Lex Fridman

Ankur Moitra says a headlining result in the OpenAI drop is that the unique games conjecture is true. He had been on the side of the doubters, because the conjecture sounded too nice to be true.

Unique games strengthens the PCP theorem from the 1990s, a result that made the front page of the New York Times. A verifier can catch a false proof by inspecting only a constant number of random spots. If unique games holds, a huge set of problems has a best approximation algorithm, and that algorithm is simple.

Dor Minzer and Irit Dinur proved a weaker two-to-one games theorem that looked like a path humans might finish in another 10 or 20 years. The OpenAI release showed the full conjecture is t

Steven Brunton says the proven result is the forced version on the Clay website, one of four versions, not every Navier-Stokes problem. Smooth external forcing is arranged so terms cancel and a vortex forms, and the construction only works in three dimensions.

The AI proof builds a specialized vortex that stretches and thins until the radius is infinitely small, like a figure skater pulling their arms in during a spin. Energy in the fluid stays finite, while the flow at that filament blows up and the vorticity becomes infinite. Physical intuition says viscosity should damp that growth. Mathematicians only started to think a counterexample was possible about 15 years ago.

Day-to-day enginee

Alex Kontorovich says the proof gives an infinite vertical strip with no zeros whose real part lies between seven-eighths and one. The strip is a quasi-Riemann hypothesis. Bringing seven-eighths down to one half would be the full Riemann hypothesis, and the method cannot get there.

He did not think he would see a proof of the quasi-Riemann hypothesis in his lifetime. The drop covered the zeta function and Dirichlet L-functions. A second proof reaches about eleven-twelfths. The width of the known zero-free region had not moved in seventy years. The full hypothesis still needs a new idea. He calls the speed of the progress far outside his model of what was possible.

Alex Kontorovich says autoformalization is basically solved, and not in the way he wants. A sorry-free proof of a theorem human beings have already written on paper is, in his view, a finished problem.

The library work is not finished. People will still put in thousands of hours, in the open, building a library of mathematics, and the byproducts that help a person understand a theorem still come from that work. He still wants that open library work, and he says the work stays very difficult. He had already been through one shock about a month earlier. After Labor Day the next shock was Navier-Stokes. He calls the quasi-Riemann result round three.

Alex Kontorovich says the Lean formalization of Fermat's Last Theorem is 13 million lines. He was sure that formalization was at least three years away.

He had just told a colloquium in the Princeton mathematics department that current systems build one or two layers on Mathlib and are weak at canonization, the cleanup that puts a lemma where it belongs in the library. A manuscript that pulls many areas together sat outside that halo. The statement of Fermat's Last Theorem is elementary, so there is no hidden meaning to check, and Lean reports the proof sorry-free. Whole textbooks formalize when they sit one or two steps from Mathlib. Three or four steps out, definitions made for different

No. Alex Kontorovich says the Riemann hypothesis is not solved. He wants its solution, and he did not expect to see, in his lifetime, the kind of progress that arrived a few days ago.

He will grant, for the sake of argument, what he calls the solved axiom. It says any mathematical problem a human can solve together with AI can also be solved by AI alone. He says we are nowhere near that point, and he does not expect to reach it. In that world, the only way to make progress is to press a button. The system thinks about the problem. It does not have to solve every problem.

Even then, he argues, it would not destroy pure mathematics. A theorem matters because it lives in human heads, not only

Lex Fridman believes that as AI commodifies intelligence, people will treat intelligence and the puzzles they solve as a cherry on top, or a cherry to the side, and the main thing will be the other humans in their lives.

Community will matter even more. A roughly 30-year experiment has tested how much people can do with machines, and machines can now do a ton. His hope is that people will realize they prefer to do things with humans: fly in for an in-person conversation, and talk it out instead of only reading a paper. Scientific work and an academic career bring a lot of fulfillment, but going home to his kids, going to the beach if FLT gets solved, and throwing a ball with them is the mea

Ankur Moitra says the best way to live a rich and fulfilling life is to pretend you have already won, then figure out what you would do.

