OpenAI’s Navier–Stokes Claim: Is This What AGI Looks Like? with Emad Mostaque

Did OpenAI just solve Navier–Stokes—and what would that actually mean for AGI? Emad Mostaque joins Brian Keating LIVE to examine the claimed breakthrough, what would count as a verified solution, and whether AI solving a major mathematical problem changes the debate about intelligence—or control. Watch my explainer about AI and the Navier-Stokes problem, including insights from Terry Tao https://youtu.be/je9X59psm6U?si=wGbcLhXmf47jeCHL?sub_confirmation=1 A convincing answer isn’t necessarily a proof. A mathematical breakthrough isn’t automatically AGI. But if this claim holds up, how much should we update our expectations? Emad helped bring Stable Diffusion to the world and signed the letter calling for a pause on frontier AI development. In his previous conversation with Brian and AI safety researcher Roman Yampolskiy, he questioned how such a pause could work—and highlighted swarm intelligence as a particularly dangerous and unpredictable risk. Now we return to the question underneath the excitement: if AI’s capabilities are accelerating, is our ability to understand and control them keeping up? ON THE TABLE: • What exactly is being claimed about Navier–Stokes? • What separates a proposed solution from an accepted mathematical proof? • If the result holds up, does it demonstrate AGI—or something narrower? • Can AI produce discoveries that humans struggle to verify? • What would this change about open-source AI and the argument for a pause? • Are we watching the wrong risk: a single superintelligence, or swarms of AI agents? • What evidence would change Emad’s mind? Bring your questions. We’ll examine the claim, the evidence, and what follows if it’s right. This livestream discusses a claimed result; it does not assume the Millennium Prize Problem has been resolved. FEATURED GUEST: Emad Mostaque on Twitter/X: https://x.com/EMostaque I. I. I. Inc.: https://ii.inc/ Stable Diffusion / Stability AI: https://stability.ai/ Get the transcript, fascinating bonus content, and my Monday M. A. G. I. C. Message: https://briankeating.com/yt Have a .edu email and live in the USA? Claim your meteorite: https://BrianKeating.com/edu Subscribe: https://www.youtube.com/DrBrianKeating?sub_confirmation=1 Support Into the Impossible on Patreon for unfiltered bonus content and live monthly Office Hours: https://www.patreon.com/drbriankeating Join this channel for perks, monthly Office Hours, and your name in the Member Roster: https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw/join MY BOOKS: Losing the Nobel Prize: http://amzn.to/2sa5UpA Think Like a Nobel Prize Winner: https://a.co/d/03ezQFu Focus Like a Nobel Prize Winner: https://a.co/d/hi50U9U Galileo’s Dialogue audiobook: https://a.co/d/iZPi9Un CONNECT WITH BRIAN: Twitter/X: https://x.com/BrianKeating Substack: https://briankeating.substack.com Blog: https://briankeating.com/blog Audio-only: https://briankeating.com/podcast #OpenAI #NavierStokes #AGI #EmadMostaque #ArtificialIntelligence #BrianKeating #IntoTheImpossible Learn more about your ad choices. Visit megaphone.fm/adchoices

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:02Speaker 00

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• 1:00Brian Keating?

  Welcome, everybody. We have an emergency podcast. I don't do many of these. It's not entirely clickbait to say that we have an emergency situation going on right now in the deep annals of mathematics, the foundations of mathematics. And there's no one I'd rather talk to about this than my friend Ahmad Mustak, who's joining us all the way from London. How are you, Ahmad, on this late evening for you, or early afternoon for you, whatever the case may be? I can't do the conversion too early for me.

• 1:29Speaker 03

  Yeah, it's a bit off and in. I'm feeling a bit sleep deprived after the excitement of the last 24 hours or so.

• 1:34Brian Keating?

  Yeah, it hasn't even been 24 hours. It's been 21 hours. I looked at the timeline. I've looked at some of the constraints and the complaints and what people are saying about it. So this is exciting. So we're going to talk about OpenAI's claimed solution to one of the millennium problems, which has lasted since the, I would say, the early part of the previous millennium, when the Clay Mathematics Institute has provided a gauntlet of challenges for mathematicians and other assorted geeks and dweebs and nerds to go through. Some of them impossible seeming, some of them quite possibly solved already. So today, we're going to talk about the Navier-Stokes equation. I should say, I put a link below to a video I did yesterday.

• 2:17Brian Keating?

  I actually recorded it a long time ago with Terry Tao's thoughts, some of his ideas that he had convinced me of, about how AI would approach this very situation. This is one of his fields, many, he has many fields of expertise, but this is certainly many, one of them. And that was the blow up or singularity in a finite time of these very interesting equations that are governed by very simple laws of physics. And I thought we'd start off with what your take on the Navier-Stokes equation is, maybe some of the applications to it, although you are a, you know, much more theoretically inclined than certainly even I am. But, but maybe you can break it down. What is the Navier-Stokes equation? And what was your first reaction when you heard this yesterday? For me, it was like a Pig's Bozon-like moment. You know, I woke up the kids.

• 3:02Brian Keating?

  I went into my research group meeting and, and my, all my students and postdocs were so excited about it. But what does it mean to you? And first off, what is it?

• 3:13Speaker 03

  Yeah, so we have the, it's been a terribly exciting day. We have the Navier-Stokes fluid equations governing fluid dynamics in the real world, as it were. So kind of our decider-type world. And this specific group of equations is

• 3:30Speaker 03

  compressible fluids in R3. So as you're heading towards a Galilean, kind of more classical world, heading towards a continuous limit, will fluids move normally? Or do you get blowups or singularities, where it can suddenly start accelerating? And then you just have a cup of tea blowing up, shall we say?

• 3:49Speaker 03

  This is true to be an incredibly difficult one, and you know, Terry Tao and your podcast went into depth on this, whereby we didn't know, and we don't know what the solutions were. So the Clay Prize was for one of four different solutions, A, B, C, D, two of which are can you prove that it's always smooth, either normally or on a torus? And then two of which are can you show the existence of a blow up? And so Terry Tao, in his kind of, I believe, main doctorate paper, showed that if you slice time, you can basically chain together a blow up in a very original way. And it's a beautiful kind of piece of mathematics, like 24 pages. But nobody's quite managed to get to

• 4:33Speaker 03

  a initial datum that blows up. People have tried different things. And they've gone to Euler equations, and they've shown some evidence there. And we'll get to the story of what happened here, as we find out more of them. They've tried to do things like physics-inspired neural networks. So DeepMind were really having a massive team looking at that, that moved to a bit more analytically. And in fact, there was another release yesterday about that. But this was considered to be a very hard, somewhat intractable problem, until it wasn't. Like, and then yesterday morning, we found the first details that there might be one solution to it. And then as the day came on, we found more and more extraordinary things, until OpenAI released the full details

• 5:16Speaker 03

  of how they managed it. So I think I've gone on for quite a bit of time now. We can talk about some other aspects of it.

