic biochemistry that underpins these processes, scientists can refine the ways we wrangle methane, from a microscopic organelle, through a teeming ecosystem, and up into the atmosphere.

How Fast Is the Universe Really Expanding?

Thu, 23 Jul 2026 02:53:45 GMT

Chanelle Nibbelink for Quanta Magazine

One of the biggest mysteries in cosmology seems to keep getting bigger. Astronomers have known since the 1930s that the universe is expanding, but in the 1990s, the discovery that this expansion is accelerating rather than slowing down came as a huge shock to the field. Something had to be driving that acceleration, and dark energy was proposed as the cause. What began as a seismic shock in cosmology eventually led to a Nobel prize.

But this story has a sequel, and it comes with another major plot twist. The two main methods for estimating the universe’s present-day expansion rate are producing significantly different answers. As a result, how fast the universe is really expanding has become a matter of considerable debate — with no small amount of angst — and the discrepancy has become known as the Hubble tension. Perhaps most surprising of all is that one of the loudest voices raising concern is Adam Riess, the astrophysicist whose Nobel Prize-winning work helped ignite the acceleration debate in the first place.

Riess joined co-host Steven Strogatz on The Joy of Why to explain how we got to this point, what the Hubble tension might be telling us, and what may happen next.

Listen on Apple Podcasts, Spotify, TuneIn or your favorite podcasting app, or you can stream it from Quanta.

Transcript

[Music plays]

STEVE STROGATZ: I’m Steve Strogatz.

JANNA LEVIN: And I’m Janna Levin.

STROGATZ: And this is The Joy of Why.

LEVIN: A podcast from Quanta Magazine, where we explore some of the biggest unanswered questions in math and science today.

STROGATZ: Well, great to see you, Janna. How’s it going?

LEVIN: Hi, Steve. Yeah, great to see you. I’m excited to hear what you have to talk about today.

STROGATZ: Yeah, good, because I could barely contain myself. This was an especially fun conversation I had with Adam Riess, who I guess is someone you would know from the circuit.

LEVIN: Yeah. Definitely. I was speaking with him not too long ago.

STROGATZ: Uh-huh. Well, right, I would think that in the astrophysical world you would have crossed paths, so I’m not super-surprised to hear it. But actually, I myself had not spoken to Adam or seen him for many, many decades. It turns out he was a, uh, a student when I was just beginning as a professor.

LEVIN: Oh, wow. In your class?

STROGATZ: He was literally one of my students at MIT in my first job.

LEVIN: Wow, how amazing to think these young kids in your class, one of them’s gonna be a Nobel prize winner.

STROGATZ: Well, exactly. Yeah, very memorable student. Really a great guy. But, I would actually like to pick your astrophysics brain if we could for a second because one of the things that I talked to Adam about is the issue of the universe expanding and also its expansion accelerating.

LEVIN: Right.

STROGATZ: You know, like you were there back in 1998 when we got the news about the acceleration. Do you, um, remember anything about that time? Like what it felt like in your community?

LEVIN: Oh, yeah. Well, I was at Berkeley, and that’s where Adam was. And also Saul Perlmutter, the other group, right? These were two different groups working. So I absolutely remember, I was at the Center for Particle Astrophysics, and Saul was kind of up in the hill in Berkeley, and he was coming down with these results, and I was like, “Come on, man.” Then there was a lot of discussion, honestly, about how there’s huge sensitivity to the temperature of the supernova, you know, very high power.

STROGATZ: And so the reason you’re bringing up this thing about the power and the sensitivity is that the results were so shocking that everybody wanted to be very, very careful.

LEVIN: Very, very careful. And this is outside my field, this is very observational. I’m more on the theoretical side. But, I remember so well, though, just being in the room while those conversations were happening between the observers, and they were really being interrogated by the theorists who were very interested in data. You know, the theorists right on the cusp of data. It was really interesting times, no question.

STROGATZ: That’s exactly where we’re gonna go. So, for our listeners who may not know about Adam, in addition to having been a student at MIT, soon afterward, he shared a Nobel Prize for his work on the discovery of the accelerating expansion of the universe. That was in 2011. But since then, as we’re gonna hear, there have been quite a few plot twists in the story. As new data have come in, he’s had to revisit some of his findings and the findings of other people in the field. So if you’re ready, Janna, should we go cosmic?

LEVIN: Let’s do it. It’s a really interesting moment in cosmology, for sure.

STROGATZ: Fantastic. Okay. Well, here we go.

[Music plays]

STROGATZ: Adam Riess is a professor of astronomy and physics at the Johns Hopkins University and a senior member of the science staff at the Space Telescope Science Institute. Among his many honors, Adam is the co-winner of the 2011 Nobel Prize in physics for his part in the discovery of the accelerating expansion of the universe. Welcome to The Joy of Why, Adam.

ADAM RIESS: Thank you for having me.

STROGATZ: Oh, well I am so excited to see you I think it’s something like, I’m guessing about 35 years from the time. When you were an undergraduate in a class that I was teaching in the math department at MIT, it was a course in complex analysis, but I’m wondering, as a couple of old men now, can you tell me what you remember from that experience?

RIESS: Sure, of course. MIT was very impactful to me. You know, being a student there felt like a big jump, and so each of those courses felt like, you know, Job’s trials. And I remember that class was a sea of tranquility in the midst of other things that were super tough and rough.

I think it was because of you, to be honest. I remember vividly sitting in that class. You were a young professor. And I remember one day sitting there puzzled and getting ready to raise my hand, and you said, “Adam, you look bothered by this concept. Is there something about it that bothers you?”

And I was amazed. No professor, first of all had ever said my name, let alone actually gauged the expression on my face and cared that something was disturbing me. And, you know, we got right into it. And, so that course was great. I’d like to say that I spent the rest of my career focused on that material, but I moved over towards physics.

STROGATZ: Well, thank you for sharing that memory. I have to say, I do sometimes look at students’ expressions on their face and I can see something. You had a very animated face. You still do.

I mean, I think I’ve taught a few thousand students now so I don’t remember all my students, but I do remember the ones that win Nobel prizes and I think you might be the only one. So it’s really very—I’m very proud of you. I’m thrilled to be able to talk to you now. Anyway, it’s great.

So you say you moved into physics after, or I guess you were already probably pretty intensely interested in physics at that point?

RIESS: Sure, I was. You know, at MIT, everything is numbers instead of names. So I was course eight, and I was taking the required courses in math, which was course 18. That course was 1804, not the year. Although sometimes we feel that old, I know. But, but, you know, really my passion was physics. It was really understanding the physical world.

STROGATZ: And so very quickly that interest led you into subfield or adjacent field of astrophysics, and into the study of very spectacular objects in the universe, called supernovas or supernovae — if we want to be in Latin about it. So I have to admit, I’m not an astrophysicist. You probably realize that, and I need some of the basics explained here. So what are supernovas and then why are they interesting objects to study?

RIESS: Right. I’ll take the second — why they’re interesting objects to study — and I’ll jump back and say, what is the question or what is the point? And so to me, when I went from physics to astrophysics and first learned what it is that we know about the universe, I was fascinated by the discovery that the universe is expanding. I just think that’s amazing. It’s, as a kid, it’s not what I would’ve expected.

I would’ve expected, the universe is just the thing that’s always been there. It’s like the bedrock, you know, it’s eternal, it’s unchanging. And so that was amazing to learn and then to further learn that we still don’t understand that much about the universe. And so by watching it expand, by measuring it expand, by seeing its expansion history, we can deconstruct the nature of the universe.

We can figure out how old it is, we could figure out what its ultimate fate is. We could figure out what it’s composed of. And so those are all really, to me, the questions that I wanted to have answered. It just turns out the means to do that is to have reliable tracers of the expanding universe. So objects in the universe that act like test particles that we could watch.

And it just so happens when I started graduate school that exploding stars, supernovae, became some of the best tracers right at that time. Because they’re so luminous, you could see them far away. So you could see far into the history, the past. But also, and this is the most important point, which I’m sure we’ll talk about, to measure the expansion of the universe, you need to measure two aspects of your tracer. You need to measure what’s called the red shift, which is essentially, the stretching of the wavelengths of light emitted by that tracer because of expansion.

So it’s a direct measure of the expansion of the universe, but then the other that you have to measure is how far away those supernovae are, which is telling you how far back in time you are looking so that you’re essentially tracking the expansion history of the universe the same way you would, you know, if you were to mark the height of a growing child on a door frame. Right, you would wanna mark their height and you’d wanna mark the time when they were at that height. And so those two quantities are how we chart the expansion of the universe. And those are observationally challenging.

STROGATZ: Well, that’s fascinating. So you’ve already anchored us in really fundamental questions here that although I was pitching it as, “Oh, you like astrophysics.” Maybe I was mistakenly emphasizing astro, like, you’re curious about supernovae as things in themselves. Like they are a tool for you. Sure they’re cool objects, but you’re using them because you wanna ask really big questions: How fast is the universe expanding? How do we know it’s expanding? That kind of thing.

RIESS: Right. This is sort of the dichotomy that we sometimes call astrophysics versus cosmology. Cosmology, the study of the structure, the shape, future, the past of the universe, as a whole entity, is really fascinating to me. And, you know, as a result, you have to study all the astrophysics and the physics and the math and the nitty gritties because, you know, you need to tease out that information.

It so happens, in my case, I tended to study various classes of stars exploding, pulsating as those critical tracers.

STROGATZ: So this question about the universe expanding and the — what you refer to as tracers — the exploding stars, and then estimating how far away they are using the redshift to tell us about how fast they’re receding. It’s really gorgeous thinking, I have to say.

I would love you to give us a little tutorial about how it is that people can estimate how far away galaxies are because it’s not an obvious thing and you have a lot of different techniques, whether using trigonometry — very near and dear to my heart — or your concept of standard candles. Just give me a little basics of the cosmic ladder.

RIESS: This is actually the meat and potatoes of what I do. I should have said, when we look at these tracers, we need to measure their red shifts and distances. And the redshift is the easy part. You just take a spectrum and you recognize certain colors or lines which have moved to a redder location. And it’s trivial.

The hard part is the distances. This is many have called the biggest challenge in all of cosmology is to figure out how far away things are. And, it’s a really fundamental problem. It goes back to, you know, almost being a little kid. You look out at the sky and everything looks very two dimensional, right? And you have no sense of depth. The depth perception is completely absent. And so, we’re in awe, but we’d be in more awe if we just understood how far away things were, how far back in time.

So how do you lick that problem? And as you said, we start out with the things we know, which is geometry. And so we measure parallaxes when we can. And so just like we have two eyes and we get a vantage point from each of them on nearby objects, and the changing perspective or angle of something nearby, relative to far away, allows our brain and eye to do the geometry and estimate how far away something is.

The problem is that space objects become very, very far away so that angle either becomes very tiny or you need a much bigger baseline, a separation between the two perspectives. And the best one, the biggest one we get is when the Earth goes around the sun and we could view a nearby star relative to a distant star, let’s say in January when we’re on one side of the sun and in July when we’re on the other.

And if you’re lucky, you might be able to tease out the little change in angle of that nearby star. And so you can gauge the distance to some of the nearest stars. And we do this with space satellites and things like that. The problem is we’re after deeper waters. This is only a technique we can apply within the Milky Way galaxy.

To be able to measure the distance to galaxies — which are thousands, millions, billions of times further away than anything in the Milky Way — that parallax angle would become imperceptibly small. So we have to switch to a completely different method.

And the method we use most commonly is what ship captains know to use at night, which is the brightness of a lighthouse, right? So, you know, if you’re a ship captain at night, you wanna make sure you’re far enough away from a rocky shore. So you look at a lighthouse and you look for it to be faint, telling you that it’s far away that the light attenuates or dilutes as one over distance squared. That’s geometry too, of course, but it requires some understanding of what it is you’re looking at. That it’s a truly luminous object, a lighthouse, not a little pen light. And then you can gauge distances.

And so that method astronomers call “standard candles,” the lighthouses. And they look for objects in space that can serve that role. And as I started graduate school, there was great recognition that a certain class of exploding stars, called Type IA supernovae could serve as outstanding lighthouses. They were very homogeneous, very uniform. They had small differences. But they gave you what was a pretty standard light source that was maybe 4 or 5 billion solar luminosity in total output for a few weeks. So that allows you to see very deep into space.

STROGATZ: So let me just underscore that last thing you said, because your whole subject is so mind blowing that you rattle off these things that, you know, you’re so used to by now. If the listener didn’t catch that, Adam just said that this one star exploding is about equivalent in brightness to about a billion stars shining normally like our sun. Okay. One star is as bright as a billion. That is a big boom.

RIESS: Yes, it really is. You know, it’s really because stars have a lot of fuel and they’ll spend billions of years putting that output at a kind of normal sun-like rate. But they have a lot of energy in reserve. And during an explosion event a fair fraction of the total available energy of the sun, instead of trickling out over billions of years, trickles out over hours, days, weeks, all the rest of it.

So, it is a big boom. It’s sort of like, you know, the difference between driving a car with a gas tank, little bit of gas at a time, versus lighting the gas tank on fire. It’s just all of the fuel just goes up.

STROGATZ: Wow. That’s amazing. And then also this idea of standard candles. I love the basic physics that goes into explaining these Type I supernovae. Whenever they blow up, they will blow up with about the same amount of energy. You said it’s not perfect, but it’s pretty darn close. So if you could just tell us a little about the theory that gives us confidence that’s true, ’cause that’s a really pretty thing too.

RIESS: So I would say throughout the last century of cosmology, cosmologists looked for the best standard candle they could find. So, you look at a distant galaxy and every galaxy looks different than every other galaxy because a galaxy is a crowd of stars and there’s no such thing as a standard crowd, right? Those are different numbers. So those are not gonna be good standard candles, right? So what you need are actually individual objects that are the same kind of object just located in different places in different galaxies. Stars work, but they’re too dim.

But this one kind of supernova, which there’s still some debate about this, but generally the general principle is it’s the center, the core of an old star called a white dwarf star, which is holding itself up against its crushing gravity by a kind of quantum mechanical pressure called electron degeneracy pressure. And this is something that the great Indian astrophysicist, Chandrasekhar first showed was stable only at a certain critical mass known as Chandrasekhar’s limit. So it’s 1.4 times the mass of our sun.

And so that means that if a star exceeds that limit — if it’s sitting there at Chandrasekhar’s limit, and let’s say it has a friend, another star orbiting it, and material gets transferred from one star onto the other — if it gets close to or even exceeds Chandrasekhar’s limit, then you will get runaway thermonuclear explosion because this electronic degeneracy pressure is no longer strong enough to hold back gravity. And it will compress and crush the star, giving you the property necessary for fusion and basically doing thermonuclear fusion over all remaining fuel.

So as I said, there’s some debate about exactly the details, but this is the general broad-brush picture that gives you a fairly uniform explosion, far more uniform than anything else we know on a kind of macroscopic scale.

STROGATZ: If I followed you correctly there, and correct me if this is too crude, it’s almost like saying rather than standard candle, it’s a standard hydrogen bomb.

RIESS: Correct.

STROGATZ: Because it sounds like that’s what you just said, that we know the amount of material in the star. It’s gonna be 1.4 solar masses approximately. And it’s gonna completely blow up through this thermonuclear, which is fancy talk for hydrogen bomb. Maybe I’m a little bit off.

RIESS: Yeah. With the one substitution of it’s carbon and oxygen instead of hydrogen, but yes.

STROGATZ: Okay, good. Great. So it’s not a hydrogen bomb, it’s a carbon oxygen bomb, but still it’s fusion, right?

RIESS: It’s fusion. And while some details about how the other star maybe donates the material or how fast the star is rotating can perturb a little bit the amount of energy you get out. And in fact that small variation, that was my thesis project, was to figure out how to account for the small variation.

That if you think of a kind of a standard light bulb, like a 60-watt light bulb — I don’t know if kids still know. But you could imagine some are 58 and some are 62, ’cause the factory doesn’t make them all the same. And that could fool you into misestimating the distance a little bit. ’Cause you may be seeing one that looks a little fainter, ’cause it was 58 watts, but instead you’re, you think, oh, it’s further away, but it isn’t.

How do you figure out from here which ones are intrinsically bright or intrinsically faint, given a little bit of distribution? And one of the things that was discovered in the early 1990s and became part of my thesis was the ones that are more powerful, rise more slowly and fall more slowly, to reach their peak than the ones that are more dim.

And another confounding effect, we sometimes have to look at a supernova through a galaxy that has dust in it and that dust can obscure the light. So going back to my analogy of a lighthouse, it would be like looking at a lighthouse on a foggy night, right? It could make the lighthouse look dimmer and fool you into thinking it was further away than it really was.

But the dust in galaxies also shifts the colors of the supernova light. And so if you could simultaneously measure the light curve shape that tells you whether it’s a bright or dim light bulb, and the colors that tell you how much dust is in the way, you could tease out these competing effects and get back to what you wanted, which was to figure out how far away the supernova was. And that was the subject of my doctoral thesis when I moved to Harvard, in the early 1990s.

STROGATZ: Well, I appreciate your going through that because this is such a bit of Sherlock Holmes work that you don’t have complete evidence. You have to do a lot of reasoning like they’re the use of the different colors. Or you didn’t use the phrase light curve yet, but you sort of hinted at this idea that the brightness — it’s not just one flash, like I said, a boom. But maybe you should tell us a little more about that, that when you’re looking at a supernova, what are you really measuring?

RIESS: I should point out that a supernova is incredibly rare like this. So it’s not like, you know, you could expect to see one on any given night when you look out at the sky.

There is one in a galaxy like ours about once a century. And so, you know, if you wanna find a supernova, you just pick a nearby galaxy and you stare at it, you’re very unlikely to find a supernova.

The breakthrough came in the 1990s, when astronomers began to build telescopes that had wide angles, and they had detectors that they could cover the focal plane with, so that you could take a single image that might contain hundreds of thousands of galaxies in one frame.

Then you take another image, maybe a month later. And by math, you’re sure that one of those galaxies will have had a supernova over that month. Because you’ve just bought so many lottery tickets that you’re bound to win the lottery. And in the 1990s we learned to collect such images, digitally subtract one from another and find a new point of light. And then the supernova, it’s what we call its light curve. It usually takes about two or three weeks to go from explosion, when you don’t see it at all, to reach its maximum output, which is the sort of standard candle, if you will. The distance indicator.

And then it will fade over the course of months. After a few months, it’ll be about 100 times fainter. And so what’s also so fascinating in this field is not only is it kind of mind blowing, but it has this kind of fire drill aspect to it where everything has to be done very fast and timely because these things are fading away. You can’t say, “Uh, we’ll put that observation off a couple of weeks and come back and figure out what we wanna do.” No, you have to be, like, figuring out exactly what measurements you wanna make before the supernova fades away.

STROGATZ: Can you give us what it was like when you were first doing this kind of thing? Like, are you just looking at a stream of numbers? I assume you are, you’re not, there’s nothing visual here?

RIESS: It is actually very visual. Yeah, you get these elegant images of, if you’ve seen or can picture in your mind’s eye, a beautiful spiral-looking galaxy. And then you will see this extremely bright knot on it that may be as bright as the entire galaxy. It just looks like somebody turned on a spotlight in one spot, and it’s just bloomed over the whole area.

Now, as you place the galaxy further and further away, and as we talk about the accelerating universe, we look so far back that this whole image shrinks to just a few pixels, so that you’re saying, “Okay, that pixel looks a little brighter than that pixel.” But when they’re nearby, they’re some of the most beautiful objects you could see with a telescope.

STROGATZ: Huh, really? I’m so surprised.

RIESS: It’s one of the great joys of working in astrophysics and cosmology. The subject’s fascinating and the pictures are pretty cool too.

STROGATZ: So tell me about that joy. Can you remember back when you first encountered this? Like, was your heart beating? Did you think this is like a holy experience, like religious almost, or what?

RIESS: I wouldn’t say religious, but I would say like a lot of us starting out in research, right? You sit down with your advisor and he — in this case, Bob Kirschner — he sort of knows everything and is wise and. He’s like, “All right, let’s study these Type IA supernovae. We need to find one.” And you’re like, okay. And you’re kind of on an Easter egg hunt at that point. And then, you know, some information comes in and you turn the telescope there and you take this picture and you see this beautiful spiral-looking-like snowflake. And then there’s that bright spot and you take a spectrum, and the spectrum reveals the chemical composition of that supernova that tells you, yes, it is a Type IA.

It turns out Type IA’s produce a lot of silicon and sulfur in their explosions. And so you look for the signature of silicon and sulfur and I remember making a gorgeous color image and putting it on my wall as the first supernova I ever observed. And, yeah, I’ll never forget its name and number and distance and everything. But then there were many more after that.

STROGATZ: Oh, I like it. This is like your first love. You never forget your first love.

RIESS: Oh, for sure. Yes.

STROGATZ: Well, now that we have a little background about how to measure distances, take us to the late 90s. We know that the universe is expanding. We knew that for a long time at that point, but what didn’t we know? What did you end up discovering?

RIESS: So, if you can understand that we could measure how far away objects are and how much the light has been redshifted, then that maps to really telling us how much the universe has expanded up to different points in its history. And so that allows us to tell the expansion rate of the universe. It’s a historic number called the Hubble Constant, since Hubble was the first to measure that. And so that’s great.

But then your question might be, you know, is that rate speeding up? Is it slowing down? What is the ultimate fate of the universe depends on how this story is changing.

And so there’s a great trick that cosmologists can use to answer that, to figure out how it’s changing. We can look further out to look further back in time and make essentially the same set of measurements, not measuring now how fast the universe is expanding today, but using distant objects to tell us how fast it was expanding in the past, and then ideally how much that expansion is changing.

Now, the prevailing wisdom, I would say, up and through the 1990s was that the expansion of the universe would be slowing down because after the Big Bang, you would have the attraction of the gravity of all the objects in the universe — the mass of the universe itself would act like a brake — and it would slow the expansion.

Just like if I toss a ball into the air, the gravitational pull to the Earth will cause it to decelerate. And if I measure that deceleration, I could essentially weigh the Earth. And I can also, if I carefully measure that, figure out whether that ball will land on the Earth or maybe it was thrown with escape velocity and that there isn’t enough mass to pull it back and it will leave. And so the question in the 1990s was: Is the universe heavy enough to stop its expansion or is it light enough for the universe to expand forever?

And the way to answer this was to see how much the expansion was now slowing down. And so after developing the techniques to measure how fast the universe is expanding with these supernovae, two teams of astronomers — a team I was on called the High Z supernova team, and a competing team called the Supernova Cosmology Project — were the first to look for and find ultra distant Type IA supernovae, which exploded eight to 10 billion years ago. So looking now halfway, two-thirds of the way, through the history of the universe to measure the change in the expansion rate.

And as I said, we thought it would be slowing down. And circa 1997, 1998 when we first got our large collection of data, and I was very fortunate to be picked to lead the analysis of the first large tranche of data, I ran the calculations after doing the analysis and I came out with a crazy results that ultimately showed the universe was accelerating, not decelerating.

STROGATZ: It’s insane. I mean, you must have thought, wait a second, it’s accelerating?

RIESS: Sure. And in fact, I was sure that I did something wrong because having taken your math class right, I was very familiar with making mistakes, you know, this is what you do as a student is you try to do things and you get the wrong answer over and over and over. And then you try to find your mistake.

And so yeah, it was very worrisome for a while. So I did a lot of cross checks — because it’s always better to find your own mistake. Then finally willing to share with the team and let them find the mistake. And then, you know, everybody cross-checked everything we could and we could not find the mistake. And then we started getting comfortable with the possibility that it was real, that this was the signal on the sky and that there was a deep physics reason why this was.

And that is that in Einstein’s theory of general relativity, gravity has another option. It has another kind of gear. You know, in Newton’s theory, it’s only attractive. It only pulls stuff together, right? In Einstein’s theory, the gravity of empty space can be repulsive. Something he called the cosmological constant, and even invoked at one point to try to keep the universe in balance when he thought it wasn’t expanding.

And it’s always been around. Physicists later interpreted this as the energy of the vacuum of space, or what we now call dark energy, and it can go the other way. And so the interpretation we came to was that apparently Einstein was onto something, and that introducing this term gave a good fit to the data. Leaving it out gave a bad fit to the data.

[Music plays]

LEVIN: Yeah, it’s quite amazing. It was like Einstein couldn’t make a mistake ’cause he famously called the cosmological constant his greatest blunder, for the reason Adam said. He originally put it into his equation to try to make the universe not expand, right? But it’s very precariously balanced. And so if the balance isn’t perfect, it doesn’t make the universe static. It actually accelerates the expansion.

STROGATZ: Well, I’m wondering, the cosmological constant was something maybe people who knew history of science would remember, but it wasn’t part of standard general relativity coursework or anything, right? Wasn’t it sort of obscure in the ‘90s, or was it always there as like we need to think about it?

LEVIN: I think that’s a good question. It was probably there for theorists who would try anything. So essentially, people were thinking about the cosmological constant more in the context of things like inflation in the early universe, but then the idea was it would evaporate away, and it would decay into all the particles that made up the primordial soup, and it had no business hanging around today.

STROGATZ: That’s really interesting to think about that, that these inflationary scenarios had sort of softened people up to starting to think again about the cosmological constant.

LEVIN: Yeah. And I think it’s really interesting the Nobel prize was for the accelerated expansion. It doesn’t mention dark energy or a cosmological constant. That’s not what they got the Nobel prize for.

They got it for the observations of the supernovae, which is really interesting, and the accelerated expansion. And I think that’s consistent with the Nobel philosophy that they award prizes for verified results. Now, we don’t know anything about dark energy, so there’s no Nobel prize for that. The best we can do is give it this proxy name. Other than calling it dark energy and musing that maybe it’s the energy of empty space, maybe it’s not.

So, it remains to be an award to be doled out one day if somebody actually discovers what the dark energy is.

STROGATZ: That’s a really good point, that the Nobel… I mean, when we talk about Einstein and general relativity, famously he didn’t get a Nobel prize for either special or general relativity, right?

His Nobel prize — I’m just chuckling because was so sure it was coming that he could promise it to his wife. Do you not know this story?

LEVIN: Really, I do not know this.

STROGATZ: He promised the money from his Nobel prize to come to his first wife, knowing when he got divorced that she would need some money.

LEVIN: That’s amazing.

STROGATZ: But he didn’t get it for relativity. He got it for you know, his explanation of the photoelectric effect.

LEVIN: Mmm-hmm, yeah, incredible.

STROGATZ: But it’s an interesting, sort of aesthetic or criterion that the Nobel Commission uses that they want, as you say, verifiable experimental or observationally solid physics.

LEVIN: And I think that’s appropriate. That’s how it should be.

STROGATZ: Well, alright. In connection with plot twists in our story, you know, if the cosmological constant was the first twist, it turns out, as we’re gonna hear after the break, that there is another plot twist coming.

LEVIN: Great. Suspense.

[Music plays]

STROGATZ: Welcome back to The Joy of Why. We’re speaking with Johns Hopkins astrophysicist Adam Riess about the accelerating expansion of the universe.

So you mentioned the cosmological constant. It’s often going back to Einstein himself. In his notation, he used the Greek letter lambda to insert what some people, dismissively or sarcastically, will call a fudge factor. But it was something that was allowed by the equations of general relativity. As you say, Einstein wanted it at first because he couldn’t believe at the time that the universe was expanding.

RIESS: Right, you have to understand Einstein, he asked experimentalists, astronomers of the day, what is the universe doing? And they told him that the motions of things were very, very small.

And the reason they did was because at that time, it was before the discovery even that galaxies were outside the Milky Way. And so astronomers thought of the universe as the Milky Way itself. And when he asked about what the Milky Way was doing — was it expanding, contracting — they were like, the motions are pretty modest, doesn’t seem like it’s expanding or contracting. And this would’ve been confusing to him because, if you had a collection of masses and it was static and you let go. Right? They would fall together.

And so what was keeping it static? And so he saw, as you said in his equations, that there was an option for something to counterbalance the attractive gravity. And so he took it and set it to his, you know, as we would say, boundary condition that the universe be static.

There were two problems, of course: One was the universe is expanding, and so that’s not the right boundary condition. The other is it’s an unstable equilibrium. It’s like taking a marble and putting it on top of a basketball. Yes, in principle it could sit there, but if you push it off, if there’s a slight difference, it’ll run away in one direction or the other. And so when he saw the universe was expanding, when Hubble and others showed it, he famously said this was the biggest blunder of his career, was to introduce this concept. And yet there’s no getting rid of it.

Like a lot of mathematics and physics, it’s allowed to be in the equations unless you have some knowledge that it can’t exist. And so here we were some, oh, 80 years later saying, actually it looks like the universe is accelerating, which would be as if that repulsive type gravity actually was now winning over the attractive gravity of matter.

STROGATZ: There’s that funny saying I’ve heard, I’m not sure who to attribute it to, that what is not forbidden is compulsory. You know, like in something like this where the lambda term, the cosmological constant, was not forbidden by the equations. It was permitted by them. And in fact, now we think there is something like that. As you say, the modern term is often dark energy. But, we could go down a big rabbit hole of asking ourselves, what is this dark energy?

But I think I would like to go in a different direction to talk about the Lambda Cold Dark Matter model, the Lambda CDM model, because I mean, I realize that you’re gonna want to tell us, there may be some tweaks needed to it, or maybe more than tweaks, but why don’t we first make the case that this is a really interesting, powerful, standard model. Tell us what this model is and what makes it compelling. What are some of its great successes?

RIESS: Sure. When we build what we call a model of the universe to first order, we’re talking about what it’s made of. What’s the recipe, if you wanted to make one. And so what is the stuff. Then we also usually talk about the laws of physics as part of that.

But in the case of the universe, what people are familiar with the elements in the periodic table of elements. That’s the small stuff that’s like 4% of the universe. And the rest is dark. Dark meaning it doesn’t emit light. And so we can’t see it directly. We have to infer it by its gravity. And so from the 1930s to the 1970s and later astronomers came to understand that there was a lot of matter in the universe that had attractive gravity, but was dark, was not emitting light, called dark matter.

It makes galaxies spin much faster than the luminous matter would indicate otherwise. Stars would just zing away from their galaxies. It makes galaxies orbit other galaxies and clusters, which again, they would just fly away if there wasn’t the extra gravitational glue. There’s bending of light called lensing. All of these techniques allow us to figure out that the universe is about 25% dark matter and about… maybe 26%… and about 4% normal matter. So 30% there and then.