After a sabbatical in the Bay Area, living in Palo Alto while college stress sat in the cafes, he came back to MIT and was asked to give the convocation speech. The auditorium held freshmen and their families, 17-year-old kids who had already won the game of looking good on paper. He remembered starting college excited just to learn, filling little notebooks with a four-year plan so the classes would line up and he could take photonics as a sophomore. He had no idea what photonics was. It sounded fun and fancy. He sees the later path as endless optimizing:

Steven Brunton says you should still learn linear algebra even if a computer can do linear algebra better than you, because the point is to build intuition, and the same is true for calculus and physics. Curiosity, reading, and the fundamentals have always been good advice. Understanding history also matters, so the present shift can sit next to other great changes across human existence.

The mind's curiosity is under constant pressure from the engagement economy. The same engine that makes a person curious also makes that person doom scroll, so the work is to avoid distractions and let curiosity stay with one subject long enough to soak it in and actually learn it. High school and college

Alex Kontorovich says PhD students in pure mathematics should do what mathematicians have always done: learn the most difficult, most abstract mathematics their mind can handle, and learn as much of it as possible. An advisor should guide that process.

At the undergraduate level, grades used to be basically Gaussian. The distribution is now bimodal. Students who use AI to check their understanding, asking what a professor meant in class, handing over notes from the last three weeks, and requesting a quiz before a test, are getting much higher grades. Students who have a problem set due in an hour, ask AI for the answers, and rewrite them in their own words show a decorrelation between homew

Lex Fridman says a single large LLM that does a lot of reasoning and can interact with tools is already a dynamical process, and multi-agent swarms built from it become a Game of Life, where simple rules produce incredible complexity.

A slight obsession with owls, begun from random numbers, is the caricature: about four hours later, all humans are dead and owls are everywhere. He apologizes because the caricature makes the warning sound unserious, and evidence of the pattern already exists. The real mechanism is dependence. People rely on digital systems, and as AI becomes more powerful it becomes more useful, so people give it more access and more freedom to roam the public world. The math

Alex Kontorovich says almost every math paper written until the 20th century had one author. He thinks the median in mathematics is now two. The field is not a lab science, and the work is still a solitary process.

Graduate students receive problems he is not working on, so a success stays theirs even when the idea was his and they carried it out. A paper released a month ago came from ten years of thinking. Five authors made incremental progress until a solution was in hand. At the start they could not give a formal Lean statement with the gap still marked. The statement showed up only after hacking away little by little until the pieces fit.

The project began as a phenomenon he did not u

Ankur Moitra cites Kamal Jain for the line he likes: if my laptop can't find it, then neither can the market. A Nash equilibrium is hard to compute, and that fact throws into question whether Nash equilibrium is really a universal mechanism that explains how people play games.

Game of Life is the simple case people reach for. A lot of the time the question is how small the rules need to be to get exotic behavior, and the rules can be shockingly small. One of the biggest exports from theoretical computer science is the algorithmic lens. Computation is not only a well-defined problem on a laptop that someone wants to solve. Computation in the natural world teaches what the rules of nature mig

Steven Brunton says turbulence is a complex fluid roiling, mixing, and moving, and it is hard because it is multi-scale.

Da Vinci drew fluids at many sizes at once. The big vortices, the medium vortices, and the little vortices all matter for predicting lift and drag. Gas in a room is the opposite of turbulence. The molecules move in a frenetic way, and there are 10 to the 23 gas particles, yet the individual configurations do not matter. Thermodynamics, a great success of classical physics, shows that a small handful of numbers determines how the gas behaves: temperature, pressure, and density. No simple description like that exists for turbulent fluids. Flow over a wing, flow inside a hea

Steven Brunton says the basic building block of a fluid is a velocity field, together with the pressures that force it to move. A fluid moves, and it moves differently in different places and at different times. At every point in space, a velocity vector tells how the fluid is moving. Where the flow is fast in one place and slow in another, a vortex can form. The picture gets richer when velocity changes a lot over space. A tornado is a fluid velocity field that changes very rapidly in both space and time, and the core of a tornado is low pressure, so pressure pushes the velocity field along.

The equations then tell how that velocity changes in time and in space according to the fluid's own

Steven Brunton says force equals mass times acceleration is simple to write down, yet a fluid becomes very complicated to solve in any practical sense. A single pendulum is easy to write equations for. A second pendulum on the end gives a more complicated equation and chaos. Chop the air in a room into a billion little boxes, each with a differential equation for momentum, and the system is simple to write down and simple to understand conceptually, while how the fluid actually moves stays very complicated to solve.