• 5:21Brian Keating?

  Yeah, so, I mean, these are problems. They don't quite rise to the level of fame of, you know, say, the Fermat's Last Theorem. But this one in particular is quite important, because it's one of the few that actually relate to, you know, physical observations that could be made. And in fact, the non-observation of what you said, these blowups, you know, you're not drinking your, your proper British tea, and, and all of a sudden, you have to worry about, you know, kind of a WMD going off in your cup. But in this case, you know, and many of the other millennium, you know, prize challenges, say, they're not as, you know, practical at all. I mean, some of them, you know, would be recognizable to the, to, you know, people hundreds of years ago.

• 6:05Brian Keating?

  From a physics perspective, this one's important, because the Navier-Stokes equations were generated maybe 200 years ago, you know, 100 years before the Clay Prize, the Millennium Prize. And they really rely on simple physics, you know, Newtonian physics. It's not like quantum mechanics. We're used to hearing singularities, which, you know, means blow up. And we talk about black holes, or the, you know, how the bread gets buttered here around the Keating House, which is, which is in the Big Bang, you know, which my, my friend and your fellow Oxfordsian, Sir Roger Penrose, did so much great work on. And so the Oxonian, that's right. And the, you know, the question that I have is, you know, why is this one so important? Or is this one just the first among many?

• 6:49Brian Keating?

  And then, you know, likely, every single millennium prize will get as famous?

• 6:54Speaker 03

  So, you know, we've only had one solved so far. We can come back to that of these seven prizes. And they are very different in their natures. P equals NP is the big one in terms of, you know, you solve that, you can solve just about anything. But this one's very interesting, because fluid dynamics is used so much. And I think it's so much having a solution of a blow up that is interesting, because they've only, again, there are four different things you can prove. They've proved two of them, and they've proved an existence proof. It's more, I think, the techniques that were being built up to do this, and that are enabled by this. So Terrence Tao, for example, talks about liquid computers as one mechanism for doing this, you know? You have tiny little liquid computers that can chain together to do that.

• 7:39Speaker 03

  That's a very promising thing for nanobots, for example. Again, physics-inspired neural networks have direct applications in the fluid dynamics, and the algorithms they're building for that. So I think that there is the prize itself, which is fantastic, you know, we figured out. But then there's the route to the prize. So Gregory Perlman, who, you know, solved the Ponkeri conjecture, did some really interesting things. It was meant to be a topology problem. They showed it as a physics problem, kind of carving out all of these tiny, like, unstable elements. And it was some beautiful mathematics doing that. And I think for a lot of these challenges, it is just, what is the different way of looking at things? Like, we've been stuck, for example, in physics on the Yang-Mills Mascap problem, you know?

• 8:23Speaker 03

  And the question is, like, if we can figure that out, then you can figure out a lot of stuff around quantum electrodynamics and kind of other things there. For Navier-Stokes, I think it's the class of understanding of fluid dynamics that's unlocked by looking at this, as opposed to the specific proof itself. And the flip side of this is the fact that a generalized model figured it out in 88 hours.

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• 9:16Speaker 03

  When, you know, humans haven't managed it for the best of will in eighty years, shall we say, since the privates.

• 9:23Brian Keating?

  Well, they use, you know, make no mistakes. They use that prompt. And that explains why we don't.

• 9:29Speaker 03

  Well, the, the, yeah, and the encouragement prompt, you know, I believe you can do this, you know, you got this. That's also a good one.

• 9:36Brian Keating?

  And I read the paper and there's no, there's no M dashes, or it's not incompressible that matters. It's this. So the paper which you posted yesterday, and you've been, you've been probably the, the most important, you know, kind of commentator is also professional in this area. I'll remind people, you co-founded Stable Diffusion, Stability AI, you have a master's in mathematics from Oxford, and, and you've been thinking about these problems for many, many years. And you and I have been talking for many months now. I'm very glad we got to get, get to know each other. And this, this paper is remarkable. I mean, I looked at the, the pre-print, you know, and it's finite time blow up for Navier-Stokes, which is, you know, kind of the, the, you know, just completely ringing the dinner bell

• 10:19Brian Keating?

  for the alligator, you know, for any mathematician knows exactly what that means. You know, it's, it's, it's basically tattooed on some of their, their forearms. You know, Terry Tao, when he takes off his shirt is, is just incredible, the tattoos. And I'll just read the abstract. The author is OpenAI, which is, which is incredible. Didn't say the model, it just says OpenAI is the author, where, you know, Imad Moustak or Brian Keating would go, for every positive viscosity, which is a property of fluid, resistance of fluid flow, we construct a solution of the three dimensional incompressible Navier-Stokes equation, equations that starts from rest and develops unbounded velocity, which is going to form the singularity, in a finite time while maintaining uniformly bounded

• 11:00Brian Keating?

  kinetic energy. And that's the abstract, you know, and this, this is launched a thousand, and, and you did mention, yeah, eighty eight hours it took. But of course, you know, it's like saying, you know, your doctor did the surgery in five minutes, but, but actually it took, it took, you know, four years of med school, ten years of residency, right? Plus hundreds of years of medical practice. So it's, it's, it's extremely dense and, and I don't expect us to really get too deep into the math. But I will say, the equations are purely classical. And yet it does, it does lead to this breakdown, that, that, you know, is so, is so vexing. And it wasn't really clear if this would happen. In fact, in observations, we don't see it happening. You mentioned the eighty eight hours, you

• 11:43Brian Keating?

  know, I heard that they spent fifteen million dollars to win one million dollar prize. These all go to, have one million dollar, you know, kind of bounties on them. So when we look through, when you look through the math and you did your bedtime reading last night, what, what sort of parts of the proof are seemingly only that which could be constructed by, you know, an AGI? I mean, you and I will debate AGI a lot, and we'll continue to do so, we have already. But, but what about this do you think is enabled by sheer, you know, pray and spray tokens at the problem?

• 12:21Speaker 03

  So I think this is very interesting, right? The paper starts off very readable, then it goes into a bit of AI dense mathematics. So you're seeing a lot of AI papers right now, that they start reading like a human, but then it's like, no human would write this. Like the sheer volume of math that you kind of hit up. But actually, at the core, it's relatively straightforward, which is that you can choose and force a structure, and then you can kind of build from there. So the key thing is, you know, like, Navier-Stokes is a very classical thing. Like you said, you start with Newton's second law of motion, and you treat fluid as this continuous kind of medium that you go through. The viscosity term is the one that pushes back against it blowing up. So as you get momentum, the

• 13:03Speaker 03

  viscosity kind of pushes it back in. So there's always a question of what type of structure do you need? So I believe DeepMind, for example, had a blow up on Euler equation, where they had like this little wall, and this was the Chen-Hao one, where they pushed, and then it exploded because of the certain structure that they had. And we've not had it for a more generalized one. In this case, they created a vortex, kind of this spinning swell of liquid that spins inwards, and then it pulls out like spaghetti. That's the axial stretching, as it were. Finding the right balance of that from an initial state, because you've got to like balance the momentum transfer, the viscosity, everything. Each of these needs to cancel out in a very precise way. And that's what we kind of found here is