With our results in the 1990s and then quickly followed up by observations of the cosmic microwave background radiation showed the other 70% is this dark energy. So we get a sort of full universe that explains what we see, but 96% of it is dark.

And to be clear, when we talk about it, we talk about its sort of gravitational action, but what we don’t talk about really, or can yet, is the microphysics, the details. Dark matter, we think it’s a particle, but we don’t know the nature of the particle. We don’t know if it’s stable, if it has other interactions.

For dark energy, we sort of generally wave our hands and say it’s the energy of the vacuum. But, people who do quantum mechanical calculations try to estimate how much that should be, and they get an answer that’s 120 orders of magnitude off from what we get. So what we have is a very good, I’m gonna say just-so-story, you know, a phenomenological model grounded on lots of strong physics concepts. But it’s still a model. It’s not the physics itself. It’s not a description of those items themselves. We, for now, treat each of those — dark matter, dark energy — in their most vanilla form because we haven’t yet found any sprinkles on them, but we’re looking.

STROGATZ: Vanilla form, I see what you mean. You were describing some of the parameters that go into the model. That is, without saying what dark energy is, we can estimate what its contribution is to the budget, the energy budget of the universe. There’s the amount of dark matter, the amount of luminous matter. And there’s a few other parameters that go into this standard model. But the advocates for it, which I think is the consensus, that it’s our best model — though it is a model, right — that it explains a lot of things.

RIESS: It absolutely does. So it explains many things. It explains why the universe is expanding. It explains why we have the particular chemical abundances of light elements. It explains the cosmic microwave background radiation that we see, the fluctuations in it that we see. The particular spectrum of fluctuations that we see. And then it predicts an expansion history of the universe, including a phase early on when it is decelerating and dominated by attractive gravity, which allows structures to form like clusters of galaxies and planets and all of that good stuff. And then a later phase when it would accelerate, when it’s dominated by this dark energy as the matter is diluted by the expansion of space.

So it explains a lot of what we see, and it should because it is developed as we look at the universe and we have added to it or changed it to match what we see. And so I would say up until the early 2000s, maybe even 2010, it fit everything really.

But because we have these deep questions, we’re not just looking for a model, we’re looking for the physics. People continue to do more precise experiments because the nature of science has always been that you have a model and it’s the best approximation for reality. But inevitably it has some shortcomings, which maybe you haven’t seen yet or understood.

In the case of Lambda-CDM as we call it, the shortcomings are partly theoretical that we don’t understand these dark parts. But observationally, it was excellent. And then as the 2010s went on, people did try to do more and more precise experiments to test this model, because we want to tease out is dark energy really a constant or is it something that varies over time?

There’s some precedent in the universe for there was an episode shortly after the Big Bang we call inflation that also would’ve been dark energy, a different dark energy that would’ve appeared and disappeared over time. We’re wondering, is our dark energy today disappearing or getting stronger? We would like to know that. We would like to know more about the nature of dark matter, and so therefore, while we do theory, we also do better experiments to try to tell us more.

STROGATZ: I think it’s super interesting to appreciate the successes and the gaps together. Right, because the rest of the story that we want to tell here is one of discrepancies but they only become really impressive, at least to me, when you understand, like, what you expect in terms of how good the theory is. Up until now, the model has been good to within 1%, as you say, by tuning parameters that you can’t otherwise estimate. But still with that tuning, you can account for lots of different things to within 1%.

RIESS: People should understand this model is very successful. It explains a lot. It’s been the standard model for about 25 years. And it has survived through many dramatic advances in the precision of experiments. But as I think we’ll talk about as well, we’ve begun to see some hints of cracks in the model as well which we’re still wrestling with I would say.

STROGATZ: So let’s go there now, because this is the, and I find this compelling in your own biography, like it’s what a true scientist you are. If you don’t mind me heaping some praise on you here that the year that you mentioned, you said 2010s, people started noticing this is you and other people started noticing and you’re going to Sweden, you’re getting the Nobel prize, you’re still a kid, you’re just 41 years old or something, and you’re not satisfied. You’re not ready to just become an administrator. You want to keep doing science.

RIESS: Yeah, well, science is fun, right? So I was 41 and, you know, a lot of people said, “Oh, what are you gonna do now, you know?” And I looked at the other Nobel laureates and, unfortunately the average age has evolved up to about your seventies. So the average person is like, well, I’ve already done my academic career, I’m emeritus. So this is like a victory lap I’m gonna do and go give talks and things like that. But I was 41 and it was too, not just too soon, it was completely unappealing to me to do that and to stop what I was actually doing.

I mean, I was in the middle of using the Hubble Space Telescope, how cool is that, to look at for distant, exploding stars and pulsating stars and mapping the expansion history of the universe. I decided that the only way forward after that trip to Stockholm was to try to push out as much as I could all those speaking things and try to really focus on the science because, you know, once you stop it’s hard to go back.

STROGATZ: Well, okay, so this is where the plot thickens. You start making these improved measurements. And then, so, tell us what you found and where tension enters our drama here.

RIESS: So, we have a new model, Lambda-CDM, and it has these parts — dark matter, dark energy — that’s all great. And the question became, what is the nature of this dark energy? And so as a physicist, we say, “Okay, let’s find a number or a property of it that we can measure and it will tell us something about it.” And so in the way that dark energy produces gravity, what matters is what’s called its equation of state, the ratio of its pressure to its energy density. And this number is called W. And so if it’s a cosmological constant, then W will be minus one for all time.

And if it’s some kind of field in space — think of a field you know of, the electric field, the magnetic field — this would be a different field, but it would’ve energy and its energy would act like dark energy, then it might not be minus one, it might be some other number. And there’s been a lot of effort in space missions built to try to study this W number.

And I saw one of the better ways to do this would be to measure the Hubble Constant, the actual present expansion rate of the universe, and compare that to the predicted value it should have following both this model Lambda-CDM and this exquisite cosmic microwave background data, that was coming from new space satellites like WMAP and Planck, flown by NASA and ESA. And I began a new project, called SHOES to leverage the Hubble Space Telescope and try to improve the measurement from 10% precision, which had been before to try to reach 1% precision.

And at first it was going really well [laughs]. We were getting measurements that were smaller and smaller uncertainties, and they were matching the cosmic microwave background to the most part. And then, a funny thing happened. It was about a little more than 10 years ago, it was 2013, and Planck, the new cosmic microwave background experiment from the European Space Agency, very state-of-the-art, came out with a pretty large adjustment of the predicted value of the Hubble Constant.

Our measurements typically had been in the low 70s in these arcane units that astronomers use, kilometers per second per mega parsec, which is a very strange number, but it’s the inverse of time. And so if you inverted it, it actually tells you the approximate age of the universe.

And so the classic number from local measurements had always been in the low 70s — 70 to 75. And we were honing in on around 73 plus or minus two. And that all looked okay with the previous cosmic microwave background data. But when better cosmic microwave background data came out, it was suddenly, “Oh no, it’s gotta be more like 67, plus or minus 0.5.”

Now, this might sound like a small difference. Again, back to your statement earlier, this is a good model, right? We’re trying to thread a needle from the other side of the universe. You know, we’re starting at the moment of the Big Bang and asking how fast the universe will be expanding some 13 to 14 billion years later. And we’re like, we’re off by 8 or 9%. That’s pretty good predictive work, I would say in almost any other field.

But we’re rigorous about this. And our error bars are small and their error bars are small. And the only thing connecting them is the theory, the model, tells us how to explain the trajectory of the universe from the Big Bang to the present time.

And something has to give either the cosmic microwave background measurement is wrong or the local measurement is wrong, or the story that connects them is not quite right. We’ve all been doing deep dives over the last decade, redoing the measurements very carefully. I’ve been using the James Webb Space Telescope now instead of the Hubble Space Telescope, but getting the same answer. People have been doing a lot of work on the cosmic microwave background side, getting the same answer.

The community has poured over this and scrutinized over it. And so it’s gotten a name called the Hubble tension, which is, as it sounds, it’s a tension between what you think the Hubble constant should be based on the model and the early universe and what it actually appears to be. And it has surpassed what we call five sigma, which, in physics talk means the discrepancy is five times larger than the error bar on the experiment, which is the point at which we say, “Hey, something’s going on.” And so it’s been a lot of fun, I would say, to try to figure out what that something is.

STROGATZ: Fantastic summary. That’s perfect. You’ve talked a lot about the cosmic microwave background, which we’ve been assuming is standard knowledge. I want to clarify. We’re taking a baby picture of the universe. Like you talked earlier about the door jam…

RIESS: Right, right.

STROGATZ: So I know at age 66, I’m 6’ 1”. Now imagine when I was in the hospital, and I’m not even one day old. I’m in the baby crib. If you had looked at me as that little baby and then you said, “Yeah, but I can tell how tall Steven is gonna be when he’s 66 because I have this great model and I’m gonna predict his height and I can predict his height to within 8 or 9% when he’s 66 from this one-day-old baby.” That’s what the cosmologists are trying to compare. The people doing the baby are the Lambda-CDM people. And you’re doing…

RIESS: Right. I’m measuring the door jam right now and the model said, in this case, “Hey, Steve was supposed to be 6 foot 1,” and we’re coming out with, he is more like seven foot tall and you’re, which, you know, might be fun, but you’re like, that doesn’t, that, that is really would be truly unexpected for you to be seven feet tall.

And you might say, “Hey, maybe somebody took that baby picture of you wrong or they were using the wrong tape measure or something.” And that’s the stuff we sort of know how to do, that we know how to double-check experiments, do it with different telescopes, have different groups of people do it, different tools, different tracers. So that work has gone on for a decade and nobody has found the problem with the measurements. And so then you start to wonder, is it the growth chart, the story that we tell the model.

And on the one hand you say, that should be pretty easy to play with. You told me this dark stuff is so vanilla that you don’t know what dark energy and dark matter are. Can’t you just turn some knobs, some features on those that change it, give yourself an extra couple growth spurts during your teenage years, and suddenly you’re seven feet tall? And the problem is it’s a fairly over-constrained problem that we do have a lot of data at other junctures along the way. And so it’s a wrestle both from the theory to come up with ideas that can do it, and from the observations to find out if there’s anything amiss with the observations. And so, that is one that I’ve been wrestling with a lot.

STROGATZ: I’m sure there are some listeners who are thinking they’ve heard about dark energy, dark matter. It seems like these are big question marks. Maybe the scientists don’t really know what they’re doing. You know, they’re using words, but it’s just to cover up their ignorance. And also these, as you pointed out, in many ways, there’s dust, there’s, these measurements are difficult, these objects are very far away. How — you know if I’m gonna be skeptical — how do you know that there aren’t errors in this whole story, systematic errors?

RIESS: The best way we know is that, first of all, we build in lots of redundancy. This is one of the things I love about science is I could sit there in my laboratory with my data and do some calculations and say, “Behold there’s dark energy,” right?

But I have to publish those results and other people check them. Meanwhile, somebody on the other side of the planet can analyze that same pile of data and they may come to a different conclusion. And if everybody’s coming to a different conclusion, we haven’t discovered anything. And so the important element of independent verification done by many people in all kinds of places over the planet with different backgrounds and whatnot. Then we come in with other telescopes. So I’ve talked about, we use ground-based telescopes. We see the same with the Hubble Space Telescope. We see the same with the James Webb Space Telescope. And so the sheer redundancy and cross-checking in this, when people get an alternative answer, we also have to run that down too and say, “Why did they get a different answer?”

STROGATZ: It’s a really tough problem. I think given how good the model is and, also given that we can’t just go around adjusting things without wrecking something else that already works. It’s not easy.

RIESS: Correct, that is the big challenge. However, having said that, if this is a hint of a crack in Lambda-CDM, there have been other hints as well, so this is not the only experiment.

So more recently, there are results from the DESI experiment, which is measuring the three-dimensional positions of galaxies over the whole universe and, compared to the cosmic microwave background, suggests that dark energy doesn’t look like the cosmological constant. Looks like there’s some change going on there. There is the way we measure the clumpiness of matter in the nearby universe that, again, based on the way the universe looked shortly after the Big Bang in the model, we thought it would look clumpier than it does. Instead, it looks smoother. So there are these hints which on the one hand could be cracks and if, you know, a really clever person eventually puts them all together might change the story.

These could be the loose thread on the sweater that you pull on and might unravel the sweater, or you just pluck it off and you’re like, “Okay, that was not that big a deal.” I think we don’t know, but I think one of the fun things in science is the adventure and the mystery of it, that this is the process. Every, everybody in the past who called something a standard model eventually had to revise it.

STROGATZ: Good point.

RIESS: I could give you historical examples of where both were the truth in the situation. The problem is that science is not history. You actually have to do the work, you have to do the experiments, you have to have the critical thoughts. That’s what makes science so much fun.

STROGATZ: It is really interesting, and I like your comment too, although I’d be tempted to push back. I mean, yes, science isn’t history, but we do have really interesting examples from history of science where sometimes a little tweak to a model was enough, and sometimes you needed a conceptual overhaul like Newton’s model for gravity to Einstein’s general relativity.

RIESS: You know, Steve, that is my favorite example of all time, is, and I’ll just tell for the listeners who may not be familiar, back in the 1800s, what astronomers did was they tracked the positions of planets religiously, and they worked out their orbits. And in the early part of the 1800s, they noticed that the outermost planet they knew at the time, Uranus, was misbehaving.

It was traveling too fast, and it was traveling too slow, and there was a speculation by scientists that there was another planet, which became Neptune, that was further out and it was pulling on Uranus, that they couldn’t see it. So they calculated with pure math where it should be and then looked for it with a telescope and found it, okay?

So that was great. So Newton’s theory was fine. It was just some missing stuff. And then later in the century, Mercury was the one that was misbehaving, the innermost planet. It travels in an elliptical orbit, and that orbit is not supposed to precess or rotate itself at the rate that it was, and people struggled with that. They came up with the same idea: “Oh, look, it’s gotta be a missing planet. We’ve seen this movie before.” And they imagined a planet called Vulcan that was between Mercury and the Sun. They looked for it. They couldn’t find it. Fifty years later, Einstein changes gravity and shows that Mercury will precess in general relativity, his theory of gravity.

And as you say, what looks like kind of a small little observational crack or, you know, loose thread on a sweater unravels the thing. And so that’s why it’s hard to tell. Is this a Neptune or is this a, you know, general relativity? I really don’t know.

STROGATZ: Perfect examples. Yeah. I’m glad you brought up the Uranus, Neptune thing because you see both types of things. Big conceptual overhaul needed or maybe just something’s missing and it’s not a big overhaul. So we don’t really know.

Okay. So as you say, it’s an adventure, this great enterprise we’re in — science — and always progressing. There’s something else coming along the Nancy Grace Roman Space Telescope.

RIESS: Yeah, the cavalry is coming. In this case, it’s many great observatories, which I’m very excited are coming online. There’s the Vera Rubin telescope, which is the biggest full view telescope that is on the ground, very powerful, just started observing a few months ago. There is the Euclid, the European Space Agency mission, which recently launched, and then there is the Nancy Grace Roman being launched by NASA in September of this year, which is kind of a Hubble Space Telescope on steroids.

It can collect in a single image about 100 times the field of view of Hubble, and it operates very quickly too. So it’s going to have a kind of collecting power that’s about 1,000 times faster than Hubble. And so with this large amount of data, we hope to tease out more information about the recent expansion history of the universe, if dark energy is changing and any other sort of hints we can get.

Yeah, so we’ll learn things about exoplanets and galaxies, all kinds of things, but this really should be a quantum leap in terms of our data capability and, as long as I’ve been in this field, data has really been crucial to making the kinds of breakthroughs that we have.

STROGATZ: If we could just close on an emotional point, our show is called The Joy of Why. Is there something that brings you particular joy? Is it what data can tell you or, what’s the fun in this for you being a physicist and an astrophysicist?

RIESS: To me it’s the mystery, and then it’s the potential to answer mystery. You know, when I was a kid, if I wanted to know, how old is the universe and what’s its fate, I would’ve thought you’re gonna ask a philosopher or rabbi, I don’t know. But these aren’t the kinds of things that mortal people answer.

And the fact that with science and with these capabilities that we could address really profound, big questions and do it in a kind of methodical way and get real answers. Yes, we end up with new questions. It doesn’t all come as one answer, like the famous number 42 in Hitchhiker’s Guide. It ends up being a kind of a riddle, but I like that.

STROGATZ: The other thing that occurs to me is an old Woody Allen movie where there’s a little boy, and he’s depressed but he says, “The universe is expanding.” And the mother says, “What is it to you? Brooklyn’s not expanding.” My question is something like, are your parents alive? Did they get to witness all of this stuff that happened to you with the expanding universe?

RIESS: They got to witness some of it. My mom is still around. She saw me win the Nobel prize. But, um, I would say that they thought these were profound things. When I was a kid, my dad would take me outside and we’d look up at the stars. And he was not a physicist, but he knew a few things, and he would say, “Isn’t it amazing when you look at the stars that the light has been traveling to us for millions of years, and so what you’re seeing is not actually the way they are now, it’s the way they were millions of years ago?”

This just kind of blew my mind. And he would say, “In fact, the stars might not even be there anymore, and we won’t know about that for millions of years.” And just this idea there’s information that’s traveling to us, the story’s changed along the way, we’re still seeing this old story. How could that be? Could I catch up to that light?

These are profound things that raise a feeling of awe in me and I think a lot of people. And so, you know, back to that kid in the Woody Allen movie, I mean, there’s kind of two perspectives there, right? The people who have awe and are curious, and more power to them. I’m that kind of person, too. And then the people who are like, “Hey, it’s not expanding in Brooklyn. Get back to work.” And I get that, too. I mean, we still need to eat, and we still need to do a lot of other things. But to those who have that awe gene or that curious gene, right, you know, once you look up and you know what’s out there, and you know the questions, you’re hooked.

And, you know, the fact that somehow nature’s put out just enough of a popcorn trail for us to follow, who doesn’t wanna follow that popcorn trail and see where it leads?

STROGATZ: Oh. I love it. Thank you so much for talking to us. This has been really great. A real pleasure to have you on The Joy of Why.

RIESS: My pleasure. And thanks for, uh, asking me what bothered me back in that class 35 years ago.

[Music plays]

LEVIN: Hmm. One thing in particular about Adam is that he hasn’t stopped. It’s not as though he won his Nobel prize, and now he’s satisfied, and he leaves it to the next generation. And I have seen this with many Nobel prize winners, actually. They continue for the rest of their lives to really have that childlike curiosity. It’s unyielding. And you hear it. It’s infectious.

STROGATZ: It’s a very uplifting story. I think it’s an almost paradigm example of how science works, in the case of Adam where we have new data coming in that’s challenging some of what we used to think. I have to say in this discussion with Adam, I hadn’t realized how good this Lambda-CDM model really is.

LEVIN: It’s very resilient, and it’s very hard to change it. It’s not like you can get away with messing with it. If that’s what you mean by a strong model, exactly right.

STROGATZ: That’s what I mean. I mean, it’s rigid. He calls it, I think at one point, overdetermined.

LEVIN: And that’s also so impressive. So a lot of times people will say, “Well, you, you know nothing about the universe ’cause 95% of it is dark. Some of it’s in the dark matter, and some of it’s in the dark energy, and you don’t know what either of those things are.” But I think what people don’t appreciate, it’s only because of how precise the observations are.

It’s only because we’re in an era of absolute precision cosmology that we’re able to look at the negative space and determine that actually we’re only 5%, you know? We’re just a little bit. We’re just a little residue. It’s amazing.

STROGATZ: It’s another humbling thought, right? So as one speck of residue to another, let me sign off and say thank you, Janna, for sharing your thoughts.

LEVIN: We’ll see you next time.

STROGATZ: Bye bye.

LEVIN: Bye.

[Music plays]

LEVIN: If you’re enjoying The Joy of Why and you’re not already subscribed, hit the subscribe or follow button wherever you’re listening. You can also leave a review for the show. It helps people find this podcast. Find articles, newsletters, videos and more at quantamagazine.org.

STROGATZ: The Joy of Why is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests, or other editorial decisions in this podcast or in Quanta Magazine.

The Joy of Why is produced by PRX Productions. The production team is Caitlin Faulds, Jade Abdul-Malik, Genevieve Sponsler, and Merritt Jacob. The executive producer of PRX Productions is Jocelyn Gonzales. Edwin Ochoa is our project manager.

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Fields and Abacus Medals 2026

Thu, 23 Jul 2026 02:20:31 GMT

A Master of the Traveling Salesperson Problem Finds His Own Path

Thu, 23 Jul 2026 02:18:20 GMT

Previous: 2026 Fields and Abacus Medals Amid Life’s Chaos, a Meticulous Mathematician Finds Stability

For Shayan Oveis Gharan, progress on hard problems often comes via unexpected detours.

Chona Kasinger for Quanta Magazine

In theoretical computer science, the key to cracking tough problems is finding the right tools. Most researchers gravitate toward tools that match the problems they hope to solve, and some devote entire careers to mastering a few familiar techniques. But Shayan Oveis Gharan, a computer scientist at the University of Washington in Seattle, has never been content with the familiar. When he sticks with the same approach for too long, he gets restless.

“I’m not learning anything new,” he said. “I’m just sort of staying where I am.”

Physically as well as intellectually, Oveis Gharan seems to have trouble staying still. Talk to him about his research, and he’ll grow increasingly animated, shifting constantly from one unorthodox position to another — first sitting cross-legged in an armchair, then hugging his knees to his chest, then turning sideways and draping his legs over the armrest.

Perhaps it’s fitting, then, that Oveis Gharan is renowned for his work on the traveling salesperson problem, a notoriously difficult computational problem about roaming from place to place. He’s also made major contributions to a seemingly unrelated subject: understanding the best way to choose randomly from a large collection of mathematical objects. For these efforts and others, Oveis Gharan has received the International Mathematical Union’s Abacus Medal, awarded every four years to a theoretical computer scientist under 40. The award committee cited his use of novel tools from far-flung reaches of mathematics that appear unrelated to computer science. It’s as if a creative carpenter discovered that for some tasks a stethoscope works better than a saw.

“This is what a lot of the brilliant, great researchers do,” said Anna Karlin, a colleague and collaborator of Oveis Gharan’s at the University of Washington. “They connect things that are seemingly disconnected.”

Oveis Gharan is known for his energy and enthusiasm. “He’s incredibly fun to work with,” said his colleague Anna Karlin. “He’s a believer that you can make progress.”

Chona Kasinger for Quanta Magazine

Researchers who draw connections between disparate fields often cultivate their breadth of knowledge at the expense of deep engagement with any one subject. But not Oveis Gharan. For all his restless energy, he has the patience to sit with hard problems for years and attend to every technical detail of a long and complex proof.

“Shayan can kind of do it all,” said Jonathan Leake, a mathematician at the University of Waterloo who collaborates with Oveis Gharan. “I don’t know how he does it, honestly.”

Restless Optimism

Oveis Gharan’s chosen field of theoretical computer science centers on understanding algorithms, the mathematical procedures that computers use to accomplish specific tasks. Some researchers seek to map the limits of computation, by identifying problems that are too hard for even the cleverest algorithms. Others aim to push the boundaries of what algorithms can do. Oveis Gharan, an optimist at heart, falls squarely in the latter group.

“I’m on the positive side,” he said. “I like to say things are possible.”

Oveis Gharan is slender and sprightly, with unruly black hair and an irrepressible smile. His enthusiasm for his work is palpable, even infectious. “He’s incredibly fun to work with,” Karlin said. “He’s a believer that you can make progress.”

Recent events outside mathematics have tested Oveis Gharan’s characteristic optimism. In the past 12 months alone, his fellow Iranians have endured a violent crackdown on protests by their government; a raft of punitive economic sanctions imposed by the United States, the European Union, and the United Nations; and airstrikes by the U.S. and Israel whose targets included Sharif University of Technology in Tehran, Iran’s leading science and engineering school and Oveis Gharan’s alma mater.

“I see a lot of my old friends and family members suffering,” he said. “It gets hard to work.”

Oveis Gharan was born in the historic city of Isfahan in 1986 during another difficult time in his country’s history — the eight-year war with Iraq. His father was a civil engineer, and his mother, Fatemeh Khoei, was a middle-school biology teacher who earlier in life had reluctantly set aside her aspirations to study mathematics.

“At the time she was growing up, the culture was ‘girls should not get into math,’” Oveis Gharan said. “She didn’t have the opportunity.”

Instead, Khoei pushed her children to excel academically. Shayan was the youngest of five. He grew up watching his siblings, who range in age from six to 13 years older than he is, studying math, science, and medicine. As a boy, he was shy but had a competitive streak, and he was eager to prove that he could match his talented siblings’ accomplishments. “He was always comparing himself with older kids,” Khoei said in Farsi as her daughter Shadi translated.

Oveis Gharan is an optimist at heart. “I’m on the positive side,” he said. “I like to say things are possible.”

Chona Kasinger for Quanta Magazine

Shayan was especially close to his brother Shahab, who studied computer science and competed in the International Olympiad in Informatics, a contest of math and programming skill, in the late 1990s. When Shayan started middle school, Shahab gave him a book of math puzzles, and he was instantly hooked. “It brought a sparkle to his mind to dig much, much deeper,” Shahab recalled. Shayan went on to compete in the Olympiad himself and won a gold medal in 2004.

Though it was the mathematical side of computer science that initially drew him to the field, Oveis Gharan studied computer engineering as an undergraduate at Sharif University, thinking it would offer a more stable career. In his first year, he began dating a fellow engineering student, Farnaz Ronaghi, and the two bonded over hikes in the mountains and wide-ranging conversations about philosophy and religion. They married at the end of college and soon faced a big decision about their future.

Oveis Gharan, who’d found work in the computer graphics industry, was inclined to stay in Iran, but Ronaghi wanted to continue her education abroad, and she convinced him to apply to graduate school. Both were admitted to Stanford University, where Oveis Gharan’s sister Shadi, the first in the family to emigrate, had just received her doctorate in electrical engineering. Shadi encouraged her still-reluctant brother to accept the offer — theoretical research would open new opportunities, she said, and he could always go back to a software job if he didn’t like it.

As it happened, a taste of research was all that Oveis Gharan needed to rekindle his love of mathematics.

Tours and Detours

Graduate school was where Oveis Gharan first encountered the traveling salesperson problem, the famously thorny question that he would wrestle with on and off for the next decade. It asks: Given any map of cities connected by a road network, what is the shortest round-trip route that passes through every city? Researchers think there’s no way to design an algorithm that can quickly find the exact solution for all possible maps. Instead, they aim to design algorithms that always find relatively short round-trip tours — reasonable approximations of the ideal route.

Oveis Gharan in his office at the University of Washington.

Chona Kasinger for Quanta Magazine

In 1976, the mathematician Nicos Christofides devised a simple algorithm that yields a remarkably good approximation: It always finds a round-trip tour that’s at most 50% longer than the shortest possible route. (In the Soviet Union, Anatoliy Serdyukov came up with the same idea independently around the same time.) Ever since then, researchers have tried in vain to craft an algorithm that’s guaranteed to get closer to the exact solution.

In Oveis Gharan’s first year of graduate school, he helped his adviser Amin Saberi and other researchers design an algorithm for the “asymmetric” version of the traveling salesperson problem, in which maps can include one-way roads. Bolstered by that success, Oveis Gharan, Saberi, and the computer scientist Mohit Singh set out to prove that a similar method could beat Christofides’ record for the original symmetric problem.

As a second-year graduate student, Oveis Gharan quickly took charge of the effort. Saberi was used to giving students feedback on their ideas, but in his meetings with Oveis Gharan, he often found himself on the receiving end.

“In his own cheerful and polite way, [he’d] explain in the first 10 minutes of the meeting why the approach I suggested is unlikely to work,” Saberi said. “Then for the other 15 minutes, we would be discussing what he thought would be the right way.”

Researchers who study the traveling salesperson problem use mathematical representations of maps called graphs: networks in which nodes represent cities, and the links between them (called edges) represent roads. The first step in many algorithms, including Christofides’, is to find a specific kind of path through the graph called a spanning tree, which touches every node but contains no closed loops. Every graph has many possible spanning trees.

Mark Belan/Quanta Magazine

Once you have a spanning tree, you can transform it into a round-trip route by adding edges or doubling back at dead ends. A key question for traveling salesperson algorithms is which of the many spanning-tree options to start with. Christofides’ algorithm picks out the one that’s shortest when you add up the lengths of all its edges. This is usually a good starting point. But for some graphs, the shortest spanning tree has many dead-end branches, so the process of transforming it into a round-trip tour can actually make the route much longer.

Oveis Gharan and his colleagues hoped to avoid these extra-long routes by first harnessing randomness to select a promising spanning tree, and then transforming it into a round-trip tour. Randomness had been the crucial ingredient in their algorithm for the asymmetric traveling salesperson problem, and they quickly worked out how to adapt that algorithm to the symmetric problem. They thought that this approach would be able to beat Christofides’ algorithm — intuitively, if you use randomness to choose a spanning tree, you won’t get stymied by cases where the shortest spanning tree turns out to be a bad choice. The more randomness, the better.

But turning this intuition into a rigorous proof was not easy. They needed a way to analyze mathematical expressions that specify the chance of getting each possible spanning tree. Even a relatively small graph can have billions of spanning trees, and it’s hard to reason about problems with so many possibilities.

The key was to transform those mathematical expressions into formulas called polynomials, in which variables are multiplied and added together. Rewriting the problem in this unusual form, with one added term for each possible spanning tree, allowed Oveis Gharan to analyze it with a new set of mathematical tools. “Then you translate your finding to the setting of the original problem,” he said. “It’s like a detour.”

Armed with these new tools, Oveis Gharan and colleagues proved that their new algorithm outperformed Christofides’ classic algorithm for an important special case of the traveling salesperson problem. They suspected that there was more to the story — that the new algorithm would actually be superior in the most general case. It would take a few more detours to prove it.

Brick by Brick

Oveis Gharan’s early work on the traveling salesperson problem was the first instance of a pattern that would recur throughout his career. He doesn’t hesitate to plunge into the literature on unfamiliar subjects, from probability theory to statistical physics to abstract math like algebraic geometry, and pluck out new tools to use in his own work.

“He always liked to read a million papers,” Ronaghi said. “He has an infinite amount of capacity for learning new concepts.”