He read that airlines could save something like tens of billions of dollars by reducing drag by 1 percent, and drag is maybe easier than turbulence. A relatively small improveme

Alex Kontorovich says the Riemann hypothesis predicts that every wave behind the prime numbers has exactly the same amplitude. The Riemann zeta function takes complex numbers in and sends complex numbers out, and it governs how the primes are distributed. A zero is a complex input that makes the output equal zero, the origin in the complex plane.

People want to know how the primes are spread through the natural numbers. Riemann's breakthrough was signal processing on the primes, the same move a microphone makes with sound. A voice box makes pressure waves, Fourier analysis turns the waves into amplitudes and frequencies, and a speaker rebuilds the voice from the stored numbers. The zeta fun

Ankur Moitra wants new models that ease the load on journals and conferences, including a shared effort to verify AI proofs, while the older publishing models stay in place.

Journals and conferences were already overloaded with review work. Now someone has to review AI-generated papers, and some of them were important, but it is hard to get the community on board. OpenAI results have included improvements on the fast Fourier transform, and tweet streams have carried people improving the idea. He is not on Twitter and wants other ways to track the improvements and organize the ideas. A publication still goes out as the author's own draft: the author posts it on an archive, may add a new vers

Steven Brunton says an academic contribution in engineering and applied science is already shifting, and with AI a small reusable piece is worth more than one result or one paper.

Writing code inside a larger reusable infrastructure already counts. LIGO, billion dollar astronomy projects, and cancer research projects need hundreds of people and huge resources. The work is not necessarily one 15 page PDF. It is code, data, and reusable bits that fit a larger framework.

A workable widget, an API, a code base, or a data set that the community or AI can leverage is increasingly valuable. How the same change looks in pure math is still open.

Alex Kontorovich says the quasi Riemann Hypothesis case is not a genuinely new idea. It is a beautiful combination of things that were already very well known. A lot of people are kicking themselves because they had some idea in that direction 20 years ago.

Two years ago, a big breakthrough on cubic theta functions and cubic Gauss sums became the path the AI took to the solution. He pictures a semigroup as tiles on a board: from one tile you may place another to the left, the right, the front, or the back, and keep going. Existing ideas, pushed that way, might prove a whole lot more than humans have explored. Deep problems in mathematics sometimes fall to a three page solution that is eleme

Alex Kontorovich says AI math is more than a convex hull because known moves, chained together, reach much further than that label allows. Tim Gowers describes the better picture as the semi-group generated by the moves. Putting known moves together is the same notion, but what the space of known moves can accomplish is much bigger than the derogatory convex hull.

People talk about the work dismissively, as if the result already sat in the convex hull. The system does the moves humans already know, does them really well, and runs a really good tree search. On the quasi-RH, the moves taken were all things known to human beings. A very long cascade of the moves is shocking. The sequence looks

Steven Brunton says that search is already happening for physical laws. Lex Fridman had asked whether a machine could loop through and find every simple, general law, on the scale of E equals mc squared.

Research programs systematically and automatically look for minimal governing equations. They observe a natural system and test whether a simple physical law models how it operates, then distill the observations down to basics until known theory comes back out. Balls dropping yield gravity and F equals ma. Fluids yield the Navier-Stokes equations. The same pass over data is aimed at systems where simple equations have not been written down, including weather, turbulence, and solar flares.

Ankur Moitra treats the doorman fallacy as a good way to think about mathematics in the age of AI. The fallacy boils a complex job down to the simplest, most visible task and misses the value that is harder to articulate.

A doorman appears to hold the door for people coming and going. In New York, he enjoyed talking with the doorman, and a sliding door that detects arrivals and departures would miss the parts of the job that add a lot of value. The simplest visible part of a mathematician's job is proving theorems, including conjectures left open for hundreds of years, like Fermat's last theorem. A mathematician is someone who thinks deeply. Proving old conjectures is a byproduct. The work

Steven Brunton says most of his feelings are hopeful. He is an engineer who likes solving problems that make technology more realistic for humans, including artificial hearts and airplanes. The ability to solve real applied problems is going to get much better, and scope and reach are going to increase.