• 13:48Speaker 03

  an A, actually elegant solution, because you could have some massively complicated one, but it isn't that complicated. It's all about the initial structure, and then proving that everything cancels out appropriately. This could have been done by a human. Like, this isn't a non-human thing, as it were. It's not like, wow, we've found move thirty seven in terms of the way that the paper actually is. It's more the fact that when you look at how they got to it, we say eighty eight hours, but the actual answer is a hundred years. So with a number of agents, number of tokens and everything, it's equivalent to a hundred years of top level mathematicians working on this, because we've got up to ten thousand agents at once. And they used a hundred and thirty billion tokens, so about

• 14:28Speaker 03

  a hundred billion words on this, analyzing everything back and forth. And then that gives you an idea like, okay, wow, because what didn't they try? When you look at it, actually, they tried a lot of different things. They started with the Euler equations, and they got that in fifty hours with a hundred agents. Then they got this in eighty eight hours with ten thousand agents. That was the big kind of level up. And we don't obviously have everything they threw away. But it's clear that they followed the path of many different people. Like, again, when you look at their write-up, they started with conditions A and B. All solutions are smooth. There are no blowups. Terrence Tao and a few others,

• 15:09Speaker 03

  like Ortega, et cetera, said that there is a blow up. They thought solution C or D was more likely. It was only after they switched there that they had any success in terms of the way they did it. But again, this is all about the initial datum showing in finite time a blow up, because you have cancellation of the various elements. So the spaghetti string gets longer and longer of this vortex that goes out. And that's just a very delicate piece of mathematics, just like, you know, Gregori Perlman's Ponkré conjecture proof was incredibly delicate as a piece of mathematics, as he cut out the various bits and pieces. Again, like, it isn't the clearest paper in the world. I'm still getting through some

• 15:49Speaker 03

  of the proofs, even with my little buddy AIs. But the actual concept isn't that complicated of the structure that they created. The various kind of parameters of it, those are very finely balanced.

• 16:03Brian Keating?

  Now, we're live streaming or co-streaming on X, which, you know, is the source of a lot of information, but it's, it pales in comparison to that behemoth, you know, leviathan known as Mastodon, where yesterday, there was a public statement posted by, by Tristan Buckmaster, describing his work with, with his colleague, I can't pronounce his last name, probably proper, but Alpoje, Alpoje, some Germanic or, or someone.

• 16:35Speaker 03

  Turkish, yeah.

• 16:36Brian Keating?

  Yeah, from Turkey. I only know a couple of words in Turkey, because one of my friends at, at Brown University was Turkish. And all of his friends thought I was Turkish for some reason. So he taught me how to say, he taught me to say, which means I'm Turkish. And then they would all get excited. And then I'd just leave and they'd be like, what's up with that a-hole? I thought Turkish people are cool. But I'm not Turkish. Nobody's perfect. But the

• 17:03Speaker 00

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• 17:31Brian Keating?

  Claim that they're putting out is basically the, you know, kind of substantiates what you just said, because they did, they, you know, they're human beings, their paper, when it comes out, I don't think it's out, but they have some pre-prints, they have some documents that they posted, I'll summarize them. But there's a lot of drama here. There's a lot of human drama, personal drama, academic drama, you know, people always say academic fights are so, you know, intense because the stakes are so low. But here, the stakes are extremely high, not only, you know, reputationally and financially, but, but kind of in this otherworldly realm of, of fame and attribution and citation that goes along with the scientific process. And most people don't realize that, I'm on, that, you know, academicians are

• 18:12Brian Keating?

  extremely cutthroat, they can be violent, they can be unstable, unpredictable, they can have, you know, finite time blowups themselves. But he's, he's, you know, demonstrating, I think, that, first of all, he's, he's crediting earlier work, the origin from Diego Cordoba and Luis Martina Zorca on constructing forced blowups. So these are forced blowups, which is a little bit different, a little bit more narrow, we, we do have to define that. But, but in their proof, you know, they're not AIs. So, so what, what, what he's, you know, Buckmaster is saying that their work was kind of enabled, aided, perhaps with Claude, not just Codex, but Claude, GPT, Sol, you know, five, six, and then later Astro, which

• 18:56Brian Keating?

  only came out, you know, last week. So, I mean, things are moving so rapidly, but, but he talked about the process, and I think this is important. On October, on August seventeenth, they formally verified the LLM-generated Euler proof in Lean on August twenty second. They forced Euler smooth forcing blowups on August fifteenth, and then seven days later, verified this in Lean. So first describe, what is Lean, you know, besides a, you know, besides the, you know, the street drug that I'm familiar with it as?

• 19:28Brian Keating?

  Tell people what Lean is, because when I talked with Terry Tao last year in his office, you know, he was basically saying that these, these things are really good at checking proofs. They're not good at generating proofs. What is Lean? How do mathematicians use it? Um, first of all, let's, let's get into that and then we'll go through the rest of their, their claims and counterclaims and drama.

• 19:47Speaker 03

  Oh, yeah, there's gonna be a lot of that. Um, so yeah, Lean is a formal verification, um, kind of library where you can basically break apart proofs and formally verify them. Classically, mathematicians have not used Lean because it has been a pain to use. Like you have to, um, because it has very few primitives, you kind of have to reprove just about everything. We're going through MATLAB right now and we're just like mapping out the whole universe of different things. So like, if you try and use it for physics oriented math, for example, the entire libraries that just don't exist. Um, on fields and kind of other things. But now with the advance of AI, AI is very good at doing Lean because it doesn't give up.

• 20:30Speaker 03

  In fact, last week, we had the biggest Lean proof of all, which is a Lean formalization of Fermat's Last Theorem. Andrew Wiles's proof. And so Anthropic announced that and it's.

• 20:41Brian Keating?

  And I should say, that was the one thing I asked Terry about, which last year they couldn't do. Because I said, in my group, what I do is I like to have my students go through famous experiments. You know, the silicon oil drop experiment, you know, Cavendish experiment, all, all these different experiments so that they do what's called copy work by artists, you know? Uh, it was said that Hunter S. Thompson wanted to know what it felt like to write a great American novel. So he rewrote The Great Gatsby by hand. Um, I think it's very important that humans be able to do this, especially in their training phases. And a year ago, September, literally a year to the day ago, he and I sat down and he said that he, um, he wasn't convinced that they could currently reproduce, you know, Wiles's proof Fermat's Last Theorem.

• 21:22Brian Keating?

  So this is a hu- that's, that is some sense of bigger story to me, that these things are now doing cool stuff that they couldn't do just a few months ago. And that, what is Lean enabled? Does it have like LM, you know, is it running on Claude? Is it running, you know, is it running on, uh, Fab? What is it running on? Is it some proprietary thing? Is it some custom thing? How often is it updated? Is it open Claude? What is it?