Yet to hear Oveis Gharan tell it, research is often a struggle. “It has a lot of ups and downs, mostly downs,” he said. “You always think, ‘Can I ever come up with something that doesn’t fail?’” He rarely experiences the eureka moments that abound in popular portrayals of mathematical research. Instead, working on a proof feels like building a house one brick at a time. There are many ways to assemble the pieces, and only when the whole thing is nearly complete can you be sure that it’s structurally sound.

“You put these bricks on top of each other,” he said. “You never know if you’re doing it the right way.”

Oveis Gharan often finds it helpful to busy himself with another activity while mulling over math problems. In graduate school, his preferred pastime was another sort of brick stacking — he played so many games of Tetris at his desk that a professor with a nearby office once asked him when he actually did his work. At one point the solution to a problem he’d been wrestling with appeared to him in a dream, but he didn’t have a notebook on hand when he woke up to jot down the idea before it faded. For some time after that, he would concentrate on mathematics as he was falling asleep, in hopes of spurring another nocturnal breakthrough, without success. “I would end up waking up with a headache,” he said.

Oveis Gharan says he does some of his best thinking when he’s surrounded by nature.

Chona Kasinger for Quanta Magazine

In graduate school, Oveis Gharan mostly worked alone, checking in with mentors periodically to exchange ideas. Since then, he’s preferred close collaborations that involve frequent marathon brainstorming sessions. In 2013, he struck up what would become a long and fruitful collaboration with Nima Anari, a fellow alumnus of the Iranian Informatics Olympiad team who was a graduate student at the University of California, Berkeley when Oveis Gharan arrived on campus for a postdoctoral fellowship.

Together, Oveis Gharan and Anari used polynomial methods to make further progress on the asymmetric traveling salesperson problem and settle a longstanding open question in graph theory. They then grew interested in a fundamental question about algorithms that harness randomness. These algorithms assume that you can easily pick a random item from a collection of mathematical objects — a task that statisticians call sampling. But how exactly do you get that random sample?

Chain Reaction

Sampling problems are common in the real world. Card games are a classic example: You want your deck to be in a random order before you deal. When you repeatedly shuffle a deck to randomize it, you’re essentially running a type of sampling algorithm called a Markov chain.

Every Markov chain algorithm starts with one item from a large collection of mathematical objects, such as all the possible ways to order a given deck, or all the possible spanning trees of a given graph. Then the algorithm repeatedly tweaks this object by introducing a bit of randomness — in the case of spanning trees, each tweak deletes a random edge and adds another to get a new spanning tree. Repeat this process until that spanning tree no longer bears any trace of the tree you started with. The output of the last step is your random sample.

To be confident that the sample is truly random, though, you need to know how many times to repeat the process — or, in other words, how long to run the Markov chain. This quantity is called the mixing time, and it depends on the mathematical structure of the sampled objects.

In 1989, the computer scientists Milena Mihail (who died in April 2026) and Umesh Vazirani made an important conjecture about sampling mathematical objects related to spanning trees called matroid bases — a task that has many applications in computer science and beyond. They proposed that a simple Markov chain could accomplish this sampling task, but they didn’t know how to establish that the Markov chain would have a short enough mixing time. For years, many researchers tried and failed to prove their conjecture. “Every technique people had tried before just didn’t get us there,” said Daniel Spielman, a computer scientist at Yale University who wrestled with the problem himself in the 1990s. “We needed some new math.”

Oveis Gharan and Anari teamed up with new collaborators and supplied that new math in 2018. Working with the mathematician Cynthia Vinzant, they translated the matroid basis sampling problem into the language of polynomials, just as Oveis Gharan had done when working on the traveling salesperson problem, and identified the key feature shared by those polynomials. The result was an important breakthrough in pure mathematics in its own right, and it provided them with a useful new tool. Joined by Oveis Gharan’s student Kuikui Liu, the team then used this key feature with other seemingly unrelated tools to finally prove the matroid basis sampling conjecture, 30 years after it was first proposed.

“It was a stunning result,” Vazirani said. “It really did seem like a piece of magic.”

Oveis Gharan (right) in 2005, with his siblings (from left) Shahab, Shahram, Sheida, and Shadi.

Courtesy of Shayan Oveis Gharan

The team’s landmark proof sparked a revolution in the study of sampling algorithms. Oveis Gharan, Anari, and Liu later developed a more general framework for identifying cases where Markov chains mix rapidly, among them mathematical models of materials that have long interested physicists. “After that, it felt like everyone and their adviser jumped into the pool,” Spielman said. “It’s really changed how the field works.”

Return Journey

In late 2018, as the sampling revolution was just beginning, Oveis Gharan was already itching for another challenge. He decided it was time to return to the traveling salesperson problem, where his intellectual journey had started a decade earlier. He’d picked up many mathematical tools on his travels in the intervening years. Now, he hoped to use those tools to prove that the algorithm he’d helped design as a graduate student would beat Christofides’ algorithm for the most general version of the problem.

“There’s a certain amount of fearlessness there, to say, ‘I’m going to take this on where everybody else has failed,’” said David Williamson, a veteran traveling salesperson researcher at Cornell University.

A decade after it first captured his interest, Oveis Gharan returned to the traveling salesperson problem in late 2018.

Chona Kasinger for Quanta Magazine

Oveis Gharan began working on the problem with Karlin and a new graduate student, Nathan Klein. They devised new techniques for handling tricky graphs with a lot of overlap between regions that the algorithm needed to analyze separately. Combining those techniques with Oveis Gharan’s polynomial methods, they resolved another important special case in the spring of 2019 and finally conquered the most general version of the problem in December of that year — breaking the record that Christofides’ algorithm had held for over 40 years. It took them another seven months to double-check every detail of the proof and write up the dense 90-page paper describing their result.

Saberi, who’d first introduced Oveis Gharan to the traveling salesperson problem, was stunned by his former student’s achievement. “For me, it was like the Wright brothers” cobbling together a primitive plane, he said, “then seeing something akin to a Boeing-747 10 years later.”

Since landing at the University of Washington in 2015, Oveis Gharan has settled into life in Seattle with Ronaghi, who works as the chief technology officer of a start-up she founded as a graduate student. He keeps notebooks stashed throughout their house, in case inspiration strikes at odd hours, but he’s grown better at setting work aside, especially when spending time with their 10-year-old son Faraz. “Shayan has an impressive, impressive ability just to play,” Ronaghi said. “His brain can have fun, like a little kid, and not take it too seriously.”

Even when Oveis Gharan isn’t working, though, the competitive spirit that animated his childhood sometimes comes through. When the Covid-19 pandemic hit, he discovered a passion for cooking, and he approaches that hobby with the same perfectionist attitude that he brings to the rest of his work, especially when he’s hosting.

“My kids believe that he’s the best cook in the world,” his sister Shadi said. “I’m like, ‘Dude, relax, you don’t have to be the best in everything.’”

Living Fully in the Math World Means Threading the Needle

Thu, 23 Jul 2026 01:55:53 GMT

Next: 2026 Fields and Abacus Medals Sometimes Being First Means Seeing the End Before Anyone Else

Hong Wang, pictured here working on a new article at the Institute for Advanced Scientific Studies (IHES) in France, is just the third woman to receive a Fields Medal in the award’s 90-year history.

Julien Pebrel/M.Y.O.P.

One might imagine that, for a mathematician, proving a monumental theorem is a blissful experience. It wasn’t so for Hong Wang. In February 2025, Wang and her collaborator Joshua Zahl presented a 127-page proof of a long-standing conjecture at the intersection of multiple branches of math. The duo had been checking their work for months and had sent it to select colleagues for review before finally mustering the courage to post it publicly. Wang worried less that the arguments were flawed than that they might be imperfectly expressed and therefore unclear.

No error was found, the proof’s logic was digested and streamlined, and everyone became convinced of its soundness. Wang and Zahl had proved the three-dimensional Kakeya conjecture.

The proof triggered a succession of prizes for Wang, who comes from Guilin, China: the Salem Prize, the Ostrowski Prize, and the International Congress of Chinese Mathematicians’ Gold Medal of Mathematics in 2025; the Antonio Ambrosetti Medal, Sadosky Prize, Clay Research Award, and New Horizons in Mathematics Prize in the first half of 2026; and finally a 2026 Fields Medal, widely regarded as math’s highest honor, given to exceptionally accomplished mathematicians under 40. Wang, 35, a professor of mathematics at New York University and the Institute for Advanced Scientific Studies (IHES) in France, is just the third female winner in the Fields’ 90-year history.

The attention has meant more speaking invitations and travel and interview requests that she struggles to refuse, which impinge on the time she can spend trying to understand how long, thin tubes pointing in different directions can overlap.

Early morning walks help Wang handle the stress and self-doubt that come with her mathematical research.

Julien Pebrel/M.Y.O.P.

This is the issue at the heart of the “Kakeya-type problems” that are Wang’s specialty, a family of mathematical questions and conjectures that lies at the center of the Venn diagram of harmonic analysis (the study of how signals break up into constituent frequencies), geometric measure theory (pertaining to the shapes and sizes of non-smooth things), and partial differential equations (which describe systems that change in multiple ways simultaneously), with further connections to number theory, combinatorics, and beyond. “All of these connections are why this area is considered so central and why Hong is celebrated so much,” said Pablo Shmerkin, a mathematician at the University of British Columbia.

When she isn’t traveling, Wang works with the devotion and discipline of a cloistered nun or elite athlete. “She’s crazy into math,” said Shukun Wu of Indiana University, a collaborator. “She’s definitely one of the most dedicated people I’ve seen.” She denies herself time-consuming indulgences like reading books or having a dog, though she does make time for friends, yoga, and early-morning walks to see the dogs at Washington Square Park, which all help relieve the stress and feelings of self-doubt that, for her, can accompany mathematical research.

The desire to feel confident in her knowledge and ability seems to have shaped Wang’s life. It is, for example, what draws her to mathematics: to her, the least doubtful thing. Even though she never took the time to celebrate her landmark proof — nor felt any consequent ego boost — at least Wang can now say with utter certainty that tubes pointing in every direction in 3D space can’t overlap very much.

Many Wonderful Things

Reserved at first but easily loosened up, Wang wears tortoiseshell panto glasses and rings on both index fingers, which would occasionally dart into the frame of video calls — silver on the left and gold on the right. From the West Coast, where she was spending a few months visiting collaborators and friends, she explained that her life started out a lot more carefree.

In Guilin in the 1990s, she would come home from school and read (Greek myths, Harry Potter, The Lord of the Rings), or watch television, or play table tennis or badminton. Her parents didn’t pressure her academically, despite both being schoolteachers. The three of them enjoyed evening walks around Guilin, often called China’s most beautiful city, situated amid steep emerald hills with a river running through it.

During Wang’s childhood in Guilin, China, math was just one pastime among many, but she clearly showed an early aptitude for it.

Julien Pebrel/M.Y.O.P.

Math began as one hobby among all the others. Whenever she got a new textbook, she’d complete all the exercises before the semester started. She’d get more math books from the bookstore and solve all their problems as well.

She remembers one brainteaser at the end of a chapter that asked: How should you plant seven trees to get the greatest number of rows of three trees? Like the Kakeya-type problems she would study later, the puzzle is about “incidence geometry,” or how objects overlap — in this case, lines (rows of trees) and points (trees). Wang quickly figured out that you should plant the trees in the shape of an equilateral triangle, with a tree at each corner, a tree at the midpoint of each side, and the seventh tree in the center. This forms six rows of trees: three along the sides and three through the middle. She got the answer faster than her father, a math teacher. She was 6.

Wang came to appreciate math for its permanence. History is forever being revised; learning English was frustrating because it seemed to have as many exceptions as rules. Only theorems seemed reliable. “No one can come and say, ‘Oh, actually, this is not true,’” she said.

Both parents wanted her to live as normal a life as possible, Wang recalled. She just wanted to learn as much as possible, so she skipped a couple of grades.

Toward the end of middle school, her grades started to matter for getting into a good high school in Guilin. Wang set her sights on studying math at Peking University in Beijing, one of the most prestigious universities in China. According to her, Peking reserved a single spot in its math program for a student from her province in 2007, with admission based on a standardized test. She did not receive the highest score.

But she did well enough to attend the university as an earth sciences major and hoped to transfer to math once there. Her geophysics professor encouraged her, affirming the importance of math to science, for instance in the way seismic waves are used to map Earth’s interior (math that, in fact, relates to the Kakeya problem, though she didn’t know it at the time). She worked hard and was eventually allowed to switch majors. She recalled an offhand remark by her father that analysis, the type of math concerned with evolving quantities, limits, measures, and approximations, is much easier than algebra, with its symbolic equations and exact solutions. Wang rebelled by focusing on algebra.

A detour into architecture while studying in France was short-lived. The tangible goals of math drew Wang back to analysis.

Julien Pebrel/M.Y.O.P.

She didn’t have top grades and doubted she would get into graduate school. Then representatives from the École Polytechnique near Paris, one of France’s prestigious, highly selective grandes écoles, held exams in Beijing for its postbaccalaureate program. In 2011 she moved to France.

All her courses were taught in French, which she didn’t speak. Fortunately, she already knew much of the math in her first-semester classes. She shared meals with her French-speaking classmates, quietly listening, politely asking for clarification, gradually understanding more. She took classes in analysis and found that it came more naturally to her than algebra.

She was faring well in her classes, but she didn’t think she was good enough to do mathematical research. For a semester, she switched to architecture and interned at a Paris firm. “I didn’t have much stress,” she said. “But I didn’t know the goal.” So she recommitted to math. “I decided not to worry about whether I would be good or not and just work on understanding better,” she said.

Strange Sets

In 2013, during a research internship at the Massachusetts Institute of Technology, Wang attended a seminar by an analyst named Larry Guth. Guth discussed his recent proof, with the mathematician Nets Katz of Rice University, of the Erdős distinct distances problem, which asks: For any finite set of points on a plane, how many distances are there between pairs of points? Guth explained the problem and his solution so clearly that Wang felt she could grasp part of the proof well, and this motivated her. She learned that it was closely related to many other problems of a similar character, all with incidence geometry at their heart. She was admitted to the doctoral program at MIT the next year and chose Guth as her adviser.

The “Kakeya-type problems” Wang focuses on are connected to harmonic analysis, geometric measure theory, and partial differential equations, as well as number theory, combinatorics, and more.

Julien Pebrel/M.Y.O.P.

Later her specialty would be the Kakeya-type problems. The most famous problem in this family and the one most of the others depend on is the Kakeya set conjecture. It’s the modern version of a question asked in 1917 by the Tohoku University mathematician Sōichi Kakeya, who wondered about the smallest area you can sweep out with a needle as you rotate it in every direction on a plane. Simply turning the needle around its midpoint sweeps out a disk. Kakeya realized that by shifting the needle as you turn it, as if making a three-point turn in a car, you can keep it within half the disk’s area, sweeping out a shape called a deltoid.

Mark Belan/Quanta Magazine

A couple of years later, the Russian and later Cambridge-based mathematician Abram Besicovitch showed that you can do dramatically better. You can point the needle in all directions while covering no area at all — at least with an abstracted version of the problem. In this case there’s no sweeping needle, but an infinite set of line segments that point in all directions on the plane — one for each possible way the needle could be pointing — called a Kakeya set. Without changing the direction of any line segment, you can move them around to pack them into a smaller and smaller area. Besicovitch found that these line segments can, in fact, be packed into zero area. How? An equilateral triangle is another shape, like a deltoid but with a larger area, that can contain a Kakeya set. Imagine cutting that triangle straight down the middle and shifting (without rotating) one of the halves so that it lies on top of the other as much as possible.

Now cut each half of the original triangle in half and shift the halves again to maximize the overlap. You’ve again squeezed the line segments into a smaller area.

Repeat this procedure ad infinitum, sliding the line segments back and forth using a geometric procedure called a Pál joint, and then rotate the triangle so you can repeat the procedure from each corner. Put the results together and you will have accounted for line segments pointing in every direction, squeezed into zero area.

Besicovitch showed that this works in higher dimensions too. Kakeya sets consisting of line segments pointing in all directions in 3D space can have zero volume.

But despite lacking area or volume, these strange, spiky sets still occupy space. The line segments in the Kakeya set were not somehow squeezed together into a single, one-dimensional line; they still point in all directions. The question is: How much space does a Kakeya set occupy? Another way to put that question, mathematically, is: How many dimensions does it exist in?

An operational way to determine an object’s dimensionality is to imagine covering it with tiny boxes of uniform size and counting how many boxes it takes. The number depends on how small the boxes are, but an object’s dimensionality relates to how that number changes as the size of the box changes. If you want to cover a 1D object such as a line segment, the number of boxes you’ll need is proportional to 1/r, where r is the width of the box. If you want to cover a 2D object, the number you’ll need is proportional to 1/r². For a 3D object, it’s 1/r³, and so on. That exponent is the object’s dimension.

However, that exponent is not always equivalent to the apparent number of dimensions of the space the object exists in. Take the case of fractals, or objects that have ever more detailed structure as you zoom in, such as the Koch curve or Koch snowflake. In these cases, the smaller the boxes are, the more structure there is for them to line up along, so they scale differently. The exponent of r in the scaling law is a fraction, which indicates how much new structure is revealed as you zoom in. Fractals such as the Koch curve or snowflake, with its infinitely detailed edge, are somewhere in between integer dimensions.

The crux of the Kakeya set conjecture is whether these sets occupy all dimensions of the space they point in every direction of: that is, whether a Kakeya set of line segments pointing in every direction on a plane is itself 2D, whether a Kakeya set pointing in every direction in a volume of space is itself 3D, and so on. The sets behave, in this specific way, like solid objects, even though, as Besicovitch showed, they can have no area or volume. It’s not clear who first posed this conjecture or when, but it existed in 1971, when the British mathematician Roy Davies proved that it is true in the 2D case. That it holds in three dimensions became known as the 3D Kakeya set conjecture. If it were to be disproved, this would mean the line segments of a Kakeya set, despite pointing in all directions, can be so cleverly bundled that they behave more like fractals than solid objects — that they have lower dimension than the 3D space they point in.

Because the Kakeya set is made up of line segments, mathematicians have reimagined the boxes used to measure dimensionality as being fused together into long, thin tubes. The question is how the number of tubes you need to cover the set scales with the thickness of the tubes. The Kakeya set conjecture says the scaling is like that of any other 3D object. If instead Kakeya sets can occupy a fraction of the full dimensionality of the space, then more detail — more line segments clustered in spaces inside — would reveal itself at smaller scales.

Wang speaks with mathematician Frank Merle over tea. Prior to the proof of the 3D Kakeya set conjecture, her reputation had been growing through a series of collaborations with blockbuster results.

Julien Pebrel/M.Y.O.P.

Interest in the 3D Kakeya conjecture rose in the 1970s when the Princeton mathematician Charles Fefferman established that it has a close connection to a powerful phenomenon called Fourier transformation, where any signal or function can be decomposed into sine waves of different frequencies and directions. A major open question in Fourier analysis (also called harmonic analysis) is what happens when the waves all have the same wavelength but are oriented in different directions. What happens to the combined signal where they interact? The Fourier restriction conjecture says that in such cases, the combined signal must be very spatially spread out and diffuse. Because the component frequencies are all traveling in slightly different directions, they can’t overlap and constructively interfere enough to form a highly concentrated wave or signal, a consideration relevant to signal processing and imaging.

“You can imagine that each wave lives on one of the long thin tubes,” Wang said. Will they overlap a lot, concentrating a signal, or not?

A Sticky Situation

A couple of years after arriving at MIT, Wang was chipping away at relatives of the Kakeya problem alongside Guth and others. Within a year, they’d solved a special case of the Falconer distance problem, a harder variant of the problem Guth solved with Katz. Wang also made progress on the Fourier restriction problem by framing it in terms of incidence geometry patterns. “It’s pretty rare that anyone could say anything new about this problem because it’s so difficult, so it was surprising for a Ph.D. student [to do so],” said Jonathan Hickman, a mathematician at the University of Edinburgh. “I sent her an email and said, ‘Wow.’”

“I decided not to worry about whether I would be good or not and just work on understanding better,” Wang said.

Julien Pebrel/M.Y.O.P.

Shmerkin, from the University of British Columbia, who had also worked on the Falconer distance problem, noticed Wang’s talent while visiting Guth at MIT. She struck him as creative, and as a sponge for new techniques. She seemed to understand incidence geometry deeply even though she had only recently started working on it.

The research area was already replete with new tools, and Wang soon imported more tools from geometric measure theory that she had learned during a collaboration with Shmerkin on the Falconer distance set problem. She was greatly inspired by Shmerkin’s “multiscale analysis” approach, a way of comparing what happens at different scales in order to arrive at contradictions. “She is always very kind and acknowledges that some of the ideas came from my work, but she was able to apply them in these fantastic ways that I couldn’t have envisioned,” Shmerkin said.

Wang’s reputation grew in 2019 when she, Guth, and Ruixiang Zhang of the University of California, Berkeley proved the 2D case of the local smoothing conjecture, one of the holy grails of harmonic analysis, which says that the solution to the wave equation can’t concentrate energy in a small region for an extended period. The same year, her doctorate complete, she moved to Princeton, New Jersey, for a postdoc at the Institute for Advanced Study. She worried that she couldn’t succeed without Guth, but gradually she began new collaborations and made headway on more Kakeya-type problems. Hiring committees took notice; she got a faculty job at the University of California, Los Angeles in 2021, and in 2023 she became an associate professor at NYU. A month after getting there, she produced another blockbuster result: Along with Kevin Ren, she proved the 2D Furstenberg set conjecture, which estimates the dimensionality of a set of points on the plane that contains a subset of lines pointing in every direction.

Despite these successes, Wang still felt like an underdog. “Each time it just felt lucky,” she said of her various proofs.

It was at the Institute for Advanced Study during the pandemic that Wang had decided to turn her attention to the 3D Kakeya set conjecture. The problem had resisted many challengers over the decades; proofs had even been announced and then shown to be wrong. “I never figured out the Kakeya conjecture, but there have been four or five times I thought I might have,” Guth said. Each time, he spotted his error before going public.

Wang read a 2014 blog post by the UCLA mathematician Terence Tao laying out a proof strategy that Tao and Katz had developed but never pursued. The approach seemed promising, so she contacted Joshua Zahl, then at the University of British Columbia, another mathematician who had studied aspects of the Kakeya problem in his thesis. They decided to investigate what Tao and Katz had described.

The strategy, which wound up requiring an enormous arsenal of techniques, was to show that any hypothetical counterexample to the conjecture — a potential way of squeezing line segments pointing in every direction in 3D space into fewer than three dimensions — must have such a rigid and efficient structure that it would contradict theorems governing the interplay between addition and multiplication. This general approach of positing a counterexample that disproves some conjecture, then twisting it into such knots that you conclude it can’t exist after all (leaving the conjecture as the only option), is a common proof strategy.

The renowned proof of the 3D Kakeya set conjecture, with Joshua Zahl, ran to 127 pages and required a range of cleverly applied mathematical tools. “You have doubt,” Wang said. “But also the argument feels natural.”

Julien Pebrel/M.Y.O.P.

In this case, Wang and Zahl focused on what are called “sticky” Kakeya sets, because line segments in these sets with similar orientations tend to stick together in space. These line segments bundle closely enough that thicker tubes could efficiently hold them, so the set as a whole could potentially exhibit fractal scaling, rather than behaving like a 3D object. They first proved that sticky sets aren’t counterexamples; they are 3D after all.

But there was more to do. “It wasn’t clear to people whether the sticky case truly was the main enemy,” said Zahl, who has the clean-cut look and comportment of a fighter pilot. So next they assumed a more general counterexample: a Kakeya set with some dimensionality less than three (say, 3 − x). By analyzing how many tubes intersect some midsize spherical region in the set, they could show that it must be either sticky (proved to be 3D) or not sticky, which, they could show, meant it must be higher-dimensional than had been assumed. “Then we win either way,” Wang said. They could repeat this argument for smaller and smaller values of x, until ultimately they could conclude that every Kakeya set must be 3D.

In early 2024, four years after they began their attempt, the proof’s complicated inductive logic seemed to be working out, though neither Wang nor Zahl let themselves draw that conclusion. “This is a difficult problem, and who am I to solve it?” Wang said. “You have doubt. But also the argument feels natural.” She could visualize the logic in her mind’s eye: tubes at one scale turning into planks on larger scales, then expanding into slabs that fill the entire volume. The way the shapes evolved into each other showed her that Kakeya sets are inevitably 3D. But it would take another year for Wang and Zahl to publicly announce the proof.

Finding Balance

As the proof was examined, studied, and confirmed, it shifted the landscape in Wang’s corner of math. “It’s a bit strange in the community because the holy grail has been achieved in some sense,” Shmerkin said. The Kakeya problem “is not solved in every dimension, but a big part of the holy grail has been achieved. So we are all asking ourselves, what do we do next? And of course, all of these techniques have opened the way to do many nice things.”

Even prior to her Fields Medal win, Wang was recognized on the street in China. The award means her profile — and the travel and distractions that come with it — will grow.

Julien Pebrel/M.Y.O.P.

The 3D versions of other, even harder problems remain open, such as the 3D restriction and local smoothing conjectures. Another obvious target for Wang and her community is the 4D Kakeya conjecture, if not a general proof in all dimensions, though no one knows what that would look like yet.

Wang said that at the moment she doesn’t want to get too invested in solving any particular problem. Her star has risen in China to the extent that she now gets recognized in public. The Fields Medal will make her a person of distinction there, and in the worldwide math community. She worries about falling behind, and still believes that she must put in more hours than her colleagues to be as good as they are. When challenged on this — everyone considers her extremely talented — she seemed genuinely surprised and pleased.

With more Kakeya-type problems in view, Wang is excited for what is to come. Another hard problem, reserved for the future, is how to feel confident as a mathematician while holding space that doesn’t center around math. Wang is encouraged that Guth, her adviser, finds time to read for pleasure. “I always wish that I could come back to that time when I just feel like I had infinite time to read,” she said. “I think that time was really nice.”

Sometimes Being First Means Seeing the End Before Anyone Else

Thu, 23 Jul 2026 01:47:40 GMT

Previous: 2026 Fields and Abacus Medals Living Fully in the Math World Means Threading the Needle

Next: 2026 Fields and Abacus Medals The Quietest Mathematician Has Always Been Worth Listening To

From an early age, Jacob Tsimerman showed great mathematical promise. “My mom told me, ‘You don’t have to be a mathematician just because you’re good at it,’” he said. “I didn’t really take her seriously.”

Caroline Gutman for Quanta Magazine

Jacob Tsimerman knows that many people see mathematics as a search for beauty. Over the course of his career, he has encountered beauty many times. But beauty is not what drives him. What he loves most is to solve hard problems, and to be the first to do so.

“In my experience, and I think many people’s experience, math is very much a goal-oriented endeavor,” he said. “The truth-and-beauty stuff is there when you’re zoomed out, but when you’re zoomed in, you just want to win.”

Tsimerman, who has slightly wild brown hair and a beard, talks fast and with visible enthusiasm. He is open and funny, but also precise — quick to pause and clarify a thought.

His fierce drive to win has fueled Tsimerman’s efforts at every stage of his career, resulting in teenage glory at the International Mathematical Olympiad, early matriculation at Princeton University, and proofs that reshaped areas of number theory and algebraic geometry, earning him a collection of top prizes.

It’s an impulse that Tsimerman has also been wary about. He knew it could consume him, especially when it came to the most entrancing honor of all — the Fields Medal, awarded every four years to the most accomplished mathematicians in the world under the age of 40 in the year the prize is given.

“I made it an explicit goal for myself not to focus on winning it,” he said. “I was like, ‘Jacob, you can’t become obsessed with it.’”

The mind trick worked, for a time. For nearly two decades, Tsimerman, 38, kept his drive focused on the math itself and became known as one of the most talented problem solvers of his generation.

But as he approached the last cycle in which he’d be eligible for the Fields Medal, he realized that his successes put him in contention. He relented and dedicated himself to the pursuit.

“Two years ago, I knew I was close, and I did let myself become obsessed,” he said.

The final push has paid off, as Tsimerman has been named one of four winners of the Fields Medal. The honor reflects a career built around borrowing techniques from one area of math and leveraging them in another to reveal surprising underlying structure.

“In my experience, and I think many people’s experience, math is very much a goal-oriented endeavor,” Tsimerman said.

Caroline Gutman for Quanta Magazine

“He’s a brilliant problem solver. He can learn anything,” said Peter Sarnak, a professor at Princeton and the Institute for Advanced Study and Tsimerman’s graduate school adviser.

Following each milestone in his career, Tsimerman has taken stock, asking himself whether math is really how he wants to spend his life, and whether he’s in fact good enough to succeed in it. And at every previous stage the answer has come back yes.

But this time may be different. As Tsimerman contemplates what’s next with a Fields Medal around his neck, he does so as a new form of problem solver rises — one that no human may be able to beat, and which has him questioning his future in math.

Competing To Learn

Tsimerman was born in 1988 in Kazan, in southwest Russia. When he was 3, his family moved to Israel, where his mother took a job as a high school math teacher.

Around that time, his grandfather, a physicist, began giving him little puzzles. There was one about how long it takes to fill a bathtub with two taps running, and another about two speeding trains on a collision course with a junction between them. His mother also began handing him textbooks. Even as she nurtured his mathematical ability, she was careful to let Tsimerman know he didn’t need to go down this path if he didn’t want to.

“My mom told me, ‘You don’t have to be a mathematician just because you’re good at it,’” he said. “I didn’t really take her seriously.”

When Tsimerman was 9, his family moved to Toronto, and he began entering math competitions. His father, a computer scientist, took him to the contests and brought him roast beef sandwiches midway through the long exams.

In seventh grade, he participated in the Canadian Mathematical Olympiad for the first time. There were five problems, and Tsimerman got most of them wrong. Afterward, he went over to the University of Toronto, near his school, and found a blackboard. For hours, the 12-year-old toiled over one of the geometry questions he had failed to solve during the competition. Eventually, he got it.

“I was super happy I’d solved an Olympiad geometry problem,” he said.

Mathematicians debate the utility of competition math as preparation for a research career. Many argue that it encourages the wrong mindset, because competition problems are guaranteed to have answers, while research requires coming to terms with the fact that many problems may not be solvable at all.

Tsimerman doesn’t see it that way. To him, competition math teaches the skill that has mattered most to him: how to stick with a problem.

“Competition math teaches you to sit with one problem for many hours, even though you’re almost certainly stuck,” he said. “If that’s not research math, I don’t know what is.”