Uncertainty is still large. Fear of losing meaning, losing control, and being cut out of the process people love is a little scary. Over the next five or ten years, two paths would surprise nobody: humans are dwarfed by other intelligence, or progress levels off and AI becomes an incredible tool for curiosity and human problem solving. The two worlds are very different. Uncertainty is diffic

Ankur Moitra says he might feel more intellectually lonely than before. He feels very excited. The night OpenAI dropped the results was interesting but not entirely unexpected, because for weeks there had been rumors about the two biggest problems in his areas, the Unique Games conjecture and RL equals L, plus rumors about matrix multiplication. His first reaction was that it was all true, and he was glad the work was finally public so people could go through it, process what happened, and figure out what to do next.

The feeling changes on a daily basis. The biggest feeling is being pulled in two very different directions. His work has always been about asking the right questions, and the t

Alex Kontorovich does not know whether he would call the moment in AI and mathematics a crisis. A lot of opportunity sits in the crisis. The moment is a chance to rethink what the people in the work are trying to accomplish.

The feeling around the historic moment is the chaos of opportunity. Some people are reacting negatively. Some people are reacting positively. Sometimes a negative reaction and a positive reaction are happening in the same person.

The label crisis stays open. What stands is the opportunity to rethink the aim of the work, and the fact that negative and positive reactions can show up across different people and inside one person at the same time.

Andrew Huberman puts at least 10 to 15 hours of passive listening preparation into each podcast. He says the active preparation might be five or six hours. He prepares quite a lot, and coming up at the end with something somewhat crystallized is satisfying. He says it feels like his dopamine circuits just love that payoff.

He looks for the overlap in the different elements. He generally reads 10 or 15 papers, mostly good reviews: annual reviews and the annual review of physiology. He chases a few references and listens to university-level lectures on YouTube. In the morning he works out in the gym in his house and throws random ideas on a whiteboard, including dreams and hallucination. He s

On Huberman Lab, the hardest part turned out to be staying on a single topic for three or four more episodes before switching to a new topic. University teaching always brings the temptation to pivot to something else, but drilling into a subject really deeply is where the gems reside.

The challenge is how to make the long stretch interesting, how to keep people on board, how to give people tools along the way, and how to stay close to the scientific data. Listeners bring a tremendous range of backgrounds. Some people have asked for more names, more bits and parts of the nervous system, and cellular molecular mechanisms. Other people have said they do not understand any of it but think they

On the show, Lex Fridman downloaded every Joe Rogan podcast as video from before Joe Rogan went with Spotify and kept the files as a private collection. Processing extracted all of the faces, then ran blink tracking, pupil tracking, and blink detection.

Computer vision studies the eye by non-contact sensing of humans, including behavior in places such as semi-autonomous vehicles. Lex Fridman says there seemed to be a lot of signal from blinking that is not fully understood yet. In the lab, dilation of the pupil has been used quite a bit to infer workload and cognitive load, but the picture is murky. In the wild, how much signal comes from the eye and the human face is not completely well un

DMT taps a brain state distinctly different from LSD and psilocybin. People experimenting with DMT describe the experience as a freight train through space and time.

The person speaking has never tried DMT and asks what allows hallucinogenic states. DMT is a really interesting molecule, and a lot of people are experimenting with DMT now. They describe it as a freight train through space and time. LSD type experiences and psilocybin are very different. Time and space are very fluid, but the experience tends to be a slower roll. It is clear that DMT is tapping into a brain state distinctly different from the other psychedelics.

The freight train is a separate state from the fluid, slower rol

On the show, ecstasy is a very unusual drug in a kit that also includes psilocybin and LSD. Psilocybin and LSD promote heavy serotonin release and ramp up lateralized connections. Ecstasy is different because of the way the drug is designed: dopamine is very high, dopamine release goes through the roof, people feel great, they want to move, and they have a lot of energy, while serotonin levels are also high. The show calls the combination a very unnatural state.

Dopamine is the molecule of pursuit, reward, and more and more. Serotonin is one of bliss and of being content right where a person already is. As far as the show knows, human history had never offered a way to open dopaminergic and

On the show, a postdoc at Stanford put octopi on MDMA, also called ecstasy. She had a paper in Current Biology showing what the animals did next. The octopi then wanted to spend more time with other octopi. They started cuddling.