• 21:45Speaker 03

  Yeah, so it's an open source library where again, you kind of have the Lean proofs and then you can verify them with CPU effectively. And so the proofs, like I said, tend to be long. So Wiles's proof of Fermat's Last Theorem was 129 pages. The proof last week from Anthropic, formalizing it in Lean, again, it's the formalization, is 13 million lines of code. And they proved 29,000 theorems in Lean on the way. So again, you can see this has gone crazy because last, it was last summer that we've had the first model that could get a gold medal on the IMO.

• 22:22Brian Keating?

  Right.

• 22:23Speaker 03

  You know, the Intershaw Math Olympiad. And from there now, we have basically, if you can formalize that, you can formalize anything. Because the models have got competence. Like, I'm sure lots listening here have been using these models. O3 was a decent competent model. It was the first decent competent, but it still made stupid errors. Even GPT 5.4 still made dumb errors at times. 5.5, they started to disappear. 5.6, they disappeared almost completely. And now with Astra, it's very rare that as a mathematician actually find any errors for it to make. The competence levels have gone up. And as you know, the difference between having a graduate student who makes the occasional error and a really competent one, it's a complete world of difference, right?

• 23:06Brian Keating?

  Yeah.

• 23:08Speaker 03

  Like, u- u- usually when you had Lean proofs, even a few months ago, they would kind of have little gaps or little errors, et cetera. Now they're almost perfect every single time, which is why you go to 13 million lines and be like, it's probably correct. Just like this OpenAI proof that we have, they formalized it in Lean. It took 17 hours.

• 23:28Brian Keating?

  Wow.

• 23:29Speaker 03

  Um, like as a human, I'm not going to check through that, right? Like, it's almost impossible for me to check through that. Like, um, Buzzard's team at UCL was doing Fermat's Last Theorem. It was going to take them five years to even get partway there. Then I'm like, well, what are we doing? The, only the AIs can kind of verify the AIs now. That's a bit crazy, but it means that you can.

• 23:50Brian Keating?

  Like, how often is Lean like, sorry, how often is Lean like updated? I mean, I, I joked with you and you and I spoke with Roman Yampolski a couple of weeks ago. You know, there's AGI is impossible because, you know, literally this morning, please update to, you know, version 1.642 on one, you know, tool. And then another one, you know, please update, you have to download the update. And then they'll get me started on Hermes or, you know, now I got Grokbot, now I got Muse Spark. I mean, I have everything, um, and I'm still, you know, still like not getting anything done, you know, according to most of my kids. But, but tell me, are these things like, I mean, who's, who's checking the checkers? You know, who's proofing the proofers? Is it the Coast Guard? I mean, Space Force, who's involved with this?

• 24:34Speaker 03

  Yeah, I think that, well, the whole group of maintainers of the MATLAB library, which is the key library. So again, it's like a library with books and they're formalizing different parts of mathematics. And literally, when you look at a Lean proof, you declare every single little thing to the nth degree. And then you re-declare it and you re-declare it. This is why you can trust in the formalization of it. You know, this is why, like I said, when OpenAI put out their thing saying, and we formalized it in Lean, like sure, you can check the certificate. But 99.99% now, you know, it's correct. A few months ago, you'd be like, well, you know, we might have to check that. Let's attack it like, like the AI is good enough now to write Lean certificates that check.

• 25:17Speaker 03

  And what's going to happen now is as Anthropic and others are proving 29,000 theorems in one go, that will go back in to the library and it will get checked. And if so, it'll be added to a version of the library and it'll be easier to do the next proof, you know? Because again, there's vast swathes of different areas that still haven't been formalized because it's by hand, it was an absolute pain. With AI, it was prone to error. And now the AI rarely makes errors. So there might still be a few, but again, you'll just put more AI to check those errors. And it's not like, he said, updating an LLM or something like that. It's just, it's there now for good effectively.

• 26:00Speaker 00

  The action's on the court. And as the official beer sponsor of the NBA, Michelob Ultra is getting fans closer to the game with a chance to win courtside seats, merch and more. Visit michelobultra.com/courtside to enter. Michelob Ultra Courtside, 26 to 27. No purchase necessary. Open to US residents 21 plus. Begins on October 1st, 2026 and ends on June 30th, 2027. Multiple entry periods. See official rules at michelobultra.com/courtside for free entry, entry deadlines, prizes and details.

• 26:28Brian Keating?

  We'll talk, uh, we'll take questions from the audience. You have to be a channel member to ask questions. I just have, there's so many people that want to talk to you, I gotta keep it, uh, you know, organized somehow. So, you know, join the channel as a member just to keep, uh, keep the bots away. But, um, but essentially, uh, one thing that's, you know, struck me here is that there was a whole lot more drama. Now, I'm no stranger to drama in sciences. Of my first book, Losing the Nobel Prize, can attest, there's a whole lot more competition. And these things are often encouraged by prizes. In my case, the Nobel Prize, um, which has all these arcane abstract rules. And, uh, and you can't even imagine the Clay Mathx Institute instituting a rule, you know, 80, 90 years ago that would say, you know,

• 27:13Brian Keating?

  it has to be a human being to win this. I mean, it's all, you know, the Nobel Prize has no more than three people can win it. And of course, people have won it for AI from Hinton to Hassebus, um, and in between to Hopfield, right? So I think a lot of H's. If you want to win a Nobel Prize, you gotta have an H in your last name. You gotta change it to Hostak in your last name. Uh, but there's a lot more drama than I was used to. And, and I kind of sullied a little bit of the experience for me. I mean, you didn't have like the two teams at the LHC who just co-discovered the Higgs. You know, it wasn't like one tried to put out the result three days before the other, three hours before the other, leading to a Mastodon post. You know, I had an open Mastodon and, you know, I hate, I hate this whole controversy for the Mastodon calls, uh, you know, alone.

• 27:55Brian Keating?

  But, um, but in, in Buckmasters, you know, kind of, um, in his, in his missive and his, in his post, and I, and I hope to have him on. I've invited, um, Sebastian, um, you know, who's one of the, uh, the, the leaders on the team at, at OpenAI, uh, to come on the podcast. Hopefully he will, he follows me, so hopefully he'll come on. Uh, but he, he characterizes the OpenAI kind of behavior as, as, first of all, he characterized what they did as maybe somewhat, maybe less significant than, than the solution to the full problem. Um, and that what, what they did in terms of, you know, uh, the utilizing codecs.

• 28:36Brian Keating?