Tsimerman at the Institute for Advanced Study in Princeton, New Jersey, where he spent the last academic year.

Caroline Gutman for Quanta Magazine

After his failed effort at the Olympiad, Tsimerman devoted himself to improving. He spent five hours every day practicing Olympiad problems after school rather than doing his regular homework.

It paid off. In 2003, when he was 15, Tsimerman won a gold medal at the International Mathematical Olympiad in Tokyo, correctly answering four of six problems. The following year, in Athens, he notched a perfect score.

After that, Tsimerman conducted what would be the first of several reassessments at critical points in his math career. He decided to retire from competition math, reasoning that after receiving a perfect score, he could only blemish his record with further participation. At that level at least, he had nothing left to win.

Learning To Fail

Tsimerman quit high school at 16 to enroll at the University of Toronto. Over the next two years, he devoured every available math course and earned an undergraduate degree at 18.

In 2006, he began graduate school at Princeton like other teen phenoms before him, including Terry Tao (Fields medalist in 2006) and Akshay Venkatesh (Fields medalist in 2018). Soon after arriving, he sought out Sarnak, a renowned mathematician with a reputation as a skilled mentor.

“I was told Peter and I would mesh well and that he’s at the center of the universe and would guide me the right way,” Tsimerman said. “It was good advice on both counts.”

Sarnak gave Tsimerman a long list of books and papers to read. Tsimerman spent the first eight months of graduate school working through it.

The more he read, the more overwhelmed he became. As he read page after page of theory, the field seemed to grow vaster, and he felt more anxious about his own place within it. Finally, he went back to Sarnak and pleaded for a concrete task, anything that would allow him to gain a foothold in the field and take stock of his chances of succeeding within it.

“I said, ‘I need a problem. I need a problem to work on because I can’t keep reading theory,’” he said.

Sarnak gave him a problem in an area of math called analytic number theory, which had been Tsimerman’s least favorite topic as an undergraduate. He had come to Princeton hoping to avoid the area completely. But here was Sarnak, offering him the problem he had asked for, and he knew there was no way he could say no.

“It took me three years to call Peter by his first name,” Tsimerman said. “I wasn’t about to say, ‘Give me a different problem.’”

He solved the problem, and he and Sarnak wrote up the proof together as Tsimerman’s first result. It changed his relationship with research. Tsimerman had arrived at Princeton knowing how to solve contest problems. Now, with Sarnak, he had gained confidence that he could succeed as a researcher too.

Tsimerman on the Princeton University campus.

Caroline Gutman for Quanta Magazine

“For the first two years I was extremely intimidated and kind of worried,” Tsimerman said. “Your first paper seems impossible to write. It seemed impossible to me until I’d done it, then I was like, ‘OK, I can do this.’”

After that, Sarnak gave Tsimerman a steady diet of hard problems. Tsimerman would go off, think about the problems for a few months, then come back and report that he’d gotten nowhere. Sarnak would say, “Great,” and then hand him another impossible task.

In Sarnak’s mind, the goal was not for Tsimerman to solve the problems. It was for him to understand what exactly makes hard problems hard, the way he might appreciate the specific technical difficulties and treacherous places that make it hard to scale a mountain — a kind of prerequisite knowledge for eventually making it to the top.

“The way you solve a problem is, you have to understand where the difficulties are, and you have to fail and develop an intuition of where the answers are,” Sarnak said. “It can be learned, but it’s much better learned when you try something, fail, form an intuition, and try again.”

Hidden Structure

Fail enough, learn where trouble lies, and maybe eventually you’ll succeed. That was Sarnak’s idea, and it was what eventually happened when Sarnak told Tsimerman to look at another difficult problem called the André-Oort conjecture.

The André-Oort conjecture, posed in limited form by Yves André in 1989 and in more general terms by Frans Oort in 1995, grows from a central idea in modern mathematics — that arithmetic and geometry are deeply connected.

To take a simple example, picture the graph of the solutions to an equation. The graph might pass through a few points whose coordinates are whole numbers. That could happen by accident. But if it passes through many points with whole-number coordinates, mathematicians take this as a sign of hidden structure in the equation that explains why it repeatedly intersects with these special points.

André-Oort is a much more sophisticated version of that idea. Instead of the two-dimensional graph of an equation, it concerns higher-dimensional geometric spaces whose points can represent entire mathematical objects.

Some of those points correspond to arithmetic objects with unusually rich numerical properties. André-Oort makes an assertion about cases when many of these special arithmetic points appear together inside the same geometric region.

“If you have an arithmetic phenomenon that you don’t expect to happen, then there should be a geometric reason for it,” Tsimerman said.

When Sarnak first introduced Tsimerman to André-Oort, the conjecture was far out of reach. But eventually Tsimerman found one hard piece of the problem he could attack.

To prove André-Oort, mathematicians needed a way to show that special points did not appear in isolation. As with ants, where there’s one, there are often many.

Tsimerman likes to move between various areas of math. “You want to learn expertise in one area and bring it to another area where it’s useful but not yet used,” he said. “That’s the golden goose.”

Caroline Gutman for Quanta Magazine

One way to get from one special point to others is via something called a Galois orbit. That is the complete collection of points produced when you start at one point and apply the symmetries of the number system in which the point is defined. Find a special point and apply the symmetries, and they’ll take you to another special point. Apply the symmetries again, get a third special point, and so on, until you’ve collected every point that can be reached in this way.

For his dissertation, Tsimerman set out to prove that in the setting of André-Oort, those orbits had to contain at least a certain number of points. That would allow mathematicians to begin turning isolated arithmetic coincidences into evidence of a larger geometric pattern.

Proof He Belongs

By 2010, when Tsimerman was approaching the end of his graduate studies, other mathematicians had made partial progress toward solving the conjecture. A group based in France had proved the conjecture if the generalized Riemann hypothesis is true, and that famously remains one of math’s great unsolved problems. Separately, a mathematician at the University of Oxford named Jonathan Pila had found a different strategy. Pila’s approach was powerful enough to prove the simplest case of the conjecture but no more.

“We quickly saw that Pila’s method has a chance to generalize, but there were millions of hurdles along the way,” Sarnak said.

Pila had also been a student of Sarnak’s, and in 2010 Sarnak invited him to Princeton to share his work. During that visit, Sarnak made sure to introduce him to Tsimerman.

In the last few years, Tsimerman committed himself to projects with the kind of depth and impact he thought would matter most to those judging his work.

Caroline Gutman for Quanta Magazine

“Peter asked me to explain the paper to him and said he has this very good student, would I mind if he sat in? That student was Jacob,” Pila said.

The timing was lucky. Pila’s method needed a way to produce many special points, and Tsimerman’s work on Galois orbits offered exactly that kind of possibility. In his dissertation, Tsimerman combined Pila’s methods with his work on Galois orbits to prove an important and difficult special case of the André-Oort conjecture.

A proof of the full conjecture was still far off — it would take more than a decade, and additional collaborators, to get there — but even the partial result established Tsimerman as a top-flight researcher, not just a competition phenom.

At that point, Tsimerman was confident he could do research and knew he could get a good job. And just as he had when he was younger, when he recorded a perfect score at the Math Olympiad, he checked in with himself, this time to assess whether the career opening up before him was one he really wanted.

“The only doubt I had about becoming a mathematician was at the end of graduate school,” he said. “I asked myself, ‘Do I really want this?’”

A Personal Edge

While in graduate school, Tsimerman did a two-month internship at Jane Street, the elite quantitative trading firm, and worked part time for another investment firm. Quantitative finance had some of the things he liked — it offered hard problems, smart colleagues, and a clear-cut sense of progress, in the form of waxing or waning account balances. But after a few months it was clear to him that he preferred the open-endedness of math research.

“I just like doing longer research projects. They were freer,” he said.

Tsimerman in his office at the IAS.

Caroline Gutman for Quanta Magazine

After Tsimerman’s flirtation with finance, he confronted his lingering doubts about his fitness as a researcher. At Princeton, he had proved he could solve research problems, but many of the problems that had shaped him had come from Sarnak. Tsimerman wanted to prove to himself that he could set his own research agenda.

He began by looking for places where the tools he knew gave him a competitive advantage. Mathematicians often talk about the value of bringing ideas from one area into another. Tsimerman talks that way too, but with a more competitive edge. To him, moving between areas of math is a way of finding problems where he has resources that established researchers in the area might not.

“You want to learn expertise in one area and bring it to another area where it’s useful but not yet used,” he said. “That’s the golden goose.”

One possibility was to focus on Hodge theory, an area of mathematics that studies geometric spaces by translating them into analytic objects — objects built from functions, integrals, and other more flexible tools than polynomial equations.

In the 1970s, a mathematician named Philip Griffiths had predicted that in some situations, even after these objects pass from the rigid geometric world into this more flexible analytic world, some underlying geometric structure should remain.

The problem, known as Griffiths’ conjecture, had the same flavor as André-Oort, where a loose analytic object, when viewed the right way, should turn out to have hidden algebraic structure. The work also brought him closer to Benjamin Bakker, a friend from graduate school.

“In grad school I had the feeling we were on pretty different paths math-wise,” said Bakker, now a professor at the University of Illinois, Chicago. “He was more on the number-theory side, and I was more on the geometry side of things. But of course you can draw a line from any one point in math to any other point, so that’s all an illusion.”

Working with Bakker and Yohan Brunebarbe, Tsimerman brought tools he had learned from André-Oort into Hodge theory. In 2018, they proved Griffiths’ conjecture and developed a framework called o-minimal GAGA, which gave mathematicians a new way to show that some analytic spaces have hidden algebraic structure.

After years of demonstrating his ability as a problem solver, Tsimerman had now shown that he could build new mathematical machinery as well.

“We like in math to say people are problem solvers and theory builders,” Sarnak said. “Jacob is a problem solver and a theory builder; I say that in a very strong way.”

The Final Push

By the early 2020s, Tsimerman had established himself as one of the best mathematicians in the world. The doubts that had followed him to Princeton and for years after had fallen away, and he began racking up results at a rapid clip.

In 2021, Tsimerman, Pila, and Ananth Shankar posted a proof of the full André-Oort conjecture, completing the long process that had begun when Tsimerman first took up the problem as a graduate student. By then he had also delved deeper into Hodge theory, where the machinery he’d helped develop kept producing new results. In 2024, Tsimerman, Bakker, and two collaborators proved a major new theorem about certain spaces arising in Hodge theory.

The results brought prizes. Tsimerman won the 2022 New Horizons in Mathematics award and the 2023 Ostrowski Prize. By the time he entered his mid-30s and last cycle of eligibility for the Fields Medal, winning it no longer seemed a remote possibility. Realizing that, he abandoned his vow not to become obsessed with the honor and made it his explicit goal.

“I worked hard and sacrificed enjoyment to try and win it,” he said.

The sacrifice was less about working longer hours and more about changing what he chose to work on.

Until then, Tsimerman had preferred to work on fun projects that caught his interest — what he describes as “cool little things here and there.” But in the last few years, he decided to commit himself to projects with the kind of depth and impact he thought would matter most to mathematicians judging his body of work, including the committee that chooses the Fields medalists.

“I stopped doing fun side projects and buckled down on projects that were high-return,” he said.

Tsimerman has stopped taking students because of the uncertainty surrounding AI’s effects on math.

Caroline Gutman for Quanta Magazine

One of those projects was a paper with Arul Shankar, a mathematician at Toronto, on “secondary main terms for quartics.” Tsimerman had wanted to finish it for a long time; however, the project required working through some dense technical details that he’d been avoiding. But with the Fields Medal in view, he and Shankar spent several months pushing through the calculations, posting the result in August 2025.

From 2024 to 2025, Tsimerman posted 11 papers to the preprint site arxiv.org across a range of fields. Then, late one Friday in January 2026, he received an email from Hiraku Nakajima, the president of the International Mathematical Union, asking to schedule a time to speak with him.

Tsimerman woke his wife to tell her that he thought he had won the Fields Medal, then spent the weekend waiting nervously to find out. When the call finally came through the following Monday, Tsimerman, who was at the Institute for Advanced Study (IAS) in Princeton for the year, went outside to absorb the good news.

“I walked in the IAS woods for a while to work off some residual nervous energy and take it in,” he said. “It was nice.”

An AI Crossroads

As before, success finds Tsimerman at another crossroads. He has received the Fields Medal at a moment when the future of mathematics feels more uncertain than ever.

As recently as 2025, artificial intelligence was still struggling to solve high-school-level competition problems. But early in 2026, AI systems began proving increasingly sophisticated results. The advance has culminated, for now, in OpenAI’s disproof in May 2026 of the unit distance conjecture, a result widely viewed as good enough to be published in the top journals in mathematics.

The rapid improvement in AI math capabilities has occurred so suddenly that mathematicians do not know what to make of it. Some remain skeptical that AI is actually useful for serious research. Others, including Terry Tao, have begun to imagine it as a powerful assistant, able to extend what human mathematicians can do.

Tsimerman has become one of the highest-profile voices for a third, more disruptive take. As he looks at the high-slope trajectory AI is on, he thinks the future of the field is in jeopardy.

“I think AI will be better than mathematicians at doing math within two years,” he said.

That belief has already changed how he spends his time. Tsimerman has stopped taking graduate students, because he worries that starting a conventional research project now could leave a student preparing for a mathematical career that may not exist.

“I don’t know what to do with a grad student in math who’s not very AI motivated,” he said.

Tsimerman now spends less time on classical math research. Rather than organize math conferences, he is coordinating events that he hopes will prepare mathematicians for the changes ahead. He has also shifted his research focus toward AI safety. Tsimerman thinks mathematicians have a role to play in understanding how systems of AI agents behave, and in deriving proofs that ensure that these complex systems won’t act in unintended ways.

“The risks are super high, the stakes are super high, so we need a very high level of assurance,” he said.

Societal impacts aside, AI’s march also has very personal implications for Tsimerman. He has always loved mathematics as a problem-solving activity, where the point is to reach the answer first. If machines become better problem solvers than any human, he is not sure the work will hold enough meaning to keep him or other mathematicians engaged. In early May 2026, making his debut on the social media platform X, he made this point bluntly.

“There are many people whose primary enjoyment of math comes through problem solving in one of its incarnations,” he wrote. “If that disappears, that is not a trivial issue and many of them might not want to do it anymore.”

Correction: July 23, 2026
The original version of this article stated that Arul Shankar was a co-author on both the André-Oort and secondary terms for quartics papers. In fact, Tsimerman’s collaborator on the on the André-Oort paper was Ananth Shankar.

The Quietest Mathematician Has Always Been Worth Listening To

Thu, 23 Jul 2026 01:40:17 GMT

Previous: 2026 Fields and Abacus Medals Sometimes Being First Means Seeing the End Before Anyone Else

Next: 2026 Fields and Abacus Medals Amid Life’s Chaos, a Meticulous Mathematician Finds Stability

John Pardon is known to his colleagues and students as quiet but insightful. As one formerstudent put it, “You really have to go fishing for his knowledge.”

Phil Yam

Several eminent mathematicians tell different versions of the same story about John Pardon.

Fifteen years ago, János Kollár was seated next to Pardon at a Phi Beta Kappa dinner. Kollár held an endowed chair as a full professor at Princeton University, where he’d been teaching for over a decade after stints at the University of Utah and at Harvard University as a member of its Society of Fellows, arguably the country’s most prestigious postdoctoral fellowship. Which is to say, Kollár is not bad at math. Pardon was an undergraduate, a few months into his senior year.

Kollár had gotten stuck on a question in the field of topology. At the dinner, he mentioned it to Pardon in passing. Two weeks later, he got an email from Pardon — with the solution. “And it’s not just that he solved the question I needed, but he did a much more general case in a very nice way,” Kollár recalled. He found working with the 21-year-old a pleasure. It felt, he said, “like working with a postdoc who had very good ideas.”

When Pardon graduated the following May, it was at the top of the Princeton class. In his valedictory address, he asked his fellow graduates, rhetorically, “When is the last time you had a truly original idea?” He proceeded to answer his own question: “The single most basic form of expression that humans draw upon is imitation of others, and so I think having an original idea may qualify you as being partially insane.”

By young Pardon’s definition, present-day Pardon, who turned 37 in June, is more than a little crazy, in that he has had not one but many original ideas. For these, the International Mathematical Union has now awarded him the Fields Medal, the most prestigious prize in math. “He started off solving well-known spectacular problems,” said Tobias Ekholm of Uppsala University. “At a slightly older age, he’s doing this same spectacular work, but he has this ability: He solves a famous problem but does it in a way that creates a framework, a whole new package, that will be useful to other people.”

Pardon, now at Stony Brook University in New York, is not particularly prolific. “His publication list is not very long,” said Kai Cieliebak of the University of Augsburg. “But every paper he wrote is some kind of breakthrough paper. All of them appeared in very top high-level journals.” Furthermore, Cieliebak said, Pardon “has done work in really a whole number of, to my understanding, completely separate areas of math. Probably somewhere in his brain these things might be connected.” As his former student Mohan Swaminathan, now at the Tata Institute of Fundamental Research, put it, “If John has a problem, he goes really deep and learns whatever is necessary for it.”

Pardon is tall and quiet. He has a gentle, unassuming affect and a reputation for kindness. He’s likely to be the best mathematician in any room he walks into, but he wears this lightly. He’s helpful to colleagues, sporadically answering graduate students’ questions on the online bulletin board MathOverflow. He sometimes weighs in on other subjects as well, with an invariable polite decisiveness. When one user, exasperated by their inability to make restaurant-quality pancakes, asked for help, Pardon offered advice: “The difference between ‘fluffy and fall-apart crumbly’ and ‘thinner, chewy, and sort of dense,’” he wrote, “is precisely governed by baking powder/soda. … If you want thin and chewy, omit the baking powder.” Pardon is as likely to ask for help as he is to offer it — airline ticketing, Schengen visas, and Wi-Fi passwords are as frustrating and confusing to him as they are to anybody. He is a father of two sons. He plays the cello well and learned to speak Chinese fluently in college, eventually winning a Chinese-language debate tournament held in Singapore.

Pardon declined to speak on the record for this profile. Many people who know him remark on his reluctance to say just about anything, least of all about himself. “He will only say something when he feels it is definitely correct,” said Shaoyun Bai, a mathematician at the Massachusetts Institute of Technology who got his doctorate under Pardon.

Pardon, though not particularly prolific, has proved major theorems in many different areas of math.

Phil Yam

“He refrains from saying too much,” said Thomas Massoni of Stanford University, another former student. “He knows so much that you really have to go fishing for his knowledge.” Multiple students recounted meetings with him where they had to do almost all the talking — but he was always available, glad to meet with them, and a patient listener. As Barış Kartal, who worked with Pardon while doing a postdoctoral fellowship, said, “He is silent, but he says very useful things.”

“I think John knows who he is and probably doesn’t want to come across as a cartoon of ‘Here’s a boy genius who’s done such-and-such a thing,’” said David Gabai, a former chairman of the Princeton math department. This is a real, reasonable concern. Nonetheless, when mathematicians speak about him, it’s hard to avoid the conclusion that he is a once-in-a-generation mathematical talent.

Like a generational talent in sports — Ohtani, Jordan, Messi — Pardon appears to be playing a different game than his colleagues, all of whom are themselves exceptionally skilled. But his achievements aren’t as easy to appreciate as a star athlete’s. Without years of study, it’s tough to understand just how surprising Pardon’s proof of a conjecture about six-dimensional manifolds really is. An earlier Fields Medal had been awarded in part just for making the conjecture.

So, with every intention of avoiding caricature, here’s a glimpse of Pardon’s work in knot theory, topology, and symplectic geometry.

Knot a Problem

Pardon was already the star of Princeton’s math department when he sat next to Kollár at that dinner during his senior year. He’d grown up in North Carolina, and by the time he was in high school, he was taking math courses at Duke University, where his father was a math professor.

Once in college, he set out to solve an open problem in knot theory that he’d first encountered in high school. As he later told his Stony Brook colleague Simon Donaldson, now at Imperial College London, he had more or less given up on it by the end of his junior year. But a line of attack occurred to him while he was walking in an English park that summer. A few months later, he had his proof.

Knot theory is one of those areas of math that are just what they sound like, but also somehow far deeper and more complicated than they seem. It is the study of knots — literally, given a length of rope, how can you tie it? (Mathematicians often splice the ends of the rope together.) But this question generalizes to higher dimensions and differently structured spaces, and in the end, the structure of knots is a powerful tool for understanding the geometry and topology of the spaces in which they can be embedded.

In 1983, the prominent mathematician Mikhael Gromov made a conjecture about a property of knots called the distortion. Consider two points on a knot. You can measure the distance between them in two different ways. Either you can travel along the rope itself, as though you were a tiny ant, or you can take a straight-line shortcut across space, as a (small) crow flies. It’s easy to intuit that the length you travel along the rope will always be at least as long as the straight-line distance. For any given knot, there will be a pair of points for which the ratio between the distance along the rope and the straight-line distance is the biggest. That ratio is the knot’s distortion.

Mark Belan/Quanta Magazine

Knots have the advantage of being flexible: So long as you don’t tear the rope, you can move it around to minimize the distortion. Gromov asked a question about “torus knots,” which can be drawn on the surface of a doughnut without crossing themselves. You can think of the doughnut as a sort of mold that helps make the structure of the knots clear, as seen below:

Gromov wanted to know if, as you wrap the rope more and more times around the doughnut to make your knot, there might be an upper bound to the distortion. He asked if any torus knot might be rearranged so as to make the ratio smaller than a fixed upper bound: 100.

One day in 2010, Gabai remembers Pardon — still an undergraduate — walking into his office and saying, “Well, I’ve proven such-and-such a theorem.” He’d shown that the answer to Gromov’s question was no: There are knots that have an arbitrarily large distortion, no matter how cleverly you try to rearrange them.

Since the distortion is one measure of how tangled a knot is, he essentially proved that it’s possible to create knots of this particular type, once thought to be relatively tame, that are arbitrarily tangled. Pardon’s proof was later published in the Annals of Mathematics, the field’s top journal — a rare achievement for an undergraduate.

Cieliebak speaks of the paper in a wistful tone. “It’s a paper you can sit down and read,” he said. “It has this genius touch to it.”

Transverse Days

If the knot distortion paper was the valedictory to Pardon’s collegiate career, he was just getting started. He arrived at Stanford as one of several standouts in a strong class of graduate students, according to Yakov Eliashberg, one of the most prominent geometers of his generation. There, Pardon could often be seen on the steps in front of the math department building, lost in thought. “He’d sit there for the longest time,” said the Stanford mathematician Ralph Cohen. “You’d go by and say hello. Sometimes he’d recognize you and nod hello. Sometimes he’d be deep in thought and wouldn’t know you’re there.”

At first, Pardon worked on some problems in low-dimensional topology. Then, after asking Eliashberg to be his adviser, he began to work in symplectic geometry.

In the web of mathematical disciplines, symplectic geometry sits somewhere between topology and geometry. Historically, it originated in the study of “phase space” — an abstract, high-dimensional space in which each possible state of a physical system (for instance, the positions and momenta of atoms bouncing around in a gas) gets represented as a single point.

Position and momentum are related in a particular mathematical way: If you change one, you change the other. Symplectic geometry begins with this relationship, which has geometric consequences, and abstracts it to other, mathematically similar objects. These objects have more flexibility than traditional geometric objects, such as a rectangle or a sphere, but have more rigidity than topological objects, which can be stretched and compressed at will.

Pardon’s doctoral dissertation on the “virtual cycle problem” made him instantly famous among symplectic geometers, said Leonid Polterovich of Tel Aviv University, who spoke of Pardon with amazement. Many of the top people in the field, he remembers, had been trying to solve the problem for years. “Some young guy comes and just does this,” Polterovich said. “He’s very precise, obviously has a fantastic skill of developing language. It’s really special. It’s not just tricks.”

To understand the virtual cycle problem, it helps to consider a concept called transversality. Two curves intersect in a transverse way if they cross like so:

If, on the other hand, they just barely “kiss” each other — intersecting at a tangent — then their intersection is not transverse.

Transverse and non-transverse intersections also arise with surfaces, which are, in the end, higher-dimensional analogues of curves.

In symplectic geometry, the basic object of study is called a symplectic manifold. One central way in which mathematicians in the field try to understand a symplectic manifold is by studying mappings that send points on other, well-studied surfaces to points on that manifold. The mappings that symplectic geometers are interested in have to satisfy certain mathematical conditions that make it possible to count them. “Rather rapidly it was understood that this counting doesn’t work very well,” Polterovich said, because the presence of non-transverse intersections in the relevant calculations can lead to incorrect counts.

In his dissertation, Pardon “succeeded in developing a novel language … which led to the resolution of this problem,” Polterovich said. By coming up with a new way to think about so-called virtual cycles — a technique for circumventing the issues caused by non-transverse intersections — he was able to count rigorously. As Polterovich put it, “It was clean. It was powerful.”

The result came at a time when symplectic geometry was in something of a slow-burn crisis, rife with disputes over whether key results had been established rigorously. “We really didn’t properly prove everything,” Eliashberg said. Pardon’s approach helped get around some of these foundational obstacles. “With some magic things he invented,” Polterovich said, “Pardon succeeded in gluing all this information together.” His wasn’t the first, or only, technique for dealing with transversality, but it was more widely applicable than any of the previous approaches. Now, Eliashberg said, “a kind of foundation for certain parts of symplectic field theory are built on his machinery.”

As Eliashberg’s Stanford colleague Mohammed Abouzaid said, Pardon’s thesis “made it possible for many people to stop worrying about things. … It was immediately impactful.”

As a mark of just how impactful it was, even before Pardon officially received his doctorate, Princeton began recruiting him to return as a full professor — unheard of for someone fresh out of graduate school. It required some explaining to the university’s dean, Kollár remembered.

Shortly after finishing his doctorate, Pardon teamed up with Sheel Ganatra and Vivek Shende to prove a series of other landmark results in symplectic geometry. “Working with John has been one of the great professional highlights of my career,” Ganatra said. “It has been wonderful for me.” He remembers visiting Pardon at Princeton and spending an afternoon eating much of a bag of “what must have been 100 peaches” while working through details of what would become their second paper together. On another occasion, they spent a week in Beijing, eating durian and doing math. “He loves fresh fruit,” Ganatra said. “He really loves fresh fruit.”

“He can be quiet at first, but his mind is always thinking,” Ganatra added. “We’ll have moments when we are talking, and all of the sudden we’re leaping forward.”

Counting Curves

In 2016, Pardon left Stanford for Princeton, where he spent six years as a professor before moving to the Simons Center for Geometry and Physics at Stony Brook University. There, he solved his biggest problem yet, proving a 20-year-old conjecture about counting curves. The unifying thread to Pardon’s work is not a particular mathematical area or theme; he simply solves problems that are, to him, interesting.

As in symplectic geometry, curve counting gives mathematicians deep insight into the spaces where those curves live. On a flat piece of paper, if you choose two points, you can only draw one line (a kind of curve) between them. This seems obvious enough, but it says something fundamental about the structure of 2D space.

Though you can draw infinitely many lines on a 2D plane or in 3D space, there’s a classic result in geometry that a shape called a quintic threefold contains exactly 2,875 lines: The geometry of the shape constrains the number of lines that are possible.

Pardon is drawn to particular problems, rather than broader fields or unifying themes.

Phil Yam

Quintic threefolds are an example of a type of six-dimensional shape called a Calabi-Yau manifold, which is not only mathematically intriguing but also useful in theoretical physics. Geometers are particularly interested in counting curves on these shapes as a way to understand them. Many versions of string theory predict that six extra dimensions are “curled up” into microscopic sizes, in the shape of Calabi-Yau manifolds. If this is true, the shapes form an inextricable, if invisible, part of our world. (In this formulation, gravity-like forces acting in the hidden dimensions are what we see as electricity, magnetism, and the strong and weak nuclear forces.)

Calabi-Yau manifolds are still not fully understood. In 2003, three mathematicians and a physicist formulated the MNOP conjecture, which states that two different ways of counting curves on Calabi-Yau manifolds are equivalent in a deep and unexpected way.

For a given Calabi-Yau manifold, mathematicians are interested in counting not just one type of curve (such as lines) but many of them, all at once. For example, a given curve has a property called a genus, a number that provides information about its structure. You might want to know how many curves you can draw on your Calabi-Yau manifold that are of a particular class and have a genus of zero — and how many curves from that class have genus 1, genus 2, genus 3, and so on.

You usually can’t count the number of curves with each genus directly, for a number of technical reasons. In order to get meaningful counts, mathematicians instead have to deploy an arsenal of tricks — resulting in an infinite sequence of numbers, which mathematicians call the “virtual” number of curves.

“The word ‘virtual’ is doing a lot of work,” notes Jim Bryan, a mathematician at the University of British Columbia who has been studying the MNOP conjecture for the past several decades. “These numbers are far from the literal count.” The numbers, which help count curves of ever-increasing genus, are called Gromov-Witten invariants. (They are named after the same Gromov whose conjecture about knots Pardon disproved, and the physicist Ed Witten.)

These invariants emerged as an object of study in the late 1980s and early 1990s. While working on his dissertation with Simon Donaldson in the late 1990s, Richard Thomas, now of Imperial College London, described another infinite sequence of numbers associated with Calabi-Yau manifolds. These numbers, called Donaldson-Thomas invariants, help count curves organized not by genus but by a different property.

These two ways of counting curves are mathematically very different. “These numbers look like they have nothing to do with each other,” Bryan said. If you take a particular Calabi-Yau manifold and a class of curves you’re interested in, the Gromov-Witten and Donaldson-Thomas invariants will give you two completely different sequences of numbers.

But the MNOP conjecture posits that they both correspond to properties of the same underlying function, called a partition function. “MNOP says these two sequences are the coefficients of the same function expanded in two different ways,” Bryan said. “The conjecture is pretty strange.”

If mathematicians could prove it was true, it would imply that both sets of invariants were indeed counting the same thing, an extremely useful equivalence. Depending on the context, mathematicians might want to use one set of invariants over the other; the MNOP conjecture, if true, would let them move between the two. “That is why people care about MNOP — it effectively doubles the number of tools one has to study the partition function,” Bryan said.

But for two decades, the conjecture remained open, despite many efforts to prove it. Then, in the summer of 2023, Pardon shared a proof online.