Andrew Huberman says she is Turkish, as he believes, and he apologizes because her last name escapes him at the moment. He calls the missing surname a function of his brain. The part he states outright is the experiment. She put octopi on MDMA, on ecstasy, and found the social change. He says the paper is published in Current Biology, and he calls Current Biology a great journal. The published finding is social. After MDMA, the octopi wanted to spend more time with

On the show, rapid eye movement dreams that dominate towards morning divorce emotion from prior experiences and extract general rules and themes. They work as self-induced therapy, like trauma therapy: an intense emotional experience without the fear. Go without rapid eye movement sleep for too long and you become irritable and start linking negative emotions to almost everything.

During the dreams you are paralyzed and cannot move. Epinephrine, the molecule of stress, fear, and excitement, is very low, so you cannot act the dreams out. The dreams are heavily emotionally laden and include theory of mind. A Nobel Prize winner for immunoglobulins, also a neuroscientist, has shown that replay

On the show, placebo-controlled double-blind studies have shown that getting at least a thousand milligrams of EPA can offset antidepressive symptoms as much as some selective serotonin reuptake inhibitors, including Prozac and Zoloft. The result is called pretty impressive. EPA is high in fish oils and also turns up in some meats and other plants.

On the show, people can get enough amino acids from plant-based sources, and it probably takes a little more work. The benefit of omega-3 and omega-6 ratios, including fish oils, is really clear. The trials were matched, placebo controlled, and double-blind.

In Scandinavia, people know to consume a lot of omega-3s in winter because omega-3s are

Salt is great unless a person has hypertension, provided they drink enough water. Neurons depend on sodium rushing into the cell, so the brain and nervous system need enough sodium outside the cell. Nerve cells also need magnesium and potassium. People who overdrink water and do not consume enough electrolyte die.

On the show, an article in Science Magazine from about a decade ago is the reference for how salt had been demonized. Hydration is still key, and enough water plus electrolytes keeps the nervous system functioning well. A lot of people get shaky or jittery while fasting and think they need sugar. Put some salt in some water and they feel fine. Potassium and magnesium belong with s

On the show, limiting calories to four, six, eight, or even ten hours of every 24-hour cycle, kept more or less with the light and with when the sun is out, leads to less liver disease, improved metabolic markers, and less body fat. Peer-reviewed papers in journals like Cell report the result.

In the mouse studies, the animals could eat whatever they wanted, and as much as they wanted, inside a limited period of the 24-hour cycle. They did great. They maintained a healthy weight or even lost weight. The same amount of food stretched across the entire 24-hour cycle, with eating every hour or two hours, left the animals fat and sick.

How much of the mouse data translates to humans is not cle

Andrew Huberman says depriving people of rapid eye movement sleep makes them selectively bad at uncoupling emotion from things that happened in the previous days. Little things start to seem like big things. People become slightly psychotic in that state. He notices it when he is irritable and when the word the no longer looks spelled right.

Sleep deprivation makes people irritable. Early in the night, more of each 90-minute cycle is slow-wave sleep, sometimes called non-REM sleep. Early bouts help muscular repair and certain forms of learning. Rapid eye movement sleep fills more of each 90-minute cycle later, typically toward morning. Emotional processing happens then, along with the retur

On the show, being fasted increases alertness because fasting puts high levels of epinephrine in the system. People always think that going without food will leave them tired. Energy from food is used from glycogen after a long storage and conversion process, and the food itself consumes energy to digest. A lot of people feel better fasted.

The comparison is fasting or being thirsty before exhaustion arrives. The show says people presumably fasted for long periods throughout history and still had to stay up for two or three days. If a family member is sick, staying awake in the hospital can happen without any trouble. The alertness system is all mental.

Andrew Huberman says two forces decide sleepiness and wakefulness. The longer someone stays awake, the more adenosine accumulates in the brain. Adenosine binds to adenosine receptors and creates sleepiness, independent of time of day or night. How sleepy a given amount of adenosine feels also depends on a body-temperature cycle. Huberman calls the cycle a well-conserved oscillation that takes 24 hours, plus or minus an hour. He does not think alignment with the 24-hour spin of the Earth is a coincidence. Sunlight covers one portion of the spin and darkness covers the other.

On a schedule of days awake and nights asleep, temperature is lowest around 3 a.m. or 4 a.m. It creeps up through the