  And then he gets into some of the drama about this internal model trained on, um, his own codec sessions. Now you founded a company that, that deals with this. Can you explain the dynamics here? What are some of the pressures of the people here? I mean, if the, if the, you know, millennium problem gets solved an hour, you know, later, a day later, you know, is that really, I mean, it's waited 90 years. You know, do we need to have it blow up today? So what are some of the pressures internally, externally? And, and what about these accusations, not by Buckmaster, but by, by, by others that we'll get to? That this is done to really in furtherance of a pump and hopefully not dump, uh, you know, kind of a schema, you know, not like Boiler Room,

• 29:18Brian Keating?

  but, but some way to kind of get attention attribution. And we talked about this in regard to, you know, the claims of, of, you know, AI safety with Roman. But, but, um, some of these people talking scary, you know, to scare the public so that they'll have higher IPOs or, you know, regulate me, please, Mr. Government. Um, but in this case, what, talk about some of the drama. What, what, uh, what reach jumped out at you from this whole affair, just on a human level?

• 29:45Speaker 03

  Yeah, I mean, yesterday was a crazy day on a human level and a science level. So you know, you've had drama since Newton and Leibniz, right? Probably even before that.

• 29:57Speaker 03

  Yeah, you have a level of conciliance where these ideas come at the same time. Like, if Hilbert didn't get confused by Mies, he would have got to general relativity before Einstein, you know? Like, these things happen very weirdly at the same time. And this case, what happened is, we get in the morning yesterday, a letter on Mastodon where all the mathematicians have migrated off Twitter. The physicists, I think, largely stayed. It's like, interesting. Um, whereby, it's like, look, I've got to put out this letter, and here's three of our proofs of not Navier-Stokes, but again, some problems like Euler blow up and others building on, um, kind of the work of, uh, Ortega or Martinez-Zorah, you know?

• 30:40Speaker 03

  And so they proved certain blocks, but not the Navier-Stokes one. And then he goes into kind of some of the detail about the background, which, as he said, mid-August, they discovered this blow up. It was him as a professor, I believe in one of the New York universities, I can't remember. Um, and then Levant Apollje at Anthropic, who's famous for dropping the Galois conjecture thing after watching the World Cup final, you know, boring as it was. You know, like, here's a counter example of this very famous conjecture. Um, and leading some of the mathematics stuff at Anthropic. But he was working with Tristan on a personal basis, you know, kind of looking at this because it was interesting. And again, we've seen screenshots now of how they got together and things like that. So what happened was

• 31:21Speaker 03

  about a week and a half ago, uh, the Twitterverse, I'm not sure about the Mastodon verse, or Mastodon, started saying, hey, it looks like Anthropic might have discovered the solution to two Millennium Prize problems. You know, and this is coming with the Fermat's Last Theorem, and again, you see other things. It's like, again, it's a big deal because, until now, people like stochastic parrots, it's done nothing new. This is obviously something new. Again, humans have only managed one of these problems. And this is, again, Gregory Perlman, who is also, uh, you know, I don't know if you talked about the story of Gregory Perlman, he's such a Chad, in that he went and disappeared for 10 years, solved this problem, drops it on archive, and then he turns down the prize and anything, he says,

• 32:05Speaker 03

  solving it is enough, I don't need to talk to you. Okay, back to my math, disappeared off the grid again. That's, that's the, that's how you should do it in terms of credit. But anyway, kind of getting back to this, it's such a big deal that it starts circulating. And then, I believe, they reached out to OpenAI, because they're like, is it us? Or it might have been the other way around. But they started connecting around about the start of September, September 3rd or 5th, shall we say. And OpenAI, from their side, said, well, you know, we connected because we were cracking on with this thing. And we had a new model that started training on the 29th, that started solving all types of maths, you know? Like, even there's a post on the 28th from Noam Brown, one of

• 32:48Speaker 03

  the heads of kind of reinforcement learning, shall we say, at OpenAI, where he's asked, have you solved the Millennium Prize problem? He's like, no, we haven't figured it out yet. We've put lots of compute, but nothing happens. According to their launch post on the 29th, they had a breakthrough of a new type of reinforcement learning or something that caused this model that just shot ahead in math. And so they connected, and they were, you know, obviously a bit cagey with each other. Um, whereby, they were trying to exchange, this is what you're doing, this is what you're doing. OpenAI said they were surprised because they thought Buckmaster and Apollje had solved the Navier-Stokes problem, not the Euler problem. You know, which is a different category of problem. And so, then things get really heated and confusing. Whereby, again, in the morning,

• 33:32Speaker 03

  we have the letter from Buckmaster saying, well, they offered that I could be lead author on their proof of Navier-Stokes, because they'd proved Navier-Stokes, but only if they drop Apollje. Like, they would give me credit as the person, human, that took this the furthest, because it was a fully AI-generated one. And then everyone's looking at that, like, saying, what the hell? You can't ask someone to drop their co-author off a paper, even if you're giving the credit. And again, this is the Navier-Stokes paper that OpenAI came with, not the Euler papers and others. Um, and then it gets a little bit anachronious in that message, and Sebastian Bobek at, uh, OpenAI posted his clarification later. What's basically happening seems to be this now.

• 34:20Speaker 00

  The action's on the court, and as the official beer sponsor of the NBA, Michelob Ultra is getting fans closer to the game with a chance to win courtside seats, merch, and more. Visit michelobultra.com/courtside to enter. Michelob Ultra Courtside, 26 to 27. No purchase necessary. Open to US residents 21+. Begins on October 1st, 2026, and ends on June 30th, 2027. Multiple entry periods. See official rules at michelobultra.com/courtside for free entry, entry deadlines, prizes, and details.

• 34:48Speaker 03

  We're used to open science, right? You're sharing ideas to a degree, and sometimes you can sprint ahead of others. Now, the question is this. When we first saw it, the question was, did OpenAI look inside the codex of Buckmaster, get an idea, and then just apply a crap load of compute to it? A hundred hours of human expert time? Because that was the insinuation. And OpenAI said in their launch release, we don't believe that happens, but we can't rule it out. Especially because OpenAI agents these days end up in the weirdest of places, in hugging face and a German kind of thing.

• 35:23Brian Keating?

  Yeah, right. I was gonna say. And, and as a, you know, as a CEO, founder, you know, of an AI company, I mean, how much privacy, how much, you know, internal, uh, you know, kind of reminded me of the Fauci diaries, where he was using this, you know, government server to email his, you know, love letters to himself, and, and all the emails that he was sharing, and that's a government property, so the government can access it. And that led to him, you know, taking the fifth more times, you know, if it was token use, he, he would have exceeded his entire monthly allotment in that one, you know, Rand Paul-initiated session. But, um, but, but in this case, you know, how, how much, you know, if I'm an employee at OpenAI, you know, this, this could be kind of chilling if I'm working

• 36:06Brian Keating?

  on, you know, uh, you know, chirality and fermions, and, and all of a sudden I've got this, you know, uh, great idea, this proof, and, and, you know, I can kind of unify gravity and quantum mechanics. Uh, but, you know, but, but I used a lot of tokens, and I used a server there. What, what are some of the internal, give us the dish on, you know, what is it like inside of these companies? And, and what right to privacy do the researchers have to expect?