“It came out of nowhere,” said Bryan, who has spent a good chunk of the past few years studying the proof. He would have dismissed it entirely if not for Pardon’s reputation. To show that the two different ways of counting were equivalent, Pardon used tools from a completely different area of math and created a whole new mathematical structure, now called a Pardon algebra. “The method of the proof is so different than what we’ve seen before that it really rewires the way I think about the entire subject,” Bryan said. “This is the biggest result in enumerative algebraic geometry for the last 20 years.”

The Big Book

Pardon is now writing a book about the foundations of symplectic geometry. He’s made his work in progress available online, since many have asked him to do so.

The book’s preface captures the gap between how Pardon discusses his own work and how others think of what he does. “The interesting material is spread a bit thin,” Pardon writes. He hopes “to formulate statements and proofs which are as simple and down-to-earth as possible.” He allows that he may have failed in this aim.

The book reworks the foundations of symplectic geometry using ideas from a branch of math called higher category theory. “Many mathematicians view it as a little esoteric,” said Hiro Lee Tanaka, who studies higher category theory at Texas State University. “John’s speaking my language, which is not the language he spoke 10 years ago.”

“John is not afraid of big machinery, of abstract nonsense,” Abouzaid said. “He isn’t afraid of it; he just uses it.” But, Abouzaid added, Pardon’s technical facility is not what’s most impressive. “That’s not the point — the point is that there is geometric insight.” It’s like one musician praising another not only for their impeccable technique but for the feeling it allows them to bring to a performance.

“Most of the real work has been in finding the ‘right’ formalism, after which the proofs fall into place with little resistance,” Pardon continues in the preface. “This work is largely hidden from the view of the consumer, and so the main results may appear deceptively trivial.”

They aren’t.

Editor’s note: The Simons Center for Geometry and Physics at Stony Brook University is funded by the Simons Foundation, which also funds this editorially independent magazine. Simons Foundation funding decisions have no influence on our coverage.

Amid Life’s Chaos, a Meticulous Mathematician Finds Stability

Thu, 23 Jul 2026 01:34:39 GMT

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Yu Deng faced waves of uncertainty and doubt before attempting the work that would earn him a Fields Medal.

Kristen Normand for Quanta Magazine

Freedom and restraint seem like opposing forces, but to Yu Deng, they go hand in hand.

Take the poem he’s just pulled up on his computer screen: a dense forest of Chinese characters corralled into eight lines of equal length — a perfect, symmetric block of text. Written in the ninth century by the Tang Dynasty poet Li Shangyin, as China teetered on the brink of civil war, “The Brocade Zither” is famous for its ambiguity. “Many people have tried to explain it,” Deng said. “But I think this is something that’s not explainable.” A single word might allude to an ancient battle or a classic fairy tale; a simple phrase might have scores of diverging interpretations.

“My personal favorite of all time,” Deng said — an example of a highly structured form of Chinese poetry that literally translates to “regulated verse.” It must satisfy all sorts of rules: parallel constructions and contrasting images, lilting tonal patterns and strict rhyme schemes. “These patterns are part of the beauty,” Deng said. “But they’re also something that restricts your expression. The fact that you can still say so many things under this restriction is another level of beauty.”

Deng, a mathematician at the University of Chicago, explores the many things you can say under a mathematical form of regulated verse. He studies equations that describe how complicated systems of waves and particles interact. Like the Tang poet packing layers of meaning into a handful of couplets, “You are going to summarize, to compress, this whole big system in terms of this single equation,” he said. The solutions to these equations have a “very rich, natural structure,” full of hidden symmetries and “so many amazing coincidences, so many interpretations.”

Deng, who turned 37 in June, has now been awarded the Fields Medal, math’s highest honor, for pushing the study of these equations — and the physical systems they model — past what anyone thought possible. He and his colleagues have proved major theorems, some in papers more than 100 pages long, on how randomness moves through systems, and on how larger-scale behaviors emerge from those interactions over time.

“People thought this was, I don’t know, a decade in the future,” said Benoît Pausader, a mathematician at Brown University and one of Deng’s collaborators.

At its core, the work is about bringing the flexible nature of probability into the rigid, structured world of wave equations. Freedom and restraint. Hand in hand.

Go Pro

In a parallel universe, Deng became not a mathematician, but a professional Go player. It was the nearest of misses that set him on his current path.

Shortly after he was born in 1989, his family moved to Shenzhen, China, at a time when the city — a cluster of fishing villages just 10 years earlier — was growing rapidly. (Today it’s the country’s third-largest metropolis, home to more than 18 million people and one of the world’s biggest tech hubs.) When Deng was young, Shenzhen’s Shekou Industrial Zone, where he grew up, was “a really underdeveloped region” where “you’d see all this waste on the street. It had a terrible smell.” But within a few years, he said, the district had clean streets, subways, parks, and luxury apartments. Billboards and posters loudly declared the city’s slogan: TIME IS MONEY! EFFICIENCY IS LIFE!

Deng’s path to math took him through the world of competitive Go.

Kristen Normand for Quanta Magazine

Deng was a quiet, contemplative child. He preferred to spend long hours alone, reading whatever he could get his hands on. His mother, a gastroenterologist, said that by the time he was 5 or 6, he’d read some of her medical textbooks, frequently asking questions about anatomy and structure. “Given how young he was, all of my colleagues thought it was quite amusing,” she said in Mandarin.

Soon enough, he had “basically read all the books in our study,” she recalled. To get him outside more, she and her husband, a software engineer, took him on hikes or walks along the beach, with the promise that he could read or visit a bookstore as soon as they finished. If he misbehaved, “the most effective punishment was to forbid him from reading,” his mother said.

On some of those hikes, his father gave him math problems to solve. He still remembers one: You have a square grid divided into a certain number of cells. Prove that if you remove any one cell from the grid — it doesn’t matter which — you can always perfectly divide the rest of the grid into L-shaped pieces made from three cells each. The solution, which Deng figured out, required a concept known as induction, usually taught in high school. Deng was 7 years old.

His parents grew concerned that Deng’s constant reading would ruin his eyesight, so they bought him a Go set. He took to the game immediately. It wasn’t long before he was spending almost all his free time exploring the universes he could create with the black and white stones — solving puzzles, finding optimal strategies, getting lost in thought for hours on end.

“Playing Go was something that allows you to focus on a single thing for some time, usually two or three hours,” he said. “I enjoyed that.”

He got good quickly, playing at a local Go club and competing in district and city-wide tournaments. “He had this unwillingness to admit defeat,” his mother said. “When he played Go with his friends, if he lost, he would insist on playing again and again until he won.”

In 2001, when he was in middle school, he competed in the national pro qualification tournament, a grueling competition to enter the world of professional Go. By the final three games of the tournament, he needed only one more win to qualify. He lost all three. He tried again the following year, but his heart was no longer in it.

Ever since those early family hikes, Deng had also been nurturing a passion for math, for the same reasons he’d been drawn to Go: He could spend long periods alone with a single problem, looking for patterns and trying to find the unique path to the right answer. And he was good at it. “But it wasn’t serious” then, he said.

After his loss at that Go tournament, though, his assessment was almost clinical: “There was a choice,” he said. “Either Go or math. Since I lost, I decided to move my focus to math.”

He set a goal: to compete in the International Mathematical Olympiad (IMO), the most prestigious math competition for pre-college students in the world. His math teacher at the time was also one of China’s best Olympiad coaches, and they started to train together on evenings and weekends. In his last year of middle school (the equivalent of ninth grade), he’d learned the entire high school math curriculum, but he failed to pass the first selection round to compete in the IMO.

“Then I felt really bad,” Deng said. So he worked harder. The next year, he made it through three selection rounds and earned a spot on the national training team. But he wasn’t one of the six students ultimately selected to represent China.

His focus and ambition never flagged. “I really wanted to win,” he said. The following year he did more than make the team; he won a gold medal.

Deng in his office at the University of Chicago, where he’s been a professor since 2025.

Kristen Normand for Quanta Magazine

His performance earned him automatic admission to Peking University, one of China’s top colleges. At first, “I didn’t even think about choosing math as a career,” he said. “I kind of gradually realized that this is a good thing for me.”

The Olympiad experience “made me think, maybe this is something I really have talent for.” So, he figured, “why don’t I just do it?”

New Perspectives

After two years as a math major at Peking University, he transferred to the Massachusetts Institute of Technology. It was common for Chinese math students to attend graduate school abroad, but rare for undergraduates. “You are going to go somewhere outside of China eventually,” Deng said — so why wait?

That first year he attended a talk that would set the course of his career. Andrea Nahmod — a mathematician visiting from the University of Massachusetts, Amherst, who would later become one of Deng’s closest collaborators — presented research on the so-called random data problem. Deng was hooked.

The random data problem asks about the solutions to certain kinds of partial differential equations, or PDEs, that describe how complex wave patterns — from water waves in the ocean to light waves in fiber-optic cables — change over time.

In particular, Nahmod wanted to show that, no matter how your waves look at the beginning, the PDE can accurately model what will happen to them at any point in the future. There might be cases where the equation breaks down and fails to describe what a wave will do next, but such cases should be extremely rare. If you start with some random wave pattern, the PDE should have a solution that describes its behavior at later times.

The problem is that for most PDEs, the existence of this solution is exceedingly hard to prove.

“I found this idea very interesting,” Deng said. Because the question involves a random starting point, it brings probability theory — used to define that starting point and to prove statements about what happens next — into the deterministic world of PDEs. “You are seeing your equation from a completely different point of view.”

After the talk, Deng asked Gigliola Staffilani, a mathematician at MIT who was acting as his informal adviser, to give him a related problem to work on over the summer. She found him one, on the behavior of solutions to a two-dimensional version of the nonlinear Schrödinger equation, a famous PDE that describes how waves move and interact.

When Deng returned in the fall, he had a completed paper in hand. Staffilani was taken aback by how sophisticated it was. “I was like, ‘Oh my God, this kid, he’s really spectacular,’” she said. “I had not seen any work like that, not even from my graduate students, at least not polished in that way. It was done.”

The paper was published in the journal Analysis & Partial Differential Equations. “I was excited about that,” Deng said. “And I was thinking, one day I could publish in an even better, top journal.”

He’d heard about a student his age named John Pardon — another Fields Medal recipient this year — who published a paper in the Annals of Mathematics, the field’s top journal, as an undergraduate. Was he envious? “A little bit,” Deng laughed.

Uneasy Tidings

Deng often gets his best ideas when he’s alone in open spaces — on hikes, near the ocean. He finds a similar feeling in the Tang poetry he’s drawn to. “It’s a lonely kind of atmosphere,” he said of one line. Of another, “I like the view. By yourself, hearing these sounds, looking at the sky, seeing the sky reflected in the river … Everything is by yourself. You stand there and think.” The stars are distant, he said, even your thoughts are distant, as you contemplate historical events from long ago; you are completely, utterly alone, the world quiet around you. “It’s really a nice feeling.”

Deng has turned to nature during times of stress and uncertainty.

Kristen Normand for Quanta Magazine

He lingers over such forlorn, isolated scenes when he writes his own poetry, too.

His living room is pretty much empty. There’s a desk, a whiteboard, a small bookshelf, and an armchair. No couch, no TV, no art on the walls, no rug on the floor. “It’s good for me,” he said. “It’s a feeling of freedom. I can just walk around and think.” Even though he’s lived there for a year and a half, it looks like he just moved in. His biggest adjustment in his undergraduate years, he said, was living with roommates.

Even when he’s around the people he’s closest to, Deng is humble and reserved. He’s eager to discuss math — when he does, he talks a bit faster, a bit louder — but according to his colleagues, when the conversation moves to other topics, his responses are short and pointed. He doesn’t see the need to elaborate or steer the discussion in new directions. (When asked if he has any favorite poets: “Yes.”)

Deng doesn’t drive — never even got a license — because he fears that his mind will drift to math while he’s on the road. As an undergraduate, he once went line-by-line through a highly technical PDE paper, all 75 pages. It took him a week, eight hours per day. “I just checked every single detail,” he said.

While he no longer has quite that level of stamina, he’s still able to devote long hours to reading a paper thoroughly, or to working on a problem. “If I don’t make good progress, I will be really disappointed, and I will keep thinking about it,” he said.

He finished his degree at MIT in 2011, then went to graduate school at Princeton University, followed by a postdoc at the Courant Institute at New York University. “He was brilliant from the beginning,” said Alexandru Ionescu, Deng’s doctoral adviser. “Even as a graduate student, without experience … he was very good at getting at the essence of the thing, picking up what matters in a problem.”

Deng wanted to make progress on the random data problem, specifically when PDEs start with “rough” initial waves — random waves that oscillate wildly or have discontinuities. If he could show that even under these conditions, a PDE must have a solution, he’d have a deeper understanding of the equation and of a particular property of physical systems called the Gibbs measure.

But he soon realized that the tools available at the time weren’t up to the task. “We could get some results, but they were not satisfactory,” he said. He moved on to other questions, but they didn’t grip him in the same way. He began to feel aimless and, at times, “a bit depressed.”

“The work I did at that time wasn’t the best,” he said.

“I think it hurt him,” said Nahmod, who would later become a close confidante and friend. “He’s very sensitive.”

For comfort, Deng turned to manga. “I remember him at Courant. He was always holding a manga,” said Jalal Shatah, a professor there who formerly chaired the math department. Deng particularly liked stories about deep friendship and romance and found himself drawn to a genre known as yuri, which focuses on those kinds of relationships between women — stories that “feel nice and warm and beautiful,” as he put it. They helped him be kinder to himself, “more comfortable with life.”

In 2017, as the end of his NYU postdoc drew near, Deng hadn’t gotten tenure-track offers from his preferred institutions. For several months he considered going back to China or taking a job in finance with one of the companies that had been recruiting him. “I told them I still want to do math, but if I realize I cannot reach what I’m aiming for, then maybe I could consider this,” he said.

Deng still liked being alone — preferred it, in fact — but for the first time, he felt lonely.

He envisioned the days and years ahead. “In the end, as a mathematician, I’m just going to do math every day,” he said. “Go to school, go home, go to school, go home.” But he felt overwhelming uncertainty about that future. Would he be able to produce great results? Would he get recognized for them?

He recalled reading a manga, “one of these idealized stories where people get together, and they work, and they have these complicated lives. Eventually, they lead a good life. So I was reading this, and suddenly I got pretty emotional. I was thinking, ‘OK, then what about myself?’”

That winter, feeling “very stressed and anxious,” he took a train to nearby Long Beach, on the south shore of Long Island, where he booked a hotel room. There, he roamed the coastline and wrote poetry, pouring himself onto the page in eight lines of restricted verse, the same style that Li Shangyin had used. He wrote about how he wanted to escape. How doing so would be a betrayal of his dream to do math. How the tides seemed anxious, unsettled.

Deng’s focus on math is so absolute that he doesn’t drive, as he worries his mind will drift to math when he’s on the road.

Kristen Normand for Quanta Magazine

Once he’d gotten it all down, “then I could say, ‘OK, this is done.’ I could go back to my life,” he said. He returned to Manhattan. He remained uneasy, but after a week without work, he “automatically felt a need to work, to do math.”

He kept grinding, and tried to push the doubts out of his mind. Then, in 2018, he got a tenure-track offer from the University of Southern California. He accepted.

Rediscovered Path

Another mathematician who was feeling lost drew Deng out of this period of anxiety — and back to the random data problem. Haitian Yue had just started his postdoctoral research at USC and was having a hard time. “I didn’t find a really good project. I didn’t have a goal,” Yue said. While driving Deng back to his apartment after a group dinner — everyone knew Deng didn’t drive, even in Los Angeles — Yue confided his worries and mentioned that he’d done his doctoral work on the random data problem.

Deng thought it was a good time to return to it and suggested that they collaborate with Nahmod, whose talk had first drawn Deng to the subject.

Deng, Nahmod, and Yue turned to the two-dimensional Schrödinger equation, and set out to show that even when you start with a random initial wave that’s particularly rough, the equation still has a well-defined solution. If they could prove this, they’d then be able to show that the equation has a hidden statistical structure.

Say you randomly choose an initial wave from infinitely many possibilities, according to a well-known rule called the Gibbs measure. That rule, which is supposed to model a system in a state of equilibrium, says that some fraction of possible initial waves has one property, and some fraction has another, and so on. Any particular wave might change over time and end up exhibiting very different properties. But Deng, Nahmod, and Yue wanted to show that if you look at all the waves you end up with, they are still distributed according to the same rule that you started with. That, as mathematicians put it, the Gibbs measure is “invariant.”

Traditionally, mathematicians would approach the problem by splitting the solution to the PDE into two pieces and analyzing them separately. But that didn’t work in this case: One of the pieces was still too complicated. So Deng, Nahmod, and Yue split up that troublesome piece even further. They then developed tools called random tensors to analyze the pieces and explore how they influenced one another.

Yue recalled that when they met in person to work on the project, Deng would often go quiet, lost in thought for five, 10, 15 minutes at a time. “Andrea and I would keep discussing, while Yu Deng kept silent and tried to think by himself,” Yue said. “In his mind he does a lot of computations. Then suddenly he’d erase what we wrote down and say, ‘We should do it like this.’”

“It was just magical,” Nahmod said. “Collaborating with him is exhilarating. When he is interested in something, he focuses like a laser beam.”

As Pierre Germain, his postdoctoral adviser, put it, “When you work with him, it’s like you are running after a train.”

This skill ultimately allowed the trio to understand the solution to the two-dimensional Schrödinger equation, and to prove that the Gibbs measure is invariant. The proof was later published in the Annals, fulfilling the goal Deng had set for himself years before.

A Secret Project

Around the same time that Deng started to work with Nahmod and Yue, he met Zaher Hani — an encounter he credits with also helping to dispel his period of doubt and depression.

Hani, a mathematician at the University of Michigan, was also studying solutions to PDEs with random initial waves, but with a different goal in mind. Take the Schrödinger equation, which reveals how individual waves will interact and influence each other over time. Physicists have long accepted that from this “microscopic” description of a system, it’s possible to derive a higher-level description of the system’s average behavior, which is given by a different equation — the so-called wave kinetic equation.

Mathematicians like Hani hoped to offer a rigorous proof of that derivation.

Deng’s attention to detail is legendary. “He knew everything, 200 pages of computations, off the top of his head,” said a colleague.

Kristen Normand for Quanta Magazine

In 2019, Hani and some colleagues had just proved that the Schrödinger equation converges to the wave kinetic equation on short time scales. But on longer time scales, waves have the chance to interact in far more complicated ways that seemed impossible to deal with. Hani realized that insights from research on the random data problem might help. “At that time, I had already asked several other experts in the field. And I didn’t get any satisfactory answer,” he said. “Until I asked Yu Deng. He had precisely the right idea that I needed.”

The two teamed up and extended Hani’s previous result to a time scale just shy of what physicists cared about. Deng was ready to stop there. “I was worried that it might not be doable, that the tools weren’t enough,” he said.

But Hani persuaded him to keep going. They ended up abandoning previous approaches and developing their own technique “from scratch,” Germain said. “It’s completely crazy … It’s nice, or scary, or however you want to put it, that they ignored everything and just went vroom.”

First they represented the longer-term solution to the Schrödinger equation as a complicated sum of diagrams that resembled trees. To prove that this sum converged to the wave kinetic equation, they needed to estimate how much each tree contributed to the sum.

“These estimates were beyond anyone’s ability,” Shatah said.

As Ionescu put it, “it requires a very strong mind to do it.”

Deng has the right kind of mind. For one, he’s very good at combinatorics, a skill that his colleagues say sets him apart. And “he’s fearless,” Hani said. “I mean, sometimes there are computations that might take me half a day to psych myself up to do them, and then take me the other half of the day in order to do them. He can do them in an hour or two.”

The duo showed that some of the trees cancel each other out, contributing nothing to the overall sum. They then found a clever way to cut the remaining trees up into smaller pieces that were easier to analyze. It required what Hani described as almost surgical precision.

“My mind was exploding,” Deng said.

By working with these smaller pieces, they proved that, indeed, the Schrödinger equation gives rise to the wave kinetic equation over the right time scales — a result that they later extended to even longer (and more realistic) time scales.

That last proof, he and Hani realized, might hold the key to another problem — one that was so ambitious, and that so many other researchers were already trying to solve, that they felt they had to work on it in secret.

At the turn of the 20th century, the mathematician David Hilbert asked a question, his so-called “sixth problem,” about bridging microscopic and macroscopic descriptions of gases. It was essentially the same problem that Deng and Hani had just solved for waves, but for particles in specific settings.

These problems only seem the same “if you look at things from afar,” said Isabelle Gallagher, a mathematician at Paris Cité University who had spent years working on Hilbert’s sixth problem. “They’re physically very different.”

Deng and Hani set their sights on the problem anyway, which had been resolved on shorter time scales only. Joined by Xiao Ma of the University of Michigan, they worked day and night, analyzing new diagrams and figuring out how to cut them up in even more complicated ways. They came close to burnout.

Deng’s office, like his home, is austere.

Kristen Normand for Quanta Magazine

Deng recalled chugging energy drinks and barely going outside as he worked out the final details. He was visiting his parents in China at the time. They’d be eating or talking, his mother said, when “suddenly a math problem would flash into his mind. We’d know at that moment we should stop talking, as he had already entered his own mathematical world.”

By August 2024, Deng, Hani, and Ma had finished their 200-page paper solving Hilbert’s 124-year-old problem for long time scales. It took months for the rest of the mathematical community to even start to digest it. “We were so lost and confused,” Gallagher said. Deng flew out to Paris to walk her and her colleagues through the work. “He really wanted us to understand,” she said. “He was incredible. During the whole week, I don’t think he took out his notes one single time. He knew everything, 200 pages of computations, off the top of his head.”

Deng, Hani, and Ma later rewrote their paper to make it more readable. This revised version is now set to appear in the Annals, too.

Something New

Deng still holds himself to extremely high standards. When he found out he’d won the Fields Medal in January 2026, he felt more relieved than excited. He hadn’t really cared about winning the award, but as rumors started to spread that he was on the short list, “I was a bit stressed,” he said.

Now he no longer worries so much about his future. He’s doing work he cares about; he’s widely recognized for it. And he sees beauty in the questions he’s exploring. That beauty might not be obvious: There’s an ad hoc, brute-force aspect to it. Each time he analyzes a different set of equations, he has to redo all the details, even if the overall approach stays the same.

“But each time,” Deng said, “we have something new, which is also interesting.”

There’s also something satisfying about the way combinatorics ended up playing such a massive role in his work. It echoes his childhood — spent on Go, one of the world’s most combinatorially rich games, and mathematical Olympiads, which tend to be highly focused on combinatorics. It echoes what first drew him to poetry, too: the seemingly endless proliferation of meanings made possible by a simple combination of words. His research has in that way become familiar, a place where he can feel at home.

His life now looks much the same as it has for the past decade. But he’s comfortable. According to Nahmod, although Deng is still quiet, he’s no longer painfully shy. He reads and writes poetry. He plays Go from time to time. He’s thinking of getting a pet snake because “it looks good. It’s beautiful,” he said. He reads manga, but purely for enjoyment, not because he’s trying to be less hard on himself.

“I have less pressure,” he said. Which means that “you can just think about math, as you want.”

“We’ll see how much I can get to.”

The Organisms That Make Earth’s Harshest Places Home

Mon, 20 Jul 2026 03:03:48 GMT

The Danakil Depression in Ethiopia is one of the hottest, lowest, and driest places on the planet… and yet some life manages to survive there.

Wysiati/Alamy

Life has scarcely found a boundary on Earth that it can’t push. While much of life’s diversity exists in lush, bountiful habitats like tropical rainforests and coral reefs, even the most brutal corners of the planet are also occupied. The organisms that thrive in extreme environments — blistering temperatures, crushing pressures, corrosive acid — are what we call “extremophiles.”

Most of these imperiled pioneers are rugged microbes, such as bacteria or archaea. Some have evolved to live in poisonous brine that would fatally pickle nearly everything else. Some can happily grow in subzero temperatures, using special enzymes that chug along where others grind to a halt. Others can shrug off the menaces of heavy metals, ionizing radiation, or the vacuum of space and still thrive.

These organisms aren’t just curiosities. Understanding their resilient biology has many possible applications. Discovering biochemicals that function under extreme temperatures, pH levels, or pressure could be a boon for a broad array of industrial processes. The organisms may also help clean up toxic pollutants by growing, thriving, and digesting where nothing else can. Extremophiles and their enzymes are even responsible for the modern era of genetics and molecular biology.

Extremophiles can also provide a window into life’s deep origins. The planet where life first evolved was a harsh place compared to today, and it likely had high concentrations of toxins and heavy exposure to radiation. By divining the limits of what life can endure today, researchers can get a better idea of what made life possible in the first place, and what has allowed life to adapt to almost any environment.

And if life can be found at our planet’s extremes, then there’s a chance that life may exist elsewhere in the universe. Extremophiles offer a hypothetical peek at alien biology, helping us better imagine what kinds of life forms might evolve on other relatively inhospitable worlds, from our neighbor Mars to far beyond.

The bacterium Deinococcus radiodurans (inset image) was accidentally discovered in the 1950s when scientists bombarded cans of meat with enormous doses of ionizing radiation. As the microbe can rebuff radiation exposure up to 1,000 times greater than what would kill a human, it may help researchers understand how life might survive on worlds with much higher radiation exposure than Earth. Its semi-close relative D. peraridilitoris was found in an arid coastal desert in Chile (main image), where it also resists intense radiation exposure.

Wescottm; Michael J. Daly/Science Source

Today, many thermophilic (heat-loving) microbes are known to thrive in near-boiling hot springs around the world. One of the most important was also one of the earliest found by science. In the late 1960s, researchers working in Yellowstone National Park described the bacterium Thermus aquaticus (inset) from Mushroom Pool (main). The isolation of its heat-stable, DNA-synthesizing enzyme, called Taq DNA polymerase, was described in a paper published in 1976. This led to the invention of the polymerase chain reaction that could replicate DNA segments in vast quantities in the lab, fundamentally revolutionizing molecular biology.

American National Park Service; PLOS ONE 10(10), e0138674 (2015)

Some microbes make a life in one of Earth’s coldest and driest permafrosts, Antarctica’s McMurdo Dry Valleys (main). Among these psychrophilic (cold-loving) microbes is Rhodococcus sp. JG-3 (inset). The bacterium can grow at minus 5 degrees Celsius and respire at minus 15 degrees Celsius. Some Rhodococcus species produce enzymes that are very active at low temperatures, making these chemicals potentially useful for cleaning up pollutants in extremely cold environments. How Rhodococcus species manage life at super-cold temperatures is also of interest to scientists exploring the potential for extraterrestrial life on other planets.

Stocktrek Images; Jennifer Ronholm

Much of the Dead Sea (main) lives up to its name. But a limited selection of extreme halophiles (salt lovers) can survive the osmotic strain of the sea’s waters. One is Haloarcula marismortui, an archaeon (inset). Halophiles survive the intense salinity of the inside of their own cells partially by protecting their own proteins with a hydrated, acidic shield.

Pawel Uchorczak; Canadian Journal of Microbiology 54, 835-844 (2008)

Life can even persist in the inhospitable ocean depths (main) where the Earth tears itself apart. Methanopyrus kandleri (inset) is an archaeon first described around 35 years ago and found living on a deep-sea hydrothermal vent in the Gulf of California. The methane-producing microbe thrives in the intense, volcanically heated water pouring out into the inky black depths, and it lives in environments that may resemble that of the early Earth. Even while enduring the crushing pressure and salty surroundings, at least one strain of Methanopyrus can grow at 122 degrees Celsius, making it one of the most heat-tolerant organisms known.

MARUM; K.O. Stetter & R. Rachel/University of Regensburg

In the mid-1990s, researchers described two acidophilic (acid-loving) species belonging to a novel genus of archaea in a hot spring in northern Japan (main). One of the organisms, Picrophilus oshimae (inset), may be one of the most acid-tolerant life forms yet discovered. The archaea thrive at a pH of 0.7, which is in the realm of gastric or battery acid. Determining how P. oshimae’s proteins and DNA can survive such a low pH may help researchers better understand how life survived any highly acidic environments of the ancient Earth.

Lanhang Ye; Int J Syst Evol Microbiol 46, 814 (1996); International Journal of Systematic Bacteriology 46, 814-816 (1996)

Some halophiles have an appetite for history. The bacterium Halomonas titanicae was described in 2010 after its discovery amid the wreck of RMS Titanic (left), where it has spent over a century chewing up the ship’s steel, leaving behind long, rusty tendrils (right). The marine microbe’s taste for iron may give it a future role in cleaning up metal waste in sensitive environments.

NOAA; Lori Johnston, RMS Titanic Expedition 2003, NOAA-OE

Some life forms are “polyextremophiles” capable of living under multiple stressful conditions at once. An example is Exiguobacterium sp. SH31 (inset), a bacterium found in the salt wetlands of Salar de Huasco in Chile (main). It can survive both high salinity and a flood of toxic heavy metals such as cadmium, chromium, and arsenic.

David Gysel; Frontiers in Microbiology 9, 2228 (2018)

First reported in the Mariana Trench (main) in 2017, the bacterium Colwellia marinimaniae (inset) is, as far as we know, the piezophile (pressure lover) that can grow at the highest pressure. The microbe was found on a decaying crustacean, and laboratory tests showed that it grows best at 120 megapascals of pressure — or nearly 1,200 atmospheres. (Without special equipment, free divers routinely withstand about 10 atmospheres underwater.) Piezophile enzymes may be useful for industrial applications that take place under high pressures.

International Journal of Systematic and Evolutionary Microbiology 67, 824-831 (2017); Courtesy of Douglas Bartlett

Antarctica’s Deep Lake (main) is an extreme habitat two-for-one. It is not just very cold, but also very salty, which allows the water to stay liquid at minus 20 degrees Celsius. Halorubrum lacusprofundi (inset) is an archaeon that takes one of the coldest plunges possible.

Courtesy of the Australian Antarctic Division; Environmental Microbiology 19, 2210-2227 (2017)

Life is pushed to its very limits in the Danakil Depression, a sweltering, volcanic, toxic depression in Ethiopia. Some tiny polyextremophile forms of archaeal life persist in some of the hot, acidic, salty surface water. Researchers have found ultra-small bacteria, up to 20 times smaller than the average bacteria, living in one of the acidic, super-hot salt chimneys.

KrasnovaE/iStock

Martin Picard’s Mitochondrial Theory of Mind

Fri, 17 Jul 2026 02:31:05 GMT

Martin Picard, director of the Mitochondrial Psychobiology Lab at Columbia University Irving Medical Center, has placed the energetic organelles at the center of his model for health and consciousness.