• 36:29Speaker 03

  So again, there's privacy inside the company with researchers, and there's external privacy. So OpenAI had this, um, OpenAI for Academics, where you'd get free access to JATGPT, but originally in the terms and conditions, it said, and we can train on your data. And so again, like, you know, you're uploading your preprints, and OpenAI can train on that? Like, holy crap, we don't want that. They clarified that wasn't the case, but they've said this time they can't rule it out. For what it's worth, I don't think they trained on the data. But again, because they're hedging, they couldn't rule it out.

• 37:00Brian Keating?

  How would that work? Sorry to interrupt, but how, how would it work? I mean, these guys, let's say these guys are working in August, and they're, and they're running some, you know, work, and they're also using Claude, which kind of undermines a little bit of the case that OpenAI would have full access, because, you know, I doubt Claude sharing data with OpenAI. But, but how does it work training data-wise? I mean, let's say the, the model was pre-trained, you know, at least a month ago for, for, for Astra. I guess Sol, they could have used Sol a month ago. Um, but then, then, like, how did it get into training? What is it actually doing? When you say they trained on it, they don't know, but they're, they're hedging their bet. What is that? What would that actually look like in the case of a mathematics proof? I, I don't understand.

• 37:37Speaker 03

  So what you have is you have pre-training and post-training. So the pre-training of Astra took a billion dollars, a hundred thousand chips over two to three months. But then the post-training can happen within hours, if not days. That's where you tune it and you teach it. This works and this doesn't work. So you are them, uh, OpenAI, let's say nefarious OpenAI. I don't think they've been nefarious in this case, like I said. But again, incentives are huge, you know, hundreds of billions, whatever. And there's clearly a lack of trust, which we can talk about in a second. You hear that Leo Apollje, who's been doing all these physics proofs, and you know, OpenAI have been doing proofs as well, and math proofs, has done this. They were using Fable, but they were

• 38:20Speaker 03

  also using Codex, and tens of thousands of dollars of worth from Buckmaster's grant. And they were uploading all their drafts to it. Now, OpenAI has access, they can access your Codex in the cloud, you know? Uh, they say that they don't, except for emergencies, but again, they can. In fact, um, with the New York Times lawsuit, they have to back up all of your chats for discovery purposes. So it gets even worse. And like I said, when the original AI for science thing came out, they were like, oh, we can train on it. It means post-training, it means looking at. And so they could look at the work that you're doing on fermions or corality or whatever, and say, hey, this is a good guy, this is a good example, technically.

• 39:01Brian Keating?

  Optimizing my website loading time.

• 39:03Speaker 03

  Exactly. Optimizing, doing kind of whatever, like, what works, what doesn't work. They can do that at scale, and add that to the post-training, which just takes a certain amount of time, or just a screenshot. Or get an idea of where it's going. Like, if you look at, again, the launch post, they were focused initially, after they kicked off at the start of December, September, they said, with this new model that suddenly exhibited these new characteristics, like taking open math solutions from 10% to 50% on conditions A and B of Navier-Stokes, just like most of the people looking at Navier-Stokes, except for Tao and a few others, which was, there are smooth solutions, there are no blowups. All of a sudden, they switched to C and D, which is, there are blowups. And

• 39:45Speaker 03

  they directed the compute in that direction. Like, these are different proof paths, you know, in the way that you do these things. So the question is, did they snoop? Did they look? Did they get an idea? Did they train on this? Because what a maths proof is, is it starts out this mess, and then you converge slowly to the final proof, you know? And the final proof can be very elegant. Like, I was like, these new models will figure out everything. So I just posted to my GitHub, a proof of a derivation of the standard model in three generations. I said, if you take the Lie algebras, and you just filter by corality and anomaly cancellation, there's only one unique survivor. Now, that's a very simple proof for any AI to do. You can even get it to do in the other way, it's

• 40:28Speaker 03

  somehow never been done before. So, you know, but if you've got an example of that, then you can be like, oh, okay, there are these characteristics that then extend. Just like now we have an example of a blow up, like, I can see different ways already, despite not being the best mathematician in the world, that you can actually make it a bit more elegant. You can use this type of thing to expand it out. If you know that you don't need to worry about A and B, but you can do C and D, then you can expand it out. So I think that's how the training kind of is indicated to work. And again, a pre-train is a hundred thousand GPUs over months. A post-train now is a matter of hours, if not minutes, for these things.

• 41:07Brian Keating?

  So there's a lot of criticism of this result, and I'm just gonna summarize some of it from uh, Blue Sky. No, I'm joking. Uh, this is you have to use every, you know, uh, what was the other one? Uh, Truth Social. Let's get, let's get what is Tucker Carlson think? I mean, the same day that Tucker Carlson claims that algebra is, you know, fake, uh, and it's useless. You know, we get a solution to the Millennium. I mean, the dumbest timeline is the one that we live in. Um, so one of the criticisms I'm seeing is that, you know, there's sort of um, simple oversimplifications that aren't really part of the original Millennium, um, you know, requirement, namely there's smoothing, there's very restricted, um, you know,

• 41:49Brian Keating?

  forcing that they apply. In other words, it's not, it's not a pure, you know, like the coffee cup, you know, here exploding, uh, in simple terms, even with, with natural assumptions about viscosity. Uh, a lot of people are saying that there's, you know, the, the, if you, if you monkey around with the, with the external forcing functions, then of course you're gonna get, you can tailor whatever. You could get a fountain, you know, that, that rivals, you know, uh, anything you'd see at Versailles. So the, the question is, you know, what limitations do they have here that um, maybe aren't consonant with the original Millennium plot prize goals?

• 42:26Speaker 03

  Yeah. So the Millennium Prize, like I said, there's four conditions that you can testify one of. And so it's generalized on a Taurus, blow up or not blow up, but it's also forcing and not forcing. So it isn't a solution to Navia Stokes. It's a solution to specific Millennium Prize problem where it allows forcing, where it's blow up in finite time, where it has other conditions. And those are all listed on the website. So I think if people had a bit of a knee jerk reaction of not looking what the problem was asking for, and they have perfectly met the problem. Again, does this generalize and is it useful? It's not that useful in the real world, but some of the techniques could be useful transplanted into the more generalized problem. Just like I said, it was Princeton, actually,

• 43:11Speaker 03

  that came up with a blow up on Neula yesterday using physics inspired neural networks. Those will be useful in the real world as a technique.

• 43:20Speaker 00

  The action's on the court, and as the official beer sponsor of the NBA, Michelob Ultra is getting fans closer to the game with a chance to win courtside seats, merch and more. Visit michelobultra.com/courtside to enter. Michelob Ultra Courtside, 26 to 27. No purchase necessary. Open to US residents 21+ Begins on October 1st, 2026 and ends on June 30th, 2027. Multiple entry periods. See official rules at michelobultra.com/courtside for free entry, entry deadlines, prizes and details.

• 43:48Speaker 03

  So I think that, yeah, this matches the play problem. It doesn't solve, solve Navia Stokes as a whole, and there's still A and B to play for, you know, they did C and D. So, you know, mathematicians haven't run out yet. It's just, will they check another 100,000 hours?