Sasha Maslov for Quanta Magazine

It was 9 a.m. on a Thursday, and Martin Picard was watching his blood flow from an IV in his arm through a hole in the wall. He was sitting on a twin bed in a claustrophobic chamber less than a shoulder’s width from a stainless steel sink and porcelain toilet. Every hour over 24 hours, including while he slept, a nurse channeled blood from his arm to a research team next door; at each time point, if he was awake, he also provided a saliva sample and filled out a survey about his mood.

The room looked like a cell, or perhaps a very cramped hotel room, but in fact it was a metabolic research chamber, one of only 50 of its kind in the world. Its conspicuously small size prevented Picard from burning extra energy beyond the bare minimum needed to keep him alive. Napping during the day was prohibited, as was eating anything but the strictly scheduled meals tailored to his caloric needs. Bedtime was at 11 p.m. sharp. Before lights-out, Picard put on a device to monitor his vitals and brain activity while he slept.

Though there wasn’t much to do — mostly he sat in bed reading or working on his laptop — excitement was the primary emotion Picard felt that day in July 2021. That’s because he was the first volunteer in an experiment run by the Mitochondrial Psychobiology Lab, which he directs at Columbia University Irving Medical Center in New York. By studying how much energy is required to sustain baseline existence, his lab aims to explore what he considers an overlooked factor in health and disease, from the level of molecules all the way up to the mind: mitochondria.

Most middle school students learn that mitochondria are the powerhouses of the cell. These organelles make adenosine triphosphate (ATP), the energy currency of life, through a cascade of chemical reactions that breaks down glucose and fat from food. But mitochondria are much more than energy factories. Studies over the past decade have shown that they process all sorts of molecules, including neurotransmitters, hormones, and metabolites, which means they directly impact what we experience as mood, stress, sexual arousal, and the need to sleep. This makes them “the consilience point for many known processes demonstrated to underlie consciousness,” Picard said.

A mitochondrion (orange) contains intricately folded structures, called cristae, that maximize surface area and enhance ATP synthesis. This transmission electron micrograph was produced by passing an electron beam through an ultra-thin cell slice.

Science Photo Library

More broadly, in what he calls his “energetic view of life,” Picard posits that distinct energetic states exist for health and disease, and that mitochondria are the tiny transformers responsible for them. According to this view, the flow of electrons from food to oxygen in metabolism, as processed by mitochondria, is the most basic level of the experience of being alive.

“If the energy stops flowing, there’s no more you,” Picard said. The genome may encode the proteins that support life, but if the energy flow required for their respective regulation and production is disrupted or absent, he said, “there’s no more consciousness, there’s no more emotion, there’s no more life.”

Picard’s ideas connecting mitochondrial biology and energy to health and even consciousness are gaining momentum. But they are so new that they do not yet have a formal field of study. Picard aims to change that, and others are getting on board.

While the importance of genes and proteins should not be dismissed, mitochondria and the metabolic pathways they control “are more important than we give them credit for, and may actually have a more important instantaneous effect on the brain,” said Jon Brestoff, an immunologist at Washington University in St. Louis.

The idea that mitochondria influence what’s happening in the brain “really isn’t far-fetched at all,” he added. “Martin just brings a fresh perspective on it.”

Being Alive

Like every other animal on the planet, Picard inherited his mitochondria from his mother. She was a nurse who ran her own home care service in a French-speaking town outside Montreal. Sometimes after she picked him up from hockey practice, they would drop in on a patient or two on the way home. Some were recovering from surgery; others were quadriplegic or in palliative care. Picard began to notice that some people progressed from one sickness to the next, never fully getting better, while others bounced back from serious injuries or illnesses “almost miraculously,” he recalled. He found this deeply perplexing.

He followed this curiosity to McGill University, where he studied physiology and neuroimmunology. As he progressed through his studies, a question began to take shape in his mind: How do molecular, cellular, and bodily processes translate into feelings, behaviors, and the ability to thrive? His coursework was not providing the answers he was looking for, so he quietly began studies in holistic health on the side. He had mixed feelings about some of what he was taught, but he learned the value of a whole-person approach to wellness and began to recognize the individual nature of disease. Most of all, he said, “I learned to connect with another human being.”

Martin Picard speaks at the Mitochondria Psychobiology, Stress, and Health Symposium, which he organized on December 12, 2025, at Columbia University.

Piotr Redlinski

In his more formal studies, meanwhile, he kept being drawn to mitochondria. Picard learned that energy transformation, vital as it is for nearly every process in our bodies, is only part of the organelles’ repertoire. They also produce a bevy of chemical signals that influence the way we feel, behave, and function. Mitochondria supply the raw materials for creating the neurotransmitters glutamate and acetylcholine, which manage our brain, nerves, and muscles. The first step in synthesizing all steroid hormones, including cortisol, estrogen, testosterone, and progesterone, occurs in the organelles, making them key regulators of sleep, sex, and stress. They’re also highly active in signaling within and between cells: Mitochondria buffer and release calcium, which is involved in everything from muscle contraction to gene transcription, as well as reactive oxygen species, which activate immune cells and relay messages involved in cell growth. Mitochondria also play central roles in detecting and reacting to stress, and even in triggering cells to self-destruct if damage is deemed too great.

The ever-expanding list of core processes that mitochondria influence — immune activity, reproduction, metabolism, cancer growth and suppression, gut health, aging and longevity, and more — strongly suggests how mitochondrial dysfunction could relate to many different diseases and disorders. And this has set off a paradigm shift in how researchers see and understand the organelles. “This is probably one of the most exciting times to be studying mitochondria ever,” said A. Phillip West, who studies how the organelles shape immune response at the Jackson Laboratory, a nonprofit research institution in Bar Harbor, Maine. “We’ve got a lot to learn, but I think we’re really entering an amazing period.”

Intriguingly, mitochondria also create the small molecules that cells use to switch genes on and off as they grow, develop, and respond to their environment. This makes mitochondria “the portal between the inert genome and the dynamic environment,” Picard said. By the end of graduate school, he suspected that the organelles might hold answers to some of his deeper questions. He leaned into that hunch by taking on a postdoctoral research position with Douglas Wallace, a University of Pennsylvania scientist credited as one of the founders of the field of mitochondrial genetics.

Mark Belan/Quanta Magazine

Since then, Picard has led studies and developed tools to explore the connections among mitochondria, energy, mood, and health, building toward his ultimate hypothesis that the organelles are a missing dimension of medicine that could explain why a person might flounder or thrive, as he first witnessed on patient visits with his mother. If the human body has a limited energy budget, trade-offs will naturally arise when one biological process consumes more than its typical share. Competing demands — for example, from illness, injury, or chronic stress — can appear not only as poor health, but also as negative conscious experiences such as anxiety, brain fog, and exhaustion. On the other hand, good health, good feeling, and good energy are frequent partners. “People experience something good and then subjectively feel there’s more energy,” Picard said.

Today he prefers to think of mitochondria as “orchestrators of cell function.” He likens the body to a circuit, with mitochondria playing the part of resistors. In an electric circuit, he explained, resistance shapes a current into something usable rather than letting it run unchecked. Mitochondria likewise hold the body’s energy flow within a narrow band of resistance — not too little, not too much — that’s compatible with a healthy state.

Picard’s office decor features mitochondrial iconography.

Sasha Maslov for Quanta Magazine

Far from being just passive channels, then, the organelles are “pattern-generating units in the circuit,” Picard said, that convert raw current into meaningful signals. He hypothesizes that differences in these patterns may help to explain why some people are prone to certain mental states and conditions, or chronic disease.

“It’s a very exciting hypothesis that [Picard is] promoting,” West said. “He’s trying to widen the lens and help us all to understand overarching principles of energy flow.”

In doing so, he is also challenging long-held assumptions in medicine and biology that genes and proteins are the main drivers of health and disease. What if, Picard asks, the amount and nature of energy transformed by mitochondria is in fact at the center of the human experience?

Energetic Pursuit

On a frigid, sunny morning in December 2025, Picard stepped up to a podium wearing a sweater embroidered with a squiggly cartoon of a mitochondrion. Behind him, windows framed sweeping views of the Hudson River. In front of him, about 100 scientists, students, entrepreneurs, investors, and patients, plus one journalist, were seated at tables around the room.

“Me standing in front of you, giving you this speech — the ego is threatened,” Picard said, his blue eyes alight with enthusiasm. The body’s nervous response to that threat — the racing heart, sweaty armpits, and hair follicles on end — offered a lesson. “Everything costs energy,” he said, even subjective psychological experiences.

Picard had organized a daylong symposium to give fellow mitochondria enthusiasts a chance to discuss the latest findings in their rapidly growing field, from immune cell bioenergetics to time perception. “When I heard Martin was having a symposium, I just had to go,” said Robin Gaines Lanzi, a health behaviorist at the University of Alabama, Birmingham, who flew in to present.

Stress was a fitting topic for Picard’s remarks, since he’d been fascinated with its energetic costs since he was a postdoctoral researcher. In one early experiment, published in 2015, he intentionally stressed mice by placing them in a tube in which they could not move. Some of them had normal mitochondria, while others had diseased or otherwise defective ones. He found that the animals’ biology produced very different reactions to the discomfort of containment, depending on the specific defects in their mitochondria, resulting in different molecular signals. “If you change mitochondria, you change how the organism perceives or responds to mental stress,” Picard said.

In another study conducted around the same time, Picard found that perturbing mitochondria changed their host cell’s gene expression and growth, even when the organelles’ ability to transform energy was unchanged. Those results brought to life the idea, Picard said, that mitochondria could function as a dynamic interface between the body and the outside world.

Mark Belan/Quanta Magazine

Since then, new methods established by Picard and others have expanded the types of studies that mitochondrial researchers can conduct. Some of the most useful are “mitotyping” technologies that allow scientists to profile and classify different types of mitochondria by their function and activity (phenotype), underlying DNA sequence (genotype), and gene expression. In 2018, Picard and his colleagues released the mitochondrial health index — a molecular measure of mitochondria’s capacity to transform energy, calculated by extracting the organelles from a tissue sample and quantifying their contents. The index allows researchers to measure mitochondrial activity at a scale and with a degree of precision previously unseen, and to process thousands of samples, compared to dozens just a few years before.

After years of being sidelined, research on mitochondria is now exploding, said Carmen Sandi, a behavioral and systems neuroscientist at the Swiss Federal Institute of Technology Lausanne. Some studies have revealed, to researchers’ shock, that mitochondria differentiate. Subpopulations of mitochondria can vary from organ or organ, or even from cell to cell, and are responsible for different amounts of energy or kinds of biochemistry. Various research groups began publishing papers linking mitochondrial biology to everything from memory formation and depression to Alzheimer’s and heart disease. Taken together, the studies have increased the respectability of mitochondria as a wide-ranging, dynamic area of study. “People literally laughed at me seven years ago, and now people are asking for help,” Brestoff said of his mitochondria research. “They are much more open-minded.”

The neuroscientist Carmen Sandi led some of the first studies showing that the activity of mitochondria in brain cells can influence mental state.

Courtesy of Carmen Sandi

Some of the first studies explicitly showing that mitochondria influence mental state in particular — and that such states can be adjusted with therapeutic intervention — came from Sandi’s lab. In 2021, she showed that some of her rats with naturally anxious or depressed behavior suffered from malfunctioning mitochondria in their brain cells. When she and her colleagues experimentally boosted mitochondrial output in the rats, the neurons recovered, and the animals showed fewer signs of anxiety. In a subsequent study, she and her colleagues showed that a commercially available supplement produced the same positive results. “It restored everything,” Sandi said.

Picard, meanwhile, has contributed a string of discoveries linking mitochondria to brain function. Notably, in 2025 he co-authored a mitochondrial map of the human brain that revealed that the organelles vary not only across brain regions but also between cell types within the organ. The map is an invitation, the researchers wrote, for other scientists to begin exploring the “molecular energetic landscape” that underlies brain structure, process, and function — including consciousness. It was a call for others to join them in creating a new field of study.

Pattern Generation

As new findings accrued, Picard came to see brain function as shaped not only by molecules, neurons, and circuits, but also by how energy is transformed and patterned. In his view, our cognition, mood, and conscious experience reflect deeper energetic processes — down to the subcellular level. He even ventures that mitochondria could turn out to be a missing piece of the mind-body puzzle — the microscopic alchemists that coax thought out of matter, responsible for nothing less than “the materialization of consciousness into life.”

In 2025, Picard co-authored a map of mitochondria across the human brain, “a milestone towards understanding how brain mitochondria are linked to cognitive function and neurological health,” the authors wrote.

Sasha Maslov for Quanta Magazine

Not everyone is on board. José Antonio Enríquez, a molecular biologist at the Spanish National Center for Cardiovascular Research, cautioned that Picard’s ideas about mitochondria and consciousness are interesting but “by no means” demonstrated. “Martin is a good thinker, sometimes a little wild,” Enríquez said. “His claims really have to be evaluated thoughtfully and scientifically.”

Picard knows that his ideas can be a challenging for some of his biomedical colleagues to accept. “I’m a little heretical for wanting to bridge the bioenergetic processes inside mitochondria to the human experience,” he said. “But my sense is, if we don’t do that, we’re failing at the biggest opportunity around.”

The metabolic-chamber study, the results of which are now under review, takes a step in that direction by exploring how mitochondria affect subjective experience. In the afternoon at the 2025 conference, Evan Shaulson, a graduate student in Picard’s lab, presented some initial results.

Participants who had one of two types of rare mitochondrial disease burned 180 more calories per day and expended 15% more energy, even when they were sleeping. “They have to pay a 180-calorie tax every day of life,” Shaulson said, about the equivalent of a slice of pizza. Those subjects reported feeling more fatigued and stressed compared to healthy controls. Biomarkers from their blood showed elevated levels of metabolic molecules such as lactate, which indicate faulty mitochondrial performance and correlate with anxiety.

Evan Shaulson, a graduate student in Picard’s lab, is leading a new study to track connections between mitochondrial metabolism and lived experience.

Piotr Redlinski

In a second part of the study, the researchers tracked participants’ energy expenditure during nine days of “free living” in their normal lives. In lieu of an IV line, they drank special water labeled with isotopes, and Picard’s lab members measured how quickly those isotopes were eliminated in urine samples (a well-established proxy for metabolic rate).

Unexpectedly, in the real world the caloric gap between the two groups nearly closed. This was because healthy subjects expended 16% more energy than they had in the chamber, compared to just 5% for the subjects with mitochondrial disease. In other words, Shaulson said, the chamber’s restrictions represented “a more typical day” for people with a mitochondrial disease, who move less because they feel low in energy.

The findings are preliminary and based on a small number of subjects; only 20 people (excluding Picard) have provided data so far. Yet they suggest how mitochondrial processes can “ripple out and affect the organism,” Shaulson said. Studying how those changes originate at the level of molecules and cells and manifest as mood and behavior can potentially lead to a new understanding of and treatments for mitochondrial diseases, he said, while also revealing more about how mitochondria keep the body healthy and functioning.

Herman Pontzer, an evolutionary anthropologist at Duke University who specializes in human bioenergetics and was not involved in the research but is familiar with it, said that the chamber study shines a light on the “control systems in our bodies regulating the calories we burn each day — systems we have yet to fully understand.”

“Picard and his team have helped open the door on these systems and set the stage for future work in metabolism and health,” he added.

The next step, Picard said, will be a bigger study, with around 100 people, led by Shaulson. In addition to spending a few hours in a chamber, participants in the new study will be monitored for six months with wearable devices, an app, saliva samples, and reports of their lived experiences. The findings could “offer a lens and a bridge between behavior, biology, and the mind,” Shaulson said.

Picard will continue exploring these questions and more at a new nonprofit he is founding to translate laboratory discoveries into real-world applications. He envisions the institute, which he plans to launch in 2027 with philanthropic support, as integrating insights about mitochondria, metabolism, and energy with the human experience, establishing a new field of healing science “that will aim to support human flourishing,” he said.

Shaulson acknowledged that it is unusual for a tenured professor like Picard, who publishes in top research journals, to talk about energy flow and holistic healing — topics that tend to fall to yogis, traditional-medicine practitioners, and self-declared spiritual healers. But skepticism among fellow scientists is usually overcome, he said, once they see the data, which justifies the unconventional approach.

Picard agreed that some of the lab’s hypotheses at first strike some academic researchers as sounding a little “woo.” But science has always been driven by bold, challenging ideas that are then rigorously tested and refined. As Picard put it, “There’s a lot of things that used to be considered ‘woo’ until we understood them.”

Thermodynamic Computers Go With the (Energy) Flow

Wed, 15 Jul 2026 03:24:33 GMT

Ada Zejun Shen/Quanta Magazine

In the quest to make computers accurate and reliable, noise is the enemy. The thermal jiggling of atoms is a constant threat to the precision needed for detailed calculations. Whether we’re dealing with familiar classical devices like the laptops or supercomputers that we use today, or fancy quantum devices that promise us faster computation tomorrow, we don’t want some haphazard heat fluctuation to flip a binary digit from a 1 to a 0, sending a calculation off course. So computer engineers work hard to make computers immune to noise, by switching bits at energies far above the random ripples of the environment.

But what if noise could be made into the computer engineer’s friend? What if, instead of trying to make devices that work despite the hubbub of thermal fluctuations that ruffle everything in the universe, we could harness that noise to actually do the computing?

That’s the goal of a nascent field called thermodynamic computing. Since the Computing Community Consortium hosted its first conference on thermodynamic computing in 2019, a small community of researchers has been laboring to put it into practice. Recently, some of them have simulated thermodynamic computation in standard silicon-based logic circuits, showing that the basic concepts seem to work in principle.

The approach could produce computers that consume little power and dissipate little heat — a huge advantage, given the power-hungry operation of today’s devices and the increasing struggle to prevent ultra-dense miniaturized circuits from melting down.

Thermodynamic computing would make use of thermodynamic processes, which distribute and dissipate energy and inevitably increase randomness at the microscopic scale. “The field is about designing computers that exploit thermodynamics as a computational resource,” said Patrick Coles, a physicist at the startup Normal Computing in New York. If it works, it could transform not only the computing industry but the very way we think about computation itself.

A Path Through the Energy Landscape

The second law of thermodynamics tells us that the entropy of a closed system should increase over time; things should become less organized overall. This means that energy gets dissipated as random thermal fluctuations, which are generally of no use to anyone. Some processes in nature, however, use those fluctuations to find their way to a more organized state.

“I think thermodynamic computing was developed with the thought that it was piggybacking on the computation that ‘already happens out there’ in the rest of the world but [is] not explicitly labeled as such,” said David Sivak, a statistical physicist at Simon Fraser University in Burnaby, Canada.

In thermodynamics, the way a physical system changes over time (its dynamics) can be described as a trajectory through an “energy landscape,” a kind of map of the total energies of different configurations of a system’s components. In this landscape, valleys are where the system settles into comfortable, low-energy configurations, while peaks are high-energy configurations that are relatively unstable. A system like this reaches equilibrium when it settles in the lowest valley and stays there.

If this all seems a bit abstract, think about milk. What allows many people to digest dairy products is a chainlike enzyme called lactase, which is produced in the small intestine and fits together like a puzzle piece with the complex sugar in milk called lactose. The compatibility between their shapes allows lactase to break lactose apart into its simple sugar components, which are more easily managed by the digestive system.

Processors called thermodynamic sampling units, produced by the startup Extropic, are designed to run generative AI algorithms.

Jory Block

But how does lactase get this useful shape? It is encoded into the sequence of amino acids that make it up. As the chain is synthesized in the cell, thermal fluctuations allow the chain to explore its energy landscape and crumple up into its most stable equilibrium state.

This process is a kind of thermodynamic computing, in that it solves the problem of folding the lactase into the correct shape using only the thermal energy in the ambient environment of the cell. Once the chain of amino acids is properly folded, continuing thermal fluctuations merely induce a bit of random wiggling. The newly formed enzyme keeps its shape as it sits stably in a deep energy well. Thus, although the operation of a natural system like a living cell proceeds in a milieu pervaded by thermal noise, it still works, often with remarkable energy efficiency.

In and Out of Equilibrium

One type of thermodynamic computing, called equilibrium thermodynamic computing, would work like a folding protein. If you encode the problem you want solved in a system, thermodynamics can drive the system through its energy landscape toward the energy minimum that corresponds to the problem’s optimal solution. “You could take a small electrical circuit, let it evolve naturally under its thermally driven dynamics, and then measure its properties once it has attained thermodynamic equilibrium,” said Stephen Whitelam, a statistical physicist at Lawrence Berkeley National Laboratory in California.

A different approach to thermodynamic computing takes place when a system is driven away from equilibrium by some source of energy, much as the sun’s heat prevents the Earth’s atmosphere from settling into some unchanging state. In this case, the computation takes place as the system moves constantly through its energy landscape. The trajectory itself encodes the calculation. These “out-of-equilibrium” processes are ubiquitous in nature; life itself is one of them, powered by a constant flow of energy and matter.

The trajectories of objects moving under such nonequilibrium conditions display a version of so-called Langevin dynamics, named after the early-20th-century French physicist Paul Langevin. Langevin dynamics represents a kind of relaxation: The system seeks to lower its energy, and it dissipates energy in the process. But the system can never settle into a fixed equilibrium state because random impulses, such as thermal fluctuations, constantly push it onto some new course.

In principle Langevin dynamics can be embodied in an electrical circuit, if it is operating at a power level low enough to be affected by random thermal fluctuations, Whitelam said. If scientists can arrange for the movement of energy through the circuit to correspond to the answer to a calculation, they can use it to do thermodynamic computing.

Both equilibrium and nonequilibrium thermodynamic computers receive continuous boosts of energy from thermal fluctuations, Whitelam explained. But an equilibrium computer must reach equilibrium to complete its calculation, while a nonequilibrium computer can be designed to complete its calculation on a set timescale. That’s why nonequilibrium approaches to thermodynamic computing are popular, Coles said: They “can potentially be faster, because you’re not waiting for natural equilibration.”

Normal Computing’s prototype thermodynamic computers are made of a small array of identical electronic circuits linked together into a network.

Courtesy of Normal Computing

Structure From Noise

Most efforts so far to put thermodynamic computing into practice use silicon-based circuits as analogues. Last year, Coles and colleagues at Normal Computing showed that such a circuit could perform various kinds of computation, including matrix inversion, a mathematical problem that has applications in diverse fields ranging from machine learning to computer graphics, engineering, and finance.

Normal was founded in 2022 by Faris Sbahi, Antonio Martinez, and Matthias Tan, former members of Google X and Google Brain. The thermodynamic computer they unveiled was a tailor-made printed circuit board containing eight clusters of components, with each cluster connected to all the others to form a network. Each cluster contained a simple RLC resonator — a resistor, capacitor, and inductor, a combination that creates an oscillating electrical signal at a particular frequency. The circuit is fed a random electrical signal: Basically, it is driven by noise.

The strength of the coupling between each pair of RLC resonators in the network can be varied, and all the couplings can be written in the mathematical form of a matrix. It’s basically an electrical version of a set of interconnected springs. The question is: If you give it a shake, how will the dynamics of the network evolve?

It turns out that, if the network is “shaken” by noise comparable to the energy of the couplings, the equilibrium fluctuations it undergoes correspond to the mathematical inverse of the coupling matrix. “So you can build your device and come back sometime later and measure its fluctuations, and you’ve done matrix inversion,” Whitelam said.

The circuit made by Coles and colleagues didn’t actually run on ambient noise, which was too low-level to affect the dynamics. The researchers had to add in extra noise by hand, using a random-number generator, which cost energy. That’s one reason this kind of analog model doesn’t itself demonstrate the promised energy advantages of thermodynamic computing. But ultimately, Coles said, the advantage comes from the fact that the computation itself runs “for free” once driven by noise. The Normal team showed that, if they scaled up a processing unit by adding more nodes to its network, it would eventually reach a point at which it could solve problems faster than a regular digital neural network, using considerably less energy and dissipating considerably less heat.

Since unveiling this prototype, Normal has announced a new thermodynamic computer called CN101 that uses digital processing on a silicon chip. The researchers say that this digital silicon technology is easier to scale up than their analog circuit and can also carry out other kinds of computation, such as image generation and simulations of molecules. The device has yet to be assessed by other experts.

The initial proof of principle by the Normal team served as an inspiration for Whitelam, who recently reported a simulation of a nonequilibrium thermodynamic computing circuit.

Whitelam used a theoretical model of a “denoising” problem, simulated on a classical computer. He trained an algorithm on a video of Paul Langevin’s face being steadily corrupted by noise, dissolving into random static. (As with the Normal Computing work, the noise was introduced artificially by a random-number generator.) He then demonstrated that the algorithm could start with the static and reconstruct Langevin’s face.

The thermodynamic computer Whitelam used was a network of connected nodes, and its state was determined by how strongly connected those nodes were. During the training process, the algorithm adjusted those connections a little at a time to find the configuration most likely to make Langevin appear.

It’s like a network of linked springs, where those springs have different (and adjustable) spring constants. Indeed, “you could build a thermodynamic computer from real springs,” Whitelam said — though that would be a curiosity rather than a practical technology.

Whitelam showed that the resulting dynamics followed a path that dissipated the minimal amount of heat — by a rough comparison, about 100 billion times less than would be produced if the same task were performed by a digital neural network.

The way Whitelam trained his algorithm is a little like the way people currently train algorithms for generative AI — and indeed this may be one of the major applications of thermodynamic computing. “My algorithm is generative in two ways,” Whitelam said. “First, it turns noise into structure, thereby generating order from disorder. Second, if you train it on a set of images, then it can generate additional images that it hasn’t seen before.”

Normal Computing is not the only startup betting that thermodynamics will feature in the future of computing. The Boston-based company Extropic was also founded in 2022 by a team from Google, IBM, Apple, and Microsoft. In October 2025 the company announced “the world’s first scalable probabilistic computer” — a grid of thousands of interconnected semiconductor-based components on a chip — which it says can run generative AI algorithms using about 10,000 times less energy than existing algorithms. (The work was recently published in the journal npj Unconventional Computing.)

Doing What Comes Naturally

In addition to potentially offering low-cost, low-dissipation computing, thermodynamic computing might also offer insights into the way natural complex systems work.

Much of what goes on in molecular biology is already described as a sort of information processing. For example, a signaling molecule (like a hormone) might arrive at the surface of a cell and have its signal “transduced” — transmitted along a chain of interacting molecules — so that ultimately it flips a switch in the cell nucleus and activates a particular gene. Cells seem able to conduct this kind of computation very efficiently, creating little energy dissipation and relying, in part, on the intrinsic thermodynamics of intermolecular interactions.

So are cells themselves a kind of thermodynamic computer? “To my physicist’s way of thinking, it would be fair to say that nature uses Langevin computers programmed by evolution,” Whitelam said.

The central idea of harnessing thermodynamic fluctuations instead of suppressing them “is indeed thought-provoking,” said Kunihiko Kaneko, a complex-systems theorist at the Niels Bohr Institute in Copenhagen. “But whether this effectively translates to computing in a biological context remains an open question.”

The field of thermodynamic computing is in its early days, “analogous to when small-scale quantum computers were built in the 1990s,” as Coles and his colleagues at Normal wrote in their 2025 paper. Quantum computing is now a global industry estimated to be worth around $12 billion. But it’s a lot easier to build circuits from simple semiconductor-based resonators than from quantum bits that have to be kept in delicate entangled quantum states and often need cryogenic cooling. “The lack of technological barriers for thermodynamic computing can potentially make it a more near-term alternative to quantum computing,” the Normal team wrote.

Whitelam makes a similar comparison with the neural networks that underpin today’s AI. “The computer designs we’ve come up with so far [for thermodynamic computing] are only as capable as the small digital neural networks of around 1990,” he said. The history of AI suggests that it should be possible to do better with larger circuits and more training, he said, “but that remains to be seen.” If it pays off, thermodynamic computing will get noisy in more ways than one.

Correction: July 16, 2026
The Extropic paper describing their scalable probabilistic computer was published in early July 2026. We have updated the reference.

Why Am I Left-Handed?

Mon, 13 Jul 2026 02:22:22 GMT

Kristina Armitage/Quanta Magazine

When I was first learning to write, my letters and words ran from right to left, reversed as if in a mirror. Being left-handed, I was imitating the hand strokes of my right-handed teachers instead of reversing their strokes to replicate the letters. I gradually got the hang of writing in the correct direction, but it still feels natural for me to mirror-write. I have a mirror-written childhood diary. Leonardo da Vinci, another lefty, did that too.

Being left-handed is mostly no big deal. It is annoying how ink smudges under my hand. And I did once have to jump out of the way of a circular saw that I was holding backward; indeed, left-handers have more accidents while operating machinery. That aside, overall, I enjoy being left-handed. It grants entry into a smug little club, whose members — 10% of the human population — carry the secret knowledge that we are overrepresented among U.S. presidents, famous artists and musicians, and top athletes.

But our difference hasn’t always been welcome. My 91-year-old Texan grandmother remembers starting out left-handed (she, too, has examples of mirror-writing from early childhood) before being forced to switch, a common practice in much of the world until about the 1970s. The deep-seated disdain for left hands runs through our very language. “Left” comes from Old English lyft, meaning weak, foolish, worthless, or useless, while “right” means correct or proper. In other languages, the word for “left” can also mean awkward, unlucky, clumsy, suspicious, or sinister.

In college, I decided to spend a semester in Ghana, unaware that left-handedness is still stigmatized across much of Africa. Upon arrival, I kept accidentally offending people by eating or paying with my left hand, because, traditionally, the left is reserved for dirty tasks and the right for social interactions. When my Twi language instructor, Professor Kofi Agyekum, demonstrated how ceremonial robes are draped around the left shoulder and arm, leaving a chief’s right arm bare and free, I asked what happens if the chief is left-handed. “Oh no, no, we don’t go in for that,” he said.

Fortunately, our brains are plastic. My grandma developed beautiful handwriting as a right-hander. I easily changed my habits in Ghana. And as a kid I learned to use scissors right-handed. Today, given a choice, I don’t think I’d be able to cut with my left.

That we can fully retrain our hands (and brains) reinforces how little it matters which hand naturally dominates. And that’s part of what makes the circumstance so mysterious. If it makes no material difference, then why am I left-handed? Or perhaps more pertinently: Why are 90% of people right-handed?

An astronomical amount of research has gone into trying to find out. Geneticists, developmental biologists, behavioral and cognitive psychologists, neuroscientists, and evolutionary biologists all seek explanations. No one has put all the pieces together yet, but over the last few years, some major new clues have emerged.

First, some key facts. Crucially, left-handers aren’t mirror-image people. My heart is on the left where it belongs, and my liver is on the right. Whatever causes left-handedness isn’t related to situs inversus, a much rarer condition where a person’s internal organs mirror the usual arrangement.

My brain might be more or less normal, too. Or maybe not. I probably process language in the left hemisphere of my brain the way almost all right-handers do, but there’s a 20% to 30% chance that I process language on the right or that I split the task between the sides. That’s one puzzle about left-handedness: As a group we have more diverse patterns of brain hemisphere specialization.

Left-handedness does not seem to be purely genetic. Two left-handed parents have a left-handed child only 25% to 30% of the time. If one identical twin is left-handed, there’s only a 20% to 30% chance the other is too. This suggests a genetic component alongside some developmental randomness.

Also, the rightward bias of human handedness is unique. Some other mammals can be right-footed or left-pawed, but there’s no statistical imbalance toward left or right across the species, except for our extreme 10-90 split.

Is there a theory of left-handedness that fits all these facts?

Scientists (and I) long assumed that handedness must originate in the brain. After all, my left hand is more dexterous than my right because of the more richly interconnected neurons that map to it, on the right side of my motor cortex. It’s a reasonable guess that the causal arrow leads from brain to hand. In fact, remarkably, it seems to be just the opposite. Our hands sculpt asymmetry in our brains.

Ultrasound studies indicate that a fetus’s dominant hand is decided before its brain even connects to its limbs. We start flailing one arm around much more than the other starting about 10 weeks post-conception, as a fishlike fetus the size of a kidney bean. The movements are entirely reflexive, yet the arm that flails more predicts future handedness with a high level of accuracy.

A 2017 study in eLife reported evidence that this asymmetry originates in the spinal cord. The authors analyzed tissue from fetuses between 8 and 12 weeks post-conception (the window when arm-movement asymmetries become detectable) and found extreme differences in gene expression, or the building of new proteins based on genetic instructions, between the left and right sides of the spinal cord. This asymmetric expression could rig up motor circuitry, such as an abundance of neurons with long, signal-carrying fibers, that leads to more involuntary movement on one side than the other. Only after this does the brain get involved, as sensory feedback reaches the developing motor cortex, strengthening the neural representation of that limb.

That could explain how handedness happens. However, it doesn’t account for why the right side wins nine times out of 10, or why there is the occasional veer to left.

Researchers in the 1970s talked about a mythical left-handedness gene, but none exists. The genetic connection is more diffuse. Recent large-scale studies have identified variants of about 40 genes that each slightly elevate the chances of left-handedness. The more of these gene variants a person has, the more likely they are to be a southpaw.

The big surprise is that most are tubulin genes, which form some of the structural components of cells. “I don’t think I had this [gene family] on my list 10 years ago, to be honest,” said Sebastian Ocklenburg, a behavioral psychologist who co-authored both the 2017 eLife paper and a 2025 review paper in Trends in Genetics on the tubulin findings. Some of these same genes are also linked to neurological disorders including schizophrenia, dyslexia, and autism. People with these conditions are more likely than the general population to be left-handed or mixed-handed.

So what might be going on?

Tubulin genes encode proteins that form “microtubules,” long filaments that act both as the skeletons of cells and as highway networks within them. It’s possible that some process involving microtubules unfolds in the neural progenitor cells that give rise to neurons of the spinal cord in a way that functionally “leans right.”

We know that proteins attach to the surfaces of microtubules and move along them to transport molecular cargo from place to place inside cells, and thus that the structure of microtubules helps determine where many molecules accumulate within cells. So perhaps a certain signaling molecule preferentially accumulates more on one side of a neural progenitor cell than the other. When the cell divides, one daughter cell might then inherit slightly more of the signaling molecule than the other. Over many rounds of cell division, the imbalance could create a discrepancy between the left and right sides of the developing spinal cord. Feedback loops would amplify the difference, strengthening gene expression on one side of the spinal cord and suppressing it on the other. Two different modes of neural development result in an asymmetry — structurally favoring the right most of the time.

The gene variants associated with left-handedness might cause proteins to lock onto the microtubules in a slightly different way, so that more of the relevant signaling molecules accumulate on the opposite side of a neural progenitor cell. Or perhaps the initial rightward bias is so weak (and further weakened by the gene variants) that sometimes chance fluctuations give the left side the upper hand.

This fits the observation that handedness is somewhat heritable, heavily biased to the right, and also quite random. The details remain mysterious, but this provides at least a plausible origin story for handedness. And yet this is only one aspect of the causal explanation I’m looking for. Why would evolution build in a bias?

A coin flip during fetal development lands on one side 90% of the time. This suggests that right-handedness is advantageous for some reason, but if so — and here I feel a slight sense of defensiveness kicking in — why are the left-leaning tubulin gene variants still around? Chris Venditti, an evolutionary biologist at the University of Reading, isn’t a lefty, but he points out that the proportion of left-handers has been consistent across time and continents. “Usually in evolution when that happens there’s a reason for it,” he told me.

In an April 2026 study in PLOS Biology, Venditti and co-authors Thomas Püschel and Rachel Hurwitz of the University of Oxford looked at any and all data on the handedness preferences of primates, such as which hand a baboon uses to reach into a tube to retrieve food. They found that many individual primates have hand preferences, and that these preferences are stronger in species with bigger brains. But across species, left- and right-favoring individuals usually balance out. Only humans exhibit an extreme population-wide bias.

By analyzing evolutionary relationships among species, the authors concluded that our strong preference to use one hand over the other (before any species-wide rightward bias emerged) began roughly 7 million years ago, around the time our ancestors became bipedal and developed big brains. We had to stand upright before we could start deploying our hands asymmetrically, and it was more efficient for our growing brains to distribute key functions to different sides, only devoting resources for fine motor skills to one hand (while remaining plastic enough to wire up the other hand if necessary). But then, the authors estimate, sometime after the emergence of the genus Homo, 2.8 million years ago, evolution coded a preference for right over left.

Of the various speculative theories for the emergence of this extreme preference, one that seems plausible to me points to our unprecedented capacity for violence.

In 1996, psychologists proposed the “fighting” hypothesis, which posits that left-handers persist at low levels in the population because, so long as they are relatively rare, they have an advantage in hand-to-hand combat; their opponents are likely to be unfamiliar with left-handed attacks. It’s not a bad theory; indeed, the element of surprise probably accounts for lefties’ success in sports. But that doesn’t explain why right-handedness prevailed in the first place.

Then, in 2023, psychologists advanced the “modified fighting” hypothesis, which says righties have a more basic advantage dictated by the position of the heart on the left side of the body. Since they wield weapons in their right hands, their most effective and potentially fatal blows can be delivered to the left side of their opponents, where the heart is. At the same time, right-handed attackers lead with their right — protecting the more vulnerable side. In 2026, the scientists behind the modified fighting hypothesis supported their case with a review of the literature on sharp-force injury. They found that people are stabbed significantly more often on their left sides, and these attacks are more often fatal.

This would, the hypothesis goes, offer a general survival benefit to the gene variants that favor right-handedness, while still allowing just some left-handers to benefit from their surprise combat advantage, “particularly in fights that do not involve sharp weapons,” the authors noted.

According to Venditti, this aligns well with his finding that right-handedness is unique to the genus Homo. “Humans are pretty violent creatures,” he said. “In most animals, fighting is not to kill your opponent. That’s not what anyone involved in the fight wants.”

On the other hand, it’s unclear whether subtle combat dynamics could fully explain the consistency and persistence of the 10-90 left-right split.

I can’t help wondering if the stigma of the kind I experienced in Ghana and my grandmother faced as a child played any role. Perhaps a small surplus of right-handers emerged early in hominin evolution because of the modified fighting hypothesis, and this fueled cultural norms that reinforced the genetic disparity over many thousands of years. Some scholars I spoke to dismissed the stigma as a recent phenomenon — a “flash in the pan” on evolutionary timescales, in Venditti’s estimation. But to me, the widespread linguistic association of “right” and “left” with good and bad suggests that the stigma may be older and more profound. Ocklenburg further pointed out that the socially mandated division of labor between hands still observed in Ghana and many other places today — right for eating, left for hygiene — would have offered a major survival benefit in helping people avoid spreading germs and contaminating food. “It’s seen as discrimination, but it’s actually a genius way to keep people from poisoning themselves and dying,” he said, noting that the taboo has surely saved countless lives.

There may never be a certain, or simple, answer to the question of why I am left-handed. Or why humanity is so right-handed. Or why left-handed people are overrepresented in some fields and slightly more likely to have certain health conditions. But as I’ve followed the clues through developmental biology, genetics, evolution, and culture, I now see that our peculiar handedness is inextricable from our humanity.

We Know Simple Fluids Can Flow. Turns Out, Some Can Fracture.

Fri, 10 Jul 2026 02:51:48 GMT

When pulled at 100 millimeters per second, a blend of hydrogen and carbon stretches. At 300 millimeters per second, the fluid breaks.

Adapted with permission from Phys. Rev. Lett. 136, 124002. Copyrighted by the American Physical Society.

Thamires Lima, a research professor in chemical engineering at Drexel University, studies the properties of thick, viscous liquids — think honey or molasses, though in a lab you’re more likely to find polypropylene or crude oil. Using a method called extensional rheology, Lima stretches liquids between metal plates to find the force that makes them flow.

A few years ago, she was conducting a test as part of a project in collaboration with the oil and gas company Exxon Mobil when she heard a short, sharp crack. “I thought it was the machine,” Lima said. But the crack came from the fluid that the machine was pulling: a gooey, black blend of hydrogen and carbon. Instead of stretching, the fluid had fractured.

Fractures are known to occur in certain elastic complex fluids, which can act like solids under certain conditions. But Lima was working with a nonelastic simple fluid. Even with almost no elasticity, it snapped apart under stress.

“Nobody expected that this would be possible in this kind of simple fluid because viscosity usually just rearranges the molecules,” said Arnold Mathijssen, a fluid physicist at the University of Pennsylvania. “You don’t expect it to crack. But it does, so I think that’s what’s really surprising.”

A Brittle Break

Lima stretched the liquid again and again to prove that the unexpected crack wasn’t a one-off. “Every time that she measured it, the material would break,” said Nicolas J. Alvarez, the professor of chemical engineering at Drexel University whose lab led the research. “It makes a loud pop. I mean, like you just took a rubber band and pulled it and stretched it and it snapped.”

Convinced the snap wasn’t a fluke, Lima and Alvarez used high-speed cameras to look at the phenomenon more closely. They realized that the break was essentially a “brittle fracture,” the kind you might see when you drop a dish made of glass or porcelain.

Brittle fractures happen to brittle solids, which have elasticity. Apply some stress to glass or porcelain and it deforms a very tiny bit, and then — if you don’t push it past its breaking point — it springs back to normal once the stress is removed. However, solids are never perfect. In most cases, a brittle solid will have a teeny, tiny defect — a crack at the scale of tens of nanometers. Once the solid is stressed past a critical point, it becomes energetically more favorable for the solid to grow the crack than to elastically store the stress. At that point, the crack grows catastrophically, rapidly breaking the solid apart.

Some complex fluids, called viscoelastic liquids, also have elasticity. For example, polymer melts — melted versions of the polymers in plastics — are made up of long chains of molecules, which become entangled with one another and increase the material’s elastic component.

In a 2016 Physical Review Letters paper, Alvarez and colleagues showed that complex fluids like melted polystyrene can fracture in the same way that solids sometimes do. “We just thought elasticity was something that was a prerequisite for such solid type of breaking, right?” Alvarez said. As a result, they theorized that elasticity was related to the fracture of liquids as well.

But the hydrocarbon blend that Lima was working with was a simple fluid. Simple fluids don’t store much elastic energy. And when they are pushed or pulled past their limits, they don’t usually bend or break — they flow.

So perhaps the old theory about what makes a liquid fracture is wrong. “If there is no elasticity in a problem, then how can you think about initiation or growth of a crack?” said Brato Chakrabarti, a physicist who works on fluid mechanics at the International Center for Theoretical Sciences in Bengaluru, India.

The cracking of the hydrocarbon blend made the researchers look back at the papers of Daniel D. Joseph, a mechanical engineer at the University of Minnesota. In 1995 and 1998, Joseph suggested that any liquid, regardless of how elastic it is, could fracture under a sufficient amount of tearing stress.

Alvarez wonders if the breaking point of a liquid is related not to a property like elasticity, but to something more fundamental to the liquid’s structure. “Maybe, just maybe, the thing that causes [certain] fluids to break … [is] somehow related to this cohesive energy that holds the molecules together,” he said.

A Burst Bubble

Simple fluids do have a way of relieving stress, no breaking required: They form intermolecular voids (bubbles) in a process called cavitation.

If the blades of a propeller spin rapidly in a simple fluid, for example, the fluid on one side of the blade can slosh much faster than the fluid on the other, leading to a drop in pressure on that side. This drop can cause the liquid to cavitate. Engineers work to avoid this, because once those bubbles collapse, they generate shock waves that can damage propellers and pumps.

In his papers in the ’90s, Joseph predicted that cavitation would allow simple fluids to fracture.

“If you think about what holds a fluid together, it’s cohesiveness, or the intermolecular interactions between the molecules,” Alvarez said. If you pull those molecules apart, you can create a bubble. Usually, viscous liquids stay cohesive when bubbles form, by changing shape around them. But if enough bubbles form in quick succession, they could theoretically crack a liquid like a pane of glass.

At Drexel, the researchers found that once a crack nucleates inside a simple fluid, it propagates extremely fast, precisely because the fluid is not elastic. “If you can get that nucleation event of the crack to begin, because there is no elasticity in the material, that crack can propagate as fast as physics will allow it,” Alvarez said.

In previous work on complex fluids, the Drexel researchers found that cracks in melted polystyrene propagate at approximately 0.07 meters per second. In their new study, Lima and colleagues showed that cracks propagate far more rapidly in the simple liquids they studied, reaching velocities of approximately 500 to 1,500 meters per second.

“That has something to do with the way that the material is able to dissipate energy,” Alvarez said. According to one hypothesis, in a complex fluid, energy is absorbed by the long chains of molecules as they break. But in a simple fluid, “there’s really nothing to slow that crack down,” he said.

This seems to affect the shape of the crack, which in complex fluids looks like the horn of a trumpet and in simple fluids looks like a crack moving through glass, the researchers found.

How To Crack a Liquid

Surprisingly, despite their different ways of cracking, both the complex fluids and the simple fluids that researchers tested tended to fracture at the same critical measure of stress: 2 megapascals. The researchers varied the temperature of the hydrocarbon blend — a simple fluid — to change its viscosity and found that only the least viscous liquid they tested failed to fracture. The team observed that the critical stress level at which liquids fracture is proportional to their viscosity times the strain rate (how quickly they are being pulled or stretched apart and how the diameter of the liquid is changing).

The machine had a limit — albeit a high one — to how quickly it could move: 500 millimeters per second. “There are very few instruments comparable to ours,” Lima said. Lima thinks that potentially, if they had a machine that could pull on the liquids faster, they could fracture less viscous liquids like honey or even water.

In the future, Lima wants to use a more transparent liquid so she can capture the crack as it forms. She would also like to try freezing the surface of the liquid as soon as it snaps and to probe it using a high-resolution microscope that scans surfaces at a nanometer scale.

Alvarez is keen to explore simple fluids in the context of spinning materials into fibers — which can have applications in engineering and medicine. Fractures in fluids could also have implications for inkjet printing, brain injury protection, and soft robotics.

But Alvarez is most excited to learn what it means for a simple fluid to fracture in the first place. “[It’s] different than what we’ve been thinking about in the literature for a very long time,” he said.

Will We Ever Find Alien Civilizations?

Thu, 09 Jul 2026 01:39:13 GMT

Chanelle Nibbelink for Quanta Magazine

Does intelligent life exist elsewhere in the universe? The question has captivated us for centuries, but despite decades of searching it remains frustratingly unanswered. Every so often a curious signal appears — fossilized structures in a meteorite, say, or an unusual gas in an exoplanet’s atmosphere — and for a moment it seems possible that we are not alone before the excitement gives way to a more mundane explanation.

So what would it actually take to find life in the cosmos — and how would we know when we saw it?

David Kipping, an astronomer at Columbia University, has spent his career finding better ways to answer these questions. His approach is statistical: rather than chasing individual detections, he develops mathematical frameworks for reasoning about where habitable worlds are likely to exist and how confidently we can interpret the signals they produce. In this episode of The Joy of Why, Kipping joins co-host Janna Levin to discuss efforts to frame one of humanity’s oldest existential questions as a tractable scientific problem, why biosignatures have proved so difficult to interpret, and why he believes exomoons may be an overlooked place to search for life.

Listen on Apple Podcasts, Spotify, TuneIn or your favorite podcasting app, or you can stream it from Quanta.

Transcript

[Music plays]

JANNA LEVIN: I’m Janna Levin.

STEVE STROGATZ: And I’m Steve Strogatz.

LEVIN: And this is The Joy of Why.

STROGATZ: A podcast from Quanta Magazine where we discuss some of the biggest unanswered questions in math and science today.

LEVIN: So Steve, I really have a good topic today.

STROGATZ: Hmmm.

LEVIN: It’s aliens. First of all, have you ever seen a flying saucer? Let’s just have it out, Steve.

STROGATZ: Okay, this is where I have to admit, no. But I would like to talk to you about aliens.

LEVIN: Okay, that’s really good because this is serious. I think scientists take very seriously the idea that there’s life out there. Have you ever pondered the question, are we alone?

STROGATZ: A little bit. Years and years ago, I read a book by Francis Crick, you know, better known for his work on structure of DNA. But Crick wrote a book called Life Itself, and he was interested in the idea that life on this planet might have been seeded by a process that people were calling directed panspermia, that maybe life had been sent here.

LEVIN: Yeah.

STROGATZ: But the thing that really sticks with me from Crick’s book was a point that he made, which is about what’s the probability of life starting on a given planet. And he said, “We really don’t know.”

LEVIN: Mmm-hmmm.

STROGATZ: Like, we just really don’t know. And if the number is sufficiently small, like astronomically improbable, it could be that we’re the only life in the universe. That’s not impossible. You know, you always hear people say, “Oh, there’s so many stars and so many galaxies,” that people just assume that’s a big number, so of course there must be life everywhere. But in my heart, I really don’t know. There might be none or there might be a lot. I don’t know.

LEVIN: Yeah. Well, I think that’s exactly the question, that this isn’t just a matter of belief, right? It’s not, I believe in aliens or I don’t. And it’s also no longer beyond quantifiability. We actually have concrete questions we can ask, parameters we can estimate, satellites that search for planets that give us data and intel. And this is kind of a modern and more sophisticated version of something called the Drake equation.

So I spoke to someone who studies deeply the mathematical underpinnings of making these kinds of assessments, and that is David Kipping, who is a colleague of mine. David is an astronomer at Columbia University, where he studies exoplanets and exomoons, and he’s really focused on developing new statistical methods in particular to detect potentially habitable worlds, which I think is a very intriguing way to get ultimately to the question that I think haunts him, which is, are we alone?

So, here’s David Kipping.

[Music plays]

LEVIN: Welcome to The Joy of Why, David. So great to have you here.

DAVID KIPPING: It’s a pleasure to finally be on. Yeah, it’s great to be here.

LEVIN: I know. It’s so great. Usually we’re in the same building at Columbia, but not today.

KIPPING: Yeah, or a bar having a cocktail or something.

LEVIN: Right. We should do this there, that’s for sure. I have to say, for a Columbia astronomy lab, you have one of the best names around. So you call your lab the Cool Worlds Lab. Can you help people understand the origin of this name?

KIPPING: Right, so when I was applying for faculty jobs way back, I was doing that usual thing of trying to come up with a good name, and my PhD advisor, Gáspár Bakos, he said, “Whatever you do, don’t call the lab “Kipping Lab.” Don’t call it after yourself. Don’t be that guy.”

And, there was a group in San Diego called the Cool Stars Group, and there’s a big conference called Cool Stars. So Cool Stars, obviously, focusing on these M dwarf stars, these low-mass stars, which it’s really easy to detect planets around them. There’s a lot of interest astrobiologically around these sorts of stars. So there was a huge amount of interest about those, and I thought, “Hey, by extension, it’s the cooler worlds that we also care about.” It’s not the hot Jupiters so much, at least not for me. It’s not the hot Neptunes. It’s the planets that are further out in the temperate zone where life is possible, where moons can be possible, not because of the thermal temperature, but almost the dynamical temperature has cooled down. So everything just gets more interesting when you’re far away from the star. So that was the story behind the name.

LEVIN: Yeah, that’s interesting. You’re already raising scientific questions because people are hearing terms like, certain dwarf stars, but also Jupiters and Neptunes. So this idea that planets are replicated, the ones that we see in our solar system, here we are with our eight planets, and then we see similar kinds of planets around other stellar systems. Is that a surprise?

KIPPING: If you go back 20, 30 years ago, before I was in the field, I think people didn’t know. There was an expectation. [Carl] Sagan was the eternal optimist, and he wrote about this a lot, and he really did expect, and many others expected there to be lots of planets out there.

But you can make an anthropic argument that it’s perfectly consistent that the solar system could be the only place that has planets, and it would be perfectly natural that we would happen to be born in the one place where there are planets, ‘cause of course, we couldn’t be born anywhere else. So you could make that argument, but I think it would be surprising, a little bit intuitively, and indeed, once we started finding planets, it reinforced that view.

But I think what’s really took us aback is just the diversity of worlds. I mean, we really expected the solar system to be a template of what other systems would look like, and it’s not, Janna. It looks radically different from place to place, and that has really blown our minds.

LEVIN: So, when Carl Sagan was working, it wasn’t clear that there were other planetary systems. That is quite amazing. When you started entering the field, it was already accepted that there were tons of exoplanets and the search for life was a real scientific pursuit. Would that be fair to say?

KIPPING: Yeah, I mean, so I was doing my PhD up to 2011. Kepler launched, 2009. This was a mission that NASA launched which really transformed our understanding of planetary systems because it discovered not only thousands of them – we went from dozens to thousands in the space of a couple of years – but it also probed down to really small worlds.

So before we were only really sensitive to largely Jupiter mass, Jupiter-size planets, and Kepler pushed us all the way down to Neptunes, super Earths and even some planets comparable to the size of the Earth. So that blew us away. But at the same time, I was thinking, “Hey, if we are able to detect Earth-sized planets, why couldn’t the universe be a little bit more creative and start making Earth-sized moons around Jupiter-sized planets?” And that was, yeah, really where I got into this idea of looking for moons.

LEVIN: So why is it important that it be Earth-sized? What’s wrong with 40% the size of the Earth for a moon?

KIPPING: Nothing’s wrong with that. It’s still fascinating. It’s still wonderful. It might be a challenge for life.

When you make a world—not necessarily just a planet or a moon—but just a world smaller and smaller, obviously, its surface gravity decreases, its escape velocity decreases, and thus it’s easier for gas, for an atmosphere to leak off through what’s called Jeans escape or even hydrodynamic escape if there’s ultraviolet radiation smashing into the top of the atmosphere.

So those processes erode away atmospheres, and we think that’s why Mars doesn’t really have a thick atmosphere. The atmosphere of Mars is 0.6%, I think, the density of Earth’s atmosphere, yet it’s further away from the sun, so it should be easier in a thermal sense for it to hold onto an atmosphere. But of course, it’s only 10% the mass of the Earth, so that explains it.

We think that it probably did have a thick atmosphere in the past because we see all this evidence for liquid water. We see these, riverbeds and river deltas and valleys that have been carved out by water. So it somehow lost it because it essentially wasn’t massive enough.

So therefore, that could be a problem. If you wanna have a habitable moon, you probably want it to be larger than that of Mars. Otherwise, you might be restricted to things which are beneath the surface. And of course, there is interest in that with Europa, Enceladus, of subsurface life.

But if something like, like we have, doing agriculture and a civilization, that might be difficult to have if you’re too small.

LEVIN: There seem to be a lot of things that went into the reason that the Earth, if it’s not the only planet in our system that evolved life ever, it’s the only one that radiated plentifully as we see now. And the factors, as you’ve already mentioned, this kind of temperate zone, the existence of oceans, and things like plate tectonics—that really surprised me—and maybe even the spin axis of the Earth, which could have been from an early collision. So how much do all of these factors participate in the ability for life to take hold and really radiate?

KIPPING: Truthfully, we don’t know. We can speculate about each of these factors, and there’s reasonable speculation about all of those. Plate tectonics, we think that’s probably necessary for a carbon cycle, and we think a carbon cycle is probably essential for having enough carbon left over for life to thrive and to keep going on the surface. Otherwise, you could just deplete it over time.

And then, you know, you’ve got other factors like the axial tilt, and again, people argue about that. You could think that an axial tilt is essential because if you had the North Pole pointed right at the sun for three months of the year or something, that would seem bad news for life. But on the other hand, we have extremophiles who seem very robust and can thrive in all sorts of environments. So maybe life would be fine without that?

But maybe it’s us really that we’re talking about. You know, it’s agriculture. It’s a Neolithic revolution. Can you really do farming and have civilizations if your climate is wildly swinging? Like in Game of Thrones, you have these insane winters, right?

LEVIN: Winter is coming, yes.

KIPPING: The winter is coming. It’d be like that kind of situation where you get these very deep winters and very extreme summers, and maybe that might be difficult to imagine a civilization thriving. It’s difficult to know exactly where these boundaries are.

But there may be a lot of other parallel tracks to the way life arrived here. Maybe on Titan. Titan’s a very alien moon. It has methane and ethane lakes. Very, very different thing from the Earth. But perhaps there is life there—some form that we can’t really even imagine thriving on the Earth.

LEVIN: Yeah. It sort of seems an insane trend to fall into given that we keep getting deposed from being special. And when we think about the kinds of organisms that exist here on Earth, the variety is tremendous.

Yeah, so you’ve made the transition from just life, which could have been bacterial, to technologically sophisticated life, which sometimes is called intelligent life, but then that has all kinds of philosophical pit holes.

And so you’ve just given this really interesting set of examples which are technological, space-faring civilizations that are trying to harness the energy and the resources, not only around them, but maybe of the entire galaxy, right? And that historically had a sort of origin in the Drake equation, which might have fallen out of favor, but really structured the conversation for a long time. Can you tell us a little bit about the 1960s astronomer Frank Drake and what he was after in terms of trying to write an equation to predict the probability of the emergence of so-called intelligent life?

KIPPING: My understanding of this story, obviously, it’s way before my time, this is back in the ‘60s, was that Frank Drake had organized a meeting to talk about searching for alien signals, radio communications. I think probably inspired by the paper by Morrison and Cocconi, the famous Nature paper which really triggered this thinking about looking for alien transmissions.

And so he had a little conference, and I believe there was only like seven or eight people at this conference, and it included evolutionary biologists, it included astronomers. Carl Sagan was in attendance at this meeting famously. They called themselves the Order of the Octopus—I do know that. But I think ‘cause there was an octopus expert there, and they were inspired to name themselves the Order of the Octopus after he gave a great talk about octopuses. It would have been a fascinating meeting to have been historically tracked.

But during that meeting, Frank Drake apparently wrote down the Drake equation for the first time, and the purpose of it was really to organize the meeting. And so it was a way of just like breaking out the problem into these bite-sized pieces. You know, how often does life start? How often does intelligence get going? How often do they communicate? Wasn’t really intended, in my interpretation, to be a calculator, and I think that’s where it’s been abused and why it has been sullied, over the years, because there have been numerous papers where astronomers have just plugged in numbers for the frequency of intelligence. And I mean, how does anyone know these numbers? It’s all just guesswork.

LEVIN: Now, you have tried to, in technical papers, reframe the Drake equation in a way where you’ve considered birth and death of civilizations, and again, returning to this possibility that we shouldn’t overestimate. We should entertain the possibility that we are alone in the universe. Can you tell us about this approach and why you think it was worth pursuing, even after everything you just said?

KIPPING: Yeah, I prefer the birth-death formalism. It wasn’t just me that’s proposed this. A few of those people have converged on this idea as well. But the attraction of it is that you get rid of a lot of these terms which seem really arbitrary.

For instance, we talked about these different qualities, like the axis of the Earth has to be tilted within a certain range or something. That’s not actually in the Drake equation, but you could imagine someone adding in more and more parameters like that. The fraction of civilizations that choose to communicate via radio. Well, what about if they choose to communicate via something else? Its utility is questionable, I think.

And so for me, I was just interested in, you know, all models are wrong, but some models are useful. Make the model as simple as you can get away with. And the simplest model you can possibly imagine is that there is some rate at which these entities, civilizations, intelligence, whatever you wanna call them, emerge, and there’s some rate at which they die.

And that’s useful to think about that way because then you would expect there to be an equilibrium over a certain amount of time after some settling time. And so you can actually do that kind of calculation of what would be the settling time for given rates? And I think you can make a fairly convincing argument that given the age of the universe and the age of the galaxy right now, you would expect to be in the equilibrium state at this point.

And so that’s interesting, I think for just dialing it back to the simplest bare bones you can. But it still leaves you ultimately with this question. And so what we argued in this paper, is that the actual number of extant present-day civilizations out there ends up being dominated by purely the ratio of the birth and the death rate. That’s it. So it’s actually just one number, the birth to death ratio. That’s all that matters.

LEVIN: It has an outsized influence on the result of the equation.

KIPPING: It’s the only thing that matters for the population. It’s exclusively down to that ratio.

In statistics, we often want priors, right? To predict a distribution, you have to have some distribution that you assume for the birth to death ratio. And so we argued that the most agnostic and least informative prior if you plug it in, it ends up giving you a very bifurcated distribution. So you end up with there either being a very crowded universe or a very lonely universe. It’s very difficult to get it intermediate.

And I think this intuitively makes sense. There was a physiologist John Haldane about a century ago who pointed this out. He said, “Well, imagine you approached a bench and there was beakers of water, and the beakers of water are almost the same.” They have more or less the same temperature, the same salinity, but there might be slight differences between them. And then you have some random chemical, let’s call it chemical X, and you’re gonna pour it into these 20, 30 beakers, let’s say. And his challenge to the listener was this: What fraction of the time would you expect this random chemical X to dissolve amongst these beakers?