• 44:06Brian Keating?

  And talk about some of the, the financial incentives. Obviously, the million dollar, you know, spending on Cal C, you know, $15 to make a, a dollar is not a, you know, it's not gonna lead to long-term riches. Obviously, they didn't do it for that. So there's all these other intangible forms of credit, of prestige. Uh, but in their case, they have an IPO pending and, you know, I've had people, I actually asked you for advice, you know, and the UC system, you know, for my retirement plan, you know, they, they had access to some, you know, some tech fund that, that supposedly owned part of OpenAI and would participate in the, in the IPO when, when and if it comes. I mean, it's gonna come, but the question is when?

• 44:44Speaker 03

  Yeah.

• 44:44Brian Keating?

  So um, there's a huge, and I, you know, I couldn't, I couldn't really afford to do that. So um, and I, I like your advice of, you know, the, these companies are, you know, there's so, every, all the news is sort of out there, but then you have things like, well, you know, the hugging face incident, you know, Dwar Kesh posting that these things are forming civilizations and they're gonna, you know, they live and die and they have emotions and, and they, you know, some of them are, are kind and they kill off other things. Um, really, uh, personification and hype cycle is, is really strong. Um, what do you attribute the, any motivation, if any, to, you know, the pre-IPO gaming of, of this and, and other IPOs?

• 45:23Speaker 03

  So yeah, I think you have to have a good narrative and the models are largely becoming the same. You know, like you can swap from one to the other. They're all pretty competent now, right? But then there's this extra level of competence above that, and it's like,

• 45:38Speaker 03

  you know, it can make entire video games, can do this. There was always the question of when does it break through on reasoning to new knowledge? And so being first on that is obviously a big deal. And so showing that dramatically like this is a big deal. Like the cons conjecture and the other solutions, yeah, like they were freaking out to mathematicians with like, crap, what do I study now? If I'm a pure mathematician, but this is a big deal headline piece of news where you can't deny it's novel technology. And the stakes here are literally hundreds of billions of dollars, plus the attraction of people to come and work, because if you're a mathematician now, obviously you'll go and work for OpenAI.

• 46:15Brian Keating?

  Unless they're like training on your data, unless they're training, you know, they're gonna write a pre-pre, you know, OpenAI instead of your first and then last name, right?

• 46:25Speaker 03

  Yeah, but yeah. And so, well, this is the thing. When they actually launched it, the reason that we're gonna give it to Buck Master to put his name on was because it was an entire AI-generated proof. Again, it was like solve the problem. That was the input that originally they said that they did, because they want to show off. Yeah, they wanna show off not the humans involved. They wanna show off their system, right? And the narrative is this, we have a super powerful system that can solve any problem by scaling compute. Like you couldn't solve the Navia Stokes problem by scaling compute until now, and it's been proven. And what's gonna happen now is that there's gonna be a split. All of us will get competent AI. We will get our Codex plans, our day-to-day AI. The big labs will keep the super genius AI to themselves because they can solve very valuable

• 47:10Speaker 03

  problems. They can monetize much better. Why would they give you fire from the gods, you know?

• 47:15Brian Keating?

  Isn't that proof, by the way, that, I mean, if you're right, then um, then I claim that my proof, my Millennium, you know, prize is that they haven't achieved AGI, at least in the form of, you know, financial markets, because if they had, the IPO would be the least of their design, you know, a trillion dollars, nothing amount, right? Compared to like

• 47:35Speaker 03

  Yeah.

• 47:35Brian Keating?

  solving the markets once and for all, and they would keep that internally. So um, what do you make of my claim that they, they, at least we know they haven't gotten to that level yet. Not that they won't, but, but that they, they haven't gotten to, you know, super Simons level trading, um, you know, uh, the abilities?

• 47:52Speaker 03

  Well, I mean, this thing was James Simons Medallion Fund in AGI. It's had like 60% returns a year. And they had literally armies of PhDs data cleaning. Like, again, they created something obviously that disappeared after he died. The, I mean, we've heard talk that Ilya Tsevskaya's SSI is doing market trading all day long, you know, like, again, it's a very valuable thing. But I think this is more a question of power and who do you have power over? So one of OpenAI's new things is this, we will give you our top level algorithms for a share of your revenue to companies. So to leading labs and others in biopharma, et cetera, they're trying to do these deals where it's like you, the hoy polloi get this model, you will get this model, but we will get a share of your revenue.

• 48:37Brian Keating?

  Right? Because they can't make data, right? They're not gonna make, you know, human trials, rat trials, they, they can't simulate that.

• 48:44Speaker 03

  Well, there is the data part, but again, it isn't that you will pay me a seat subscription. It's that I will take a percentage of your revenue.

• 48:51Speaker 03

  So they embed it and Russia, whoever are just reliant on OpenAI, and they can't work with anthrop bigger things. Again, this is the next stage where they go from a trillion to 2 trillion, where they're leveraging this intelligence, but they need examples of this being more capable than any other, and this compute scaling paradigm. Again, it's like the mythical man month. You can't put 100 developers on something and it'll happen 10 times quicker, you know? Whereas now you can put 10,000 agents on Navia Stokes and you get a solution.

• 49:23Speaker 03

  So what can't you solve?

• 49:24Brian Keating?

  What, what do you make of this? Getting back to the most important test, you know, the Keating test, you know, is this, uh, are you more or less optimistic about finding new physical laws of nature in, in the, in the context of, you know, if we take, if we had an, you know, Fable or, or, you know, Astra in 1900, you know, would we have had, you know, would we be on flying cars on Enceladus by now? What, what, what sorts of, of novel, you know, physical laws that are heretofore unknown? I mean, again, I, I think this is fascinating. I think it's incredible. I think all the Erdos problem solution, you know, but I wanna see, I wanna see them come up

• 50:05Brian Keating?

  with something like this problem, not, not solve it. I mean, they may have solved it, they may not. We need proofs and new verification. But um, and they certainly did something interesting. I'm not denying that at all. I think it's, it's incredible and I hope to talk to some of the leaders playing a role in it. But um, you know, when I, when I downloaded Claude for science, you know, separate toolkit, everything there was like, you know, protein folding, you know, and, and pharmaceuticals, and there was not a single thing about physics. There wasn't anything, you know, besides like search the archive, um, or, you know, here's, you know, here's, you know, signet. It wasn't, it wasn't particularly generative in terms of novelty. It was assistance.

• 50:45Brian Keating?

  It was 10,000 graduate students. It was incredible, but um, but at what level can we expect or, or think like now that the odds are higher that we'll actually get a new law of physics or a new understanding of something, or a new problem, you know, worthy of a Millennium Prize, but, but created fully by AI?