And he reasoned that you should expect either it to be almost 100% or 100%, or almost 0% or 0%. But it’d be very weird if half of the time this chemical dissolved in the water and half of the time it didn’t, given the water is more or less the same water. It’s more or less the same stuff each time.

And so by the same extension, there’s all these Earth-like planets out there. You would expect that once the rules are in place, if life is the way it goes, then life will just pop up everywhere. Or it’s incredibly unlikely to get to life, and therefore we would necessarily live in one of those rare places.

So we kind of argued this bifurcation that you would end up with either a crowded universe or a lonely universe. And then we more provocatively said that we think the crowded universe is, certainly for technology, incompatible with observations. It is a very quiet cosmos out there.

LEVIN: The famous question Fermi asked many years ago in the wake of the UFO craze and the Roswell incident and all of these sightings of flying saucers. He said, “Where is everybody?” It did raise a question. And in this statistical distribution that you’re suggesting, wouldn’t we already know if it was crowded?

KIPPING: I think we would. I mean, so our claim is that if you’re an optimist for SETI—

LEVIN: Search for extraterrestrial intelligence. Just for the rare person who doesn’t know SETI.

KIPPING: Correct. Yes. So conventional SETI is listening for radio waves, right? They’ve surveyed now millions of stars—which is still only a tiny fraction of the galaxy, but millions of stars. They’ve done it for seven decades—not continuously, but on and off. So lots of gaps, I’ll grant you, but there’s been a lot of SETI work.

And certainly the universe is not screaming. It is not full. It is not saturated with radio transmitters. We are absolutely confident that is not the case. So in this framework where you would expect to have either crowded or empty, it more or less rules that out ab initio. It’s done. You can’t possibly have that.

So therefore, in our thinking, a SETI optimist has to live in this valley where it’s not zero, but it’s not 100%. And they are hoping that basically 10 more years of SETI will push us just over the edge from 55% coverage to, you know, there’ll just be enough that you’ll get over. And we just argue that’s statistically very unlikely that you’d live on that knife edge where we’re just behind the curve.

So I don’t want to say don’t do SETI, ’cause it’s always a surprise, especially if we’re gonna in different ways rather than radio SETI, looking for laser signals, thinking about other means of communication, even neutrino beams, gravitational waves. But I think looking for simple life is a complete unknown. Like in that dichotomy of crowded or empty, it could be full. Like Mars could have life beneath its surface, Europa, Enceladus. We have no constraint on that. It’s just that for whatever reason, it doesn’t ever get to radio transmitters all over the place.

LEVIN: So what’s also interesting is the sort of mathematical techniques that you use to explore these problems theoretically. It’s not simply evaluate this parameter, plug it into the equation. You’re actually thinking more about this in a statistical approach that allows you, in some sense, to transcend some of the details precisely because you can make assessments. It’s sort of fine-tuning, right? It’s either crowded or rare.

So in a way, you seem to be saying that just statistically using that kind of analysis, technology might be rare, but life could still be plentiful—just simpler life.

KIPPING: I mean the idea of SETI pessimism, you might call it, of being down on the odds of this. This actually goes all the way back to Sagan, who was an optimist, but he got into a big debate with Frank Tipler in the 1980s because Tipler pointed out that imagine we have self-replicating probes, right? A machine that can make another version of itself, duplicate itself. Now then, in the 1960s, John Von Neumann, who first imagined that, that seemed kind of fantastical. He was looking at trends in technology and doing a big extrapolation.

But I think today it seems quite prescient. It seems possible. There was a recent study that estimated a machine now could reproduce 70% of its mass. So we’re 70% of the way there to a self-replicating probe. It’s not that hard to imagine someone launching one of these things.

And in some extreme versions of this, you could imagine it just propagating across the galaxy—1% the speed of light is plenty—and you could convert the entire galaxy into computer substrate, which the galaxy just becomes a giant data center in space for AI training or something. It does feel very prescient right now, and that clearly has not happened. The galaxy hasn’t been converted into a giant computer substrate because otherwise we wouldn’t be here.

So Tipler argued that this is the strongest constraint that we have. This requires that less than one in a hundred billion stars ever produces self-replicating probes that just do their own thing. Now, however contrived you think that might be, one in a hundred billion is a really small odds for, like, just someone somewhere has to do it once.

And so Sagan didn’t like that because Sagan was an optimist, and so he was pushing back saying, you know, there’s all these reasons, like the probe might have finite range. It might be like there’s a zoo hypothesis. Aliens is watching us. It’s like the Star Trek Prime Directive a little bit.

But, all of those have been studied really in-depth. We could talk about any of them, but they’ve all been thrown aside, largely. And I think the original claim by Tipler that this is really difficult to reconcile with our very existence, that self-replicating machine has never done this. The universe has not woken up. Matter has not transformed into intelligent substrate at this point. Apart from like our brains maybe. And so that, that is kind of a profound constraint on what happens in the universe.

LEVIN: Yeah. Okay, so I have to, at this juncture, ask you to address the issue of the UFO files. People are very caught up in this. What do you say when people are arguing, “Well, how do you explain three dots on the horizon from the Apollo mission?” Or, “How do you explain these grainy photos these expert pilots are seeing in their equipment?” What’s the response you have to that?

KIPPING: Well, obviously, there’s a lot we can’t explain. You just have to be candid about that. I mean, there’s plenty of observations that James Webb has taken that we can’t explain. We don’t fully understand why galaxies are so fully formed in the early universe as they are, and why there are quasars in the early universe. I mean, there’s always stuff we don’t understand.

LEVIN: It’s aliens, David.

KIPPING: Yeah. And that’s actually exactly the point that worries me, Janna. That the aliens is like the Band-Aid explanation. It’s God. It’s just saying God did it. Aliens did it. Because it’s too flexible as a hypothesis. It can explain anything you want. Why did your alarm clock not go off this morning? Aliens did it, and so that worries me a bit as a hypothesis, just from the point of like the Popperian standards of how we even talk about falsifiability in science. So the fact we don’t have an explanation is not evidence for aliens. That’s just the first thing we should discount.

And then the idea of more specific evidence for UFOs, it’s mostly actually personal testimony. But the actual videos we’ve seen—not very convincing. So you know, there’s these three videos the Pentagon released. There’s no range information on any of that. So it’s very difficult to know whether you’re looking at something like right in front of you in the foreground or far away. And the pilot said, “Oh, no, I had a good idea of where it was. I knew where it was.” But it’s not reproducible and of course, science is all about reproducibility. If you can’t reproduce it we just don’t know what to do with that.

So I think, in a nutshell, my big issue with the UFO claims has been that we can’t even ingest it into science. If I’m going to ingest any scientific claim, I need to know two numbers: the false positive rate of that experiment and its true positive rate. And I’ve proven this in a Bayesian paper, there’s no way to interpret an experiment if you don’t know those two numbers. Because if your false positive rate is 99% and someone says, “I saw a UFO,” it’s almost certainly a false positive. You have to know these numbers in order to make sense of it. There’s no way to even ingest these claims into science as they currently stand.

[Music plays]

STROGATZ: Oh, that’s a very interesting take, the statistical argument from Bayesian thinking that we can’t even assess these claims properly.

LEVIN: That’s very much his expertise. He’s really brought to the fore these kinds of ways of thinking that have allowed him really to make progress instead of saying, “Hey, does this specific one planet right here have life?” Right. It’s easier to talk about the collective, and what trends we might expect and to deduce from there.

STROGATZ: Yeah, I was very interested—I would say captivated—because we are hearing so much these days from what seem like credible, maybe not quite credible? I guess what I’m thinking is the people that were military, you know, that don’t seem like they’re prone to exaggeration.

LEVIN: Mmm-hmm.

STROGATZ: That saw something they can’t explain.

LEVIN: Oh yeah.

STROGATZ: And I thought the humility of David’s reaction, that there’s so much that we can’t explain. Why would we leap to the alien idea? Why don’t we just say there’s a lot of things we can’t explain and just live with that?

LEVIN: Yeah, I absolutely agree with you. I don’t feel that we should be disparaging people who are coming forward and reporting sightings. We should absolutely be collecting all kinds of data and information on observations citizens and experts are making of unidentified aerial phenomena. That’s respectable, admirable. But the leaping to “this is aliens” is problematic.

STROGATZ: I wanted to ask you some things about that because it seems like it’s right in your wheelhouse. I mean, it is so problematic given what we know about cosmic distances. And given our understanding of the speed limit of the universe set by the speed of light.

LEVIN: Yeah.

STROGATZ: I mean, I was just looking up the numbers to remind myself this morning. Just within our galaxy, the types of numbers we would be talking about. Like, if we imagine that an alien came by spaceship from a planet around some star in our galaxy, that would be on the order of tens of thousands of light years. Even if they were going at the speed of light. We didn’t even have civilization ten thousand years ago.

LEVIN: Yeah. We’re talking to David’s point. Either there have to be a huge number of civilizations for that to be viable that we overlap and communicate. Huge number, because you’re traveling, let’s say, 100,000 light-years to cross the galaxy at the speed of light, right? To get all the way across the galaxy.

So yes, there’s a lot of planets and star systems and moons within that range, but we haven’t had civilizations for hundreds of thousands of years. We’ve had civilization, as you said, really just for a few thousand, and we’ve only had technology for a couple hundred years, right? A couple hundred years, and it’s unclear that our technology is sustainable, that we’ll be able to keep having electricity and energy for everybody on this planet sustainably. So we might only have had a few hundred years of technology total, and that might be it.

So you’re talking about trying to overlap across these incredibly vast spatial distances in this incredibly long timescales in a bleep, right? An absolute bleep. And then it becomes, well, if we do overlap, then probably there are a whole huge ton of civilizations ’cause then they’re in our backyard, and they came really close, and then by coincidence, they overlapped with us in time. And if we don’t, well, you know, that kind of seems like, yeah, maybe that’s just the odds.

STROGATZ: Can I just ask one thing that’s silly? I mean, ’cause there’s always this question of is there biological evidence? Like, do we have the dead alien from the crash?

LEVIN: Right.

STROGATZ: And then they’re… It’s so perplexing that these civilizations would be good enough to travel at close to the speed of light, or they develop wormhole technology, but they can’t land safely in Kansas.

LEVIN: Exactly. Or, where they can’t keep hiding from us very successfully? Well, can’t get enough of aliens. I think we’ve locked that down.

STROGATZ: Good. Well, I wanna listen to more.

LEVIN: After the break, we’re gonna zoom out to exomoons—and that refers to moons outside of our solar system. So we’re going to discuss what exomoons mean for the search for life in our universe.

[Music plays]

Welcome back to The Joy of Why. We’ve been speaking with Columbia University astronomer David Kipping about the probability of life in our universe.

So you’ve used this sort of deep statistical thinking not just to analyze theoretical concepts like the Drake equation, but really importantly, to actually search for places where life might emerge, and we already mentioned it lightly, but the idea that moons are a really interesting place to consider.

From our own experience in our system moons are plentiful. There are hundreds of moons in our solar system, which is really kind of amazing. What advantage are the exomoons offering you over an exoplanet in the search for life?

KIPPING: Yeah, I’ll give you my sort of four boilerplate reasons why I always say we should look for moons. One is that, of course, as you alluded, they could be habitable themselves. Two is that they could influence the habitability of the planet they orbit. So you might have an Earth-sized planet, and I think an obvious question is, well, does it have a moon-like moon around it as well? Because that seems like it had a big influence on our history. We probably want to know that. So you’ve got those two kind of habitability aspects.

Then there’s just the pure, like, uniqueness question. Maybe come back down to that more kind of mechanistic astrophysicist view. Just how did we get here? What’s our origin story? Is the Moon like a one-off fluke that just very rarely happens, or is that an inevitable part of terrestrial planet formation, that you end up with these large, almost quasi-binary objects? There’s lots of strange moons, and it’s like Triton goes around backwards around its parent planet. You’ve got Uranus tilted over with its moon system. So there’s lots of curiosities in the solar system that from a singular example, it’s difficult to know, like, really how does this story play out in other environments. So I think just uniqueness is another reason.

And the fourth one is kind of subtle, and that’s thinking about next generation missions. I mentioned we wanna build a successor to James Webb one day, probably called at the moment the Habitable Worlds Observatory, HWO. But it will hopefully one day take a photo of another Earth. It’ll be a single pixel. It’ll be a single blob of light. They’re like the pale blue dot. And from that pale blue dot, we’ll split the light up into a rainbow, essentially like the prism, like Newton did, and we’ll look for those atmospheric biosignatures that we’re so interested in. And moons here can really screw us over.

If anyone’s ever seen that famous pale blue dot image that I think it was Voyager 1 took, as it looked back at, sort when it was like the orbit of Neptune. It turned around, it looked back and took a picture of the Earth. It’s this beautiful image if you’ve never seen it before. And in that image, it’s not a pale blue dot, even though Sagan described it as a pale blue dot. It’s a pale blue-gray dot because the Moon’s in there. The Moon’s right, it’s photobombing right along, right? You can’t distinguish it. You can’t separate it. They’re just one smudge of light.

So when HWO takes these images, it’s gonna be in the same situation. It’s seeing what it thinks is a planet, but it’s really a planet plus however many moons it has. And when we look at moons like Titan. Titan has a methane atmosphere, methane lakes. It’s full of interesting hydrocarbons. You could easily, if you didn’t know that was a separate moon, get confused.

You could imagine having an ocean world, a terrestrial ocean world, where the water undergoes photolysis, and that means that the H2O splits into hydrogen and oxygen. So you’ve got an oxygen-rich planet. No life involved, just oxygen from UV radiation. That’s it. And then you’ve got Titan mixed in there, which has methane.

So now, from the astronomer’s perspective, everything looks beautiful. You’ve got methane, you’ve got ozone, you’ve got oxygen. You’d be like, “We’re done. That’s life.” But it’s a confounder. It’s just something we hadn’t thought of. So that’s why I think moons are really important. I don’t know how we could even look for life with HWO unless we resolve the moon problem.

LEVIN: So can you catch us up to date as to where we are in terms of actually observing, not just theorizing, but actually observing with the satellite missions exo-moons.

KIPPING: So this has been obviously a long quest in my entire career. During my PhD, I came up with one of the methods that we are using today to try and look for these moons, thinking about the dynamical perturbations that a moon would impart upon its parent planet gravitationally. And that’s kind of how we look for planets. We often look for planets by detecting the gravitational influence it has on the star. So we kind of extended that to looking for these moons.

And I think what we know for sure is that Kepler, which as I said, was this transformative mission, had this sensitivity down to about Earth-sized stuff – moons, planets, whatever it. And it really didn’t throw out many candidates. There’s just not a lot there. So out of the 4,000, 5,000 candidate exoplanets, we have just a couple of hints of moons in that entire database. So that already tells you Earth-sized moons are not that normal. I’m not saying they never happen, but they’re certainly not par for the course.

We did find a couple of interesting candidates that I hinted at there, but they both have been very surprising because they’re so large. They are Neptune-sized or even mini Neptune-sized moons orbiting Jupiter-sized or super-Jupiter-mass planets. So nobody really expected that. I mean, reminds me a bit of hot Jupiters, some of the first exoplanets ever found. They’re Jupiter-like worlds but are about 10 times closer to their star than Mercury is around the sun.

LEVIN: Very close.

KIPPING: Yeah, scorching temperatures, thousands of degrees Celsius, on their day side. And so it was very surprising. Actually, a lot of people didn’t believe them. They thought, how could you possibly get Jupiter there? Because we think we know how Jupiter formed. It formed from ices. It formed from essentially the same kind of cometary material that you find out in the distant solar system. So that stuff just wouldn’t be stable close to a star. It would boil off, so you can’t make Jupiter-like planets there.

But we now know they’re definitely real because we’ve just found like so many of them, and it still puzzles us how they got there. We still don’t understand it.

And so we found these two large moons. 1625b-i And then there’s also Kepler-1708b-i. So the b is the planet, the number plate is the star, and then the -i is the moon. Those are the only two we’ve found. Other teams have seen hints in different observations as well. No one yet has like a crisp, clear slam dunk signal.

And I think that’s what we really need. The field’s in desperate need of that kind of clear signal. Obviously, a big thing close to the star is the easiest signal you can possibly get. And I think a general story in astronomy is that often the first examples of things we discover are not typical. They’re often very unusual beasts, and the reason we find them first is ’cause they’re so loud. They’re disproportionate. They’re tail-end members of their population. They’re not representative. And so it wouldn’t surprise me if these things turn out to be real, but they’re still requiring follow-up to ultimately figure out what they are. But James Webb has been opening up a lot of doors for that.

LEVIN: So the Kepler sample you’re talking about is within few thousand light years. So our galaxy’s over 100,000 light years across. So this is still pretty much, as you’ve said, we’re really only probing our region of the galaxy. How is James Webb Space Telescope changing some of this story?

KIPPING: Yeah, so James Webb is not really trying to discover new planets. It’s certainly more than capable of doing so. It’s just that the telescope time is so precious, a better use of its time is to do stuff like look for exomoons. We’ve done that experiment recently. Unfortunately, it came out flat. We looked at this beautiful Jupiter analog planet. It’s really kind of had a similar orbit, a similar star to our own solar system, this Jupiter-sized planet on a nice long orbital period far from its star. We searched it for moons down to about the size of sort of Ganymede, so the largest moons of Jupiter, and we don’t see them. So that’s already, really interesting.

Another experiment we’ve been doing is actually measuring the oblateness of exoplanets, which has never been done before. But you can actually tell whether the planet is a pure sphere, or slightly ellipsoidal—which of course planets really are. They’re oblate spheroids, because as they rotate, they bulge out at the sides. And so they get these kind of love handles, like the Earth has, you know, slightly wider equator than it does the North-South Pole.

And Saturn’s actually pretty extreme. That’s actually quite detectable with James Webb. So it’s such an impressive machine. There’s no need to use it to find planets, ’cause it can really characterize the planets, and especially atmospheres.

LEVIN: Well, let’s talk about atmospheres. We’ve talked a little bit about technological signatures. We haven’t talked that much about the biosignatures. Would that be a reason why astronomers are obsessed with atmospheres, ’cause they’re looking for biosignatures for the emergence of life?

KIPPING: I think we wanna get there. I think a lot of us are dubious James Webb is sensitive enough to detect biosignatures. If you take the Earth, and even if you put the Earth around a very favorable star, so a nearby star, and make it a small star, because the smaller the star is, an Earth-sized planet will block out more of its starlight. And so it’s easier for us then to actually measure these atmospheric signals.

And even in those very favorable conditions, the signal we’re looking for is that the planet effectively appears different sizes at different wavelengths of light, and the wavelengths of light corresponding to, say, ozone absorption, you see the planet puff up a little bit. And what that’s telling us is that there’s a molecule, ozone in that case, that really likes to absorb that wavelength of light and therefore make the planet appear a little bit larger. So we think that’s how you would potentially detect ozone. It’s just that the telescope isn’t quite sensitive enough, unfortunately, to get most of those biosignatures.

We think of things like methane, ozone, phosphine, dimethyl sulfide has been proposed recently as well. There was a claim actually of dimethyl sulfide, maybe some your listeners might know in that using James Webb, but it’s really spectacular levels compared to what we have on the Earth, so a lot of people are skeptical it’s remotely possible that could be a biosignature.

There’s just way too much of it to make sense for certainly an Earth-like biosphere. But there’s a lot of controversy with some of these detections, but I think most of my colleagues think that it’s just beyond the ability of James Webb to detect biosignatures, but that’s fine.

Probably a more basic question you might ask is, do Earth-like planets even have atmospheres to begin with? Or are they barren rocks? ’Cause the Moon doesn’t have an atmosphere, Mars doesn’t have much of an atmosphere, Mercury doesn’t have an atmosphere.

And so there’s a huge program right now with James Webb called the Cosmic Shoreline Program, which is to look at a group of planets which are Earth-sized in the habitable zones of their stars. And the question is whether the planets even have atmospheres, because M dwarfs are quite active. They throw out these huge coronal mass ejections, these stellar flares, and so there is a concern that maybe the atmospheres are gone. Maybe these planets can’t even sustain an atmosphere.

James Webb can answer that question, so that’s what this program’s doing. So it should be able to tell whether Earth-sized habitable zone planets have an atmosphere or not. And that would already be a massive breakthrough.

LEVIN: Amazing. So clearly, if they have atmospheres, the prospects for life goes up, loosely speaking, in that Drake equation kind of a way. Some of these biosignatures, though, are confounding. If you could find the atmospheres, and you were to look for some of these signatures, you’ve mentioned certain elements that we’re looking for, certain molecules that we’re looking for in the atmospheres, because the presumption is that these are outgassings of metabolism presumably or something like that. But we don’t even really know that, do we?

KIPPING: No, I mean, we just have one example, right? The confounders is a really big problem, and I’ve been thinking about that a lot. And what worries me a lot is that when you look at the history of biosignatures, just very broadly there’s been so many spurious claims.

I mentioned very briefly the Allan Hills meteor, which was a rock on Mars 4 billion years ago that knocked off, it landed on the Earth, landed in Antarctica, I think in 1984 or something. And they collected it, they studied it, and they found these, like things which looked like little worms under the electron microscope.

And so that was essentially a biosignature. It’s not a gas, but it is a biosignature. It’s a signature of biology. And it turned out that even though it looked like life, other geochemists and scientists were able to show that you can make structures like that without biology involved whatsoever, just basically through water and high pressure water in particular. And so that really killed the momentum behind that claim.

Another example, if we go really far back, would be Martian canals. Seems silly now, but Percival Lowell—he thought there was canals on Mars ’cause he thought that was a biosignature. He saw these lines on Mars, and he thought, “I know what causes that. It’s a canal system.” So often we are tripped by what we don’t know. It’s not Percival Lowell’s fault that he didn’t know about those psychological biases ’cause nobody had published on them yet.

And a very recent example was DMS, dimethyl sulfide. Dimethyl sulfide was claimed, as we mentioned earlier, in the, in an exoplanet atmosphere recently, K2-18b. Cambridge University did a huge press release talking about this being, you know, a historic moment in the search for life. But we now know that DMS is on comets in the solar system. Unless you think there’s living creatures on all the comets, it seems difficult to believe that this is an unambiguous biosignature anymore. So just time after time after time, it’s like Groundhog Day, Janna. You just keep waking up, we hear these claims of life, and then we all know what’s gonna happen. Happens every time. It just dissolves.

So I’ve been thinking about this really hard recently. And yeah, I do kind of make the case that I think the current approach we’re using just will never work, and we do need to really rethink how we do this.

LEVIN: And have you made progress in suggesting a way that we should do this differently?

KIPPING: Yeah. So my tentative suggestion is to do what I call A/B testing, which in YouTube landscape is something we’re very familiar with. Like, you have two thumbnails, and you challenge them against each other and see which one gets the most clicks. And so the way we do it here is you’d have two samples of planets, for example, and you have some reason to believe this is the condition for this experiment to work. You have reasons to believe that the occurrence rate of life is different. It can’t be the same. If they’re the same, this doesn’t work. There has to be a difference in the life occurrence rate. But the confounder rate—how often natural geochemistry or whatever it is producing ozone or whatever signature you’re looking for—that has to be the same.

So the confounder rate’s the same between the two samples, but the life rate is different. And so really then you’re doing a differential measurement. Any difference you observe in biosignatures between those two populations, therefore, in a differential sense, has to be due to life.

It doesn’t tell you how much life there is in an absolute sense. You still don’t know, but you know that that excess must be driven by life. So that statistically is very clean. It resolves a lot of these problems and these unknowns. But you might reasonably question whether it’s even possible to set up such an experiment, and that’s what I’m thinking about now.

LEVIN: Amazing, so again you’re kind of returning to those statistician’s roots, right? That the observations aren’t going to be one moon with one obvious signal. It’s more large samples, and large statistics.

KIPPING: Yeah, I’m skeptical it would be a slam dunk in the same way maybe we’ve had with other fields. To quote Donald Rumsfeld, it’s the “unknown unknowns” that get you, right? And so there’s so much we don’t know about chemistry and geochemistry and other planetary environments that it feels like we are doomed to always be caught out by those things.

I think the only exception to this I can imagine is actually a really strong information-rich SETI signal. So if it was like a laser beam with a video transmission encoded within it, there’s just no plausible natural confounder to that. You just can’t imagine it. It just seems impossible.

But with biosignatures, those gases are very information weak. Really, all you measure is that gas is there and an abundance maybe, if you’re lucky. And that’s about it. So it’s that informatics perspective, I think, that really endangers biosignatures. They just don’t carry a lot of information to begin with.

LEVIN: So, how do you place yourself in the optimism-pessimism spectrum? Are you searching for life scientifically because you believe that this is a viable result within your scientific lifetime? Or are you more, “I’m interested in planets and moons from the aspect of astronomy, regardless of the discovery of life?”

KIPPING: I’d say I’m hoping and I’m more interested in the idea of life. That is a great dichotomous split I think that you just gave there, and I think a lot of astronomers are driven by how does the universe work or are we alone? And those are like two very basic drivers to a lot of astrophysicists in different ways. I mean, I’m interested in both, but I’d say I’m probably more driven by the latter.

However, am I an optimist or a pessimist? I’d honestly try to be, it’s a little bit of a cop-out, but agnostic and forcefully agnostic because I’m so terrified of experimenter’s bias. And we’ve seen this so many times in history of scientists even claiming life, claiming this comet is an interstellar ship, claiming this little rock on Mars is a face, claiming this fossil from the Allan Hills meteor—Bill Clinton stood on the White House lawn and talked about that as evidence for life on Mars, and now nobody believes it.

So many times we’ve got caught up in that excitement of optimism, and I think the lesson for me has always been like just try and remain sober. Just try and look at it objectively and require those high standards of evidence that we apply in all other aspects of our science. It is not different when we look for life. So I try to remain objective, and I think honestly, it is perfectly consistent with everything we know about the universe that we are alone. There’s nothing we know about the universe that rules that out. It is within the realms of possibility.

LEVIN: Well, given that we’re alive and we’re here and we have the luxury of looking deep into the sky, what is it about this exploration that makes this the way you wanna spend this precious life that we have?

KIPPING: For me, it’s very much just curiosity-driven. It’s just these are the things I’ve always wondered about life in the universe, what else might be out there. I’ve always dreamed of visiting other stars and seeing their planets. It’s just that pure very simple curiosity-driven fascination with what’s out there. And I think if you don’t have that life can feel a bit empty, at least for me.

Like, I always get a little bit depressed when we’re asked sometimes as scientists to defend the technologies or industrial applications of searching the universe for gravitational waves or something. Sure, there is many side benefits, and we can list those off. But in a very pure sense, the reason for doing it is the same reason why we do poetry. It’s the same reason why we do art. It’s that, what is the point of being on this Earth if our sole interest is bread on the table, feeding myself, going to sleep, waking up the next day, going back to work, and that’s your whole life? It’s just this pure machine-like process.

We’re more than that, I believe. And I think looking out and wondering about the universe, it enriches our soul, enriches our human nature. I would hate to live in a world where we didn’t ask these questions. And I think it’s a real privilege, certainly, that I’ve had a career where I’ve been able to dwell on some of these questions and think about them so much.

LEVIN: Such a pleasure to talk to you and to share your stories and your insights and your ideas about the future of discovering whether or not we’re alone. This is really a delight. Thank you so much.

KIPPING: It’s always a pleasure, Janna.

[Music plays]

STROGATZ: Well, I want to agree with that. I have often tried to make that argument myself about enriching our soul. But there’s very natural reaction to have to that, which is we fund—or at least we used to fund science—but we don’t really fund poetry. You know, why should the taxpayer invest in science if it’s another form of poetry?

LEVIN: Yeah. And what do you think the answer to that question is?

STROGATZ: I think it’s much more than poetry. It’s at least it’s very different from poetry. It’s partly poetry. It’s many things. I mean, it’s a really serious question, especially in the age of artificial intelligence, where so many of the things that we’re doing, we have to ask why are we doing them. I don’t know. Yes, part of it is for soul enrichment, part of it is for helping future technology or helping, you know, new medicine or improve the quality of life of all of us. I want all of it. I don’t know. What do you think?

LEVIN: Well, I would say, that it obviously really resonates with me what David’s saying, but for a reason that I think is also transformative for humanity. If you think about the shift with Copernicus from thinking we’re at the center of the universe to understanding and comprehending that we are not, that has untold implications, consequences, ramifications for the entire paradigm of civilization, and what we’re doing here and how we handle each other.

And so I think it can both be the dreaming blue skies approach and have implications for the future of humanity. I think Earthrise is a very good example of that. Looking back at the Earth as it rose over the moon in the Apollo missions initiated environmental movements. It really gave people a strong sense of connectivity on the Earth and kind of the limitations and evils of tribalism. So it changed culture, right? It changed civilization. So I think we can do both those things.

STROGATZ: Hmm, I like your answer a lot, that it gives, that this cosmic perspective as someone like Carl Sagan might have called it, maybe he even used that phrase, gives us a kind of humility and maybe makes us better people. You know, and if, as you say, like when we’re talking about alien civilizations, that our whole civilization is a blip in time, each of our individual lives is an even shorter blip in time, and why not be as good as we can be for that blip?

You know? I mean, this, here we’re getting into theology and ethics and all of that, but maybe science, which is often seen as somehow separate from all of that, is really a very good teacher about how to live ethically.

LEVIN: I think it is. Yes, And I think about how to cooperate internationally, how to transcend belief systems and trappings of nation and faith and, and to instead view ourselves as one species playing out on this one place. Together. Well, on that note, man, yeah, I, I need to go meditate.

STROGATZ: Okay. Ommm.

LEVIN: Yeah, exactly. I need some universal transcendence, yeah.

[Music plays]

STROGATZ: If you’re enjoying The Joy of Why and you’re not already subscribed, hit the subscribe or follow button wherever you’re listening. You can also leave a review for the show. It helps people find this podcast. Find articles, newsletters, videos and more at quantamagazine.org.

The Joy of Why is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests, or other editorial decisions in this podcast or in Quanta Magazine.

From Quanta Magazine, Simon Frantz and Samir Patel provided editorial guidance with support from Samuel Velasco, Simone Barr, and Michael Kanyongolo. Samir Patel is Quanta’s editor-in-chief.

The episode art is by Chanelle Nibbelink and our logo is by Jaki King and Kristina Armitage. Special thanks to Garth Avery at the Cornell Broadcast Studio.

I’m your host, Janna Levin. If you have any questions or comments, please email us at [email protected]. Thanks for listening!

[Music fades]

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