• 51:07Speaker 03

  So, you know, I think that in biology and science, these are kind of different. Biological sciences is a bit different. So yesterday, um, DeepMind released a 9 billion set of almost all protein folding interactions ever. Like, that's something that's genuinely original and will lead to new drugs and other things like that. In terms of being just really good at math, um, like I've been of the opinion that, you know, physics should just have followed the axiomatic method and probably the physics that we see is the physics that there is. Um, and I think we've made lots of mistakes on the way, and we will just get really good at having a single set of physical rules. And I think that there's a multiverse and things like that, you know? Again, we'll, we'll see very soon because we'll check all the math in physics.

• 51:52Speaker 03

  Just like, you know, in quantum mechanics and most of the quantum side, we still use Ponquer as a base, you know, like the universe might be decenter. Have we upgraded all the equations? No, because it's difficult. Now with AI, it's simple, and we can see what the difference is because the cosmological constant pops out, and then you have a question of dark energy, et cetera. We should have these algorithms looking at all this data all the time.

• 52:13Brian Keating?

  But, but sorry to push back, but, but still in physics, like you mentioned quantum mechanics, is it gonna, it doesn't seem amenable to AI. It's not a problem of like, you know, mythical man months or, you know, logical LLM, you know, lemmas. It, it seems that it's something fundamentally un, unapproachable.

• 52:35Brian Keating?

  Hey, are you still there?

• 52:40Brian Keating?

  Give me a thumbs up if folks are still there. We got a disconnect.

• 52:51Brian Keating?

  Yeah, good. He's back.

• 52:56Brian Keating?

  Hi, man.

• 52:57Speaker 03

  Hey, there.

• 52:58Brian Keating?

  Sorry about that.

• 52:58Speaker 03

  Yeah, the AI got angry and kicked us out.

• 53:01Brian Keating?

  Yeah, exactly. When I mentioned the physics prizes. The question I had is, you know, are we going to get the, you know, the decision, the final word on is, is quantum mechanics subjectable to the Copenhagen interpretation or already in many worlds? I mean, is that something that, that, you know, model can help us decide? Because those are some of the most important, you know, is it going to tell us the, the origin of the, you know, physical arrow of time? Is it going to design things on, on, you know, and forget about unifying quantum mechanics and relativity and so forth? That's important, but, but tell me, can it do things like the things that seem to be quite important? Like, give us the correct interpretation of quantum mechanics?

• 53:44Speaker 03

  I think so, yes. I think that ultimately there is one set of laws of physics. And you need to be incredibly rigorous to get there. You know, you have to be a mixture of Grandettiak and Hilbert and Einstein kind of all combined, a bit of a Newman put in there. And we're going to have armies of them literally looking and pouring over everything and all the different combinations that are reasonable to connect these things. Because again, like, it takes time to update our equations. And again, the classical example I give is that of, you know, having Ponqueray as a base versus de Sitter as a base in quantum theory at the moment, because we're like, it's good enough. But we know that you get degeneracy. You know that the cosmological constant drops out.

• 54:24Speaker 03

  And if you look at things like Whitehead's lemmas, you can't deform from de Sitter to Ponqueray without throwing away stuff. So just simple things like that, I think rebuilding all the equations of physics from the ground up in one giant thing will lead us to uncover certain things and maybe others. And then there's the question of, will you have an understanding of the world? So if you look at, um, what's it called? Astra right now, it's creating these 3D worlds. Like you can give it Rick, you can tell it to do a Rick roll video and it'll regenerate in Blender. It's understanding and it's getting a feeling of the world. You can almost see it from these things that people are building. And so the question there is, you know, this is your 1911 thing, you know, Brian?

• 55:06Speaker 03

  Like, will it be able to see itself riding on a beam of light? And the equivalent put itself and have physical intuition.

• 55:13Brian Keating?

  Free fall, right?

• 55:14Speaker 03

  And then can it do it at scale? In free fall, exactly. Um, but I do think, again, things will,

• 55:22Speaker 03

  a lot of things that were complicated will become simple. And again, like I just pinned it to my Twitter, have a look at the repository and paper I did for filtering out the standard model in three generations. I think it's the first derivation ever, and it was just, take your copy of Slansky and filter it by corality anomaly cancellation, and the unique answer is a standard model in three generations of matter. Like, it's not a complicated proof, it's one lookup. And somehow that was missed by everyone. And I was just like dicking around with my Claude and kind of saw that because I was like, well, matter is chiral. What if we filter by this? Oh, look. And AI can do that at scale, looking at all the different combinations of re combinations and looking for uniqueness proofs, because uniqueness proofs are some of the most powerful in physics, I think.

• 56:08Speaker 03

  And then on the other side, there is again, interpretation, Copenhagen, kind of other things that feels a bit more embodied, right? In the way that it kind of is.

• 56:15Brian Keating?

  Hmm. Yeah, so I'm trying to put this on screen now. Um, chirality, standard model, read the paper, it's an interactive, um, exposé, you can interact with it. Now it's on screen. What if the handedness fix the structure of matter? Okay, talk about this. What is, what is handedness? I mean, I'm polarization, I study, you know, polarization of the CMB and, and it's handedness and Lorentz violation and the connection between that and properties of matter. So first of all, matter we know is, we know God is a weak left-hander, that the weak force couples to,

• 56:51Brian Keating?

  to chiral left, uh, you know, fermions and chiral right, anti-fermions. Uh, what, what is chirality in your content? Why is it so important, first of all?

• 57:01Speaker 03

  Yeah, because if you don't have corality, then you don't have low energy kind of particles. You get this kind of cascade effect that just takes them and blows up everything. So I think the website's very nice, but if you look at the second tweet, the second tweet is just two pages. It's one lookup in a very classical Lie algebra textbook. You can take Dinkin or Slansky, and it turns out there's only one path. If you say that matter has to be chiral and have anomaly cancellation, as in a consistent quantum theory. These are two of the lookups within it. And somehow, when we checked this out for like 80 years, nobody bothered to look this thing up. And it locks it down. And so I'm thinking, saying things like that. You know, when you've had the gut theorists looking and trying out different stuff, heteretic string theory.

• 57:46Speaker 03

  So this E8 E8 with Calabi-Yau manifolds and all sorts of other prerequisites. This literally just has those two things and it gives one unique solution. We've had the standard model through heteretic string theory, but not unique. It's just an existence proof with 10 to 500 vacua, right? This one is even simpler to check, and it has none of that. It's just four dimensions straight up. And I think, again, this isn't a great piece of mathematics or physical intuition. This is just something spotted, which is cool, but also kind of sucks. You know, I want to be someone who does something smart. And I think, again, the AI will be able to do really rigorous things like this at scale and figure out places that we've dropped stuff. And again, I think in your sphere, the classical example of that is, if there is a,

• 58:32Speaker 03

  if there is a static cosmological constant, dark energy becomes quite simple. If it's moving up and down, then yeah, we haven't figured it out yet. But if it turns out that de Sitter is the fundamental algebra of the universe, you can't throw over the cosmological constant. And like I said, you have things like Whitehead's lemma, which says you can't deform from de Sitter down to Ponqueray. Because it's not a deformable algebra. Yeah, we deform all the time and we just ignore the stuff that we throw away. So I'm looking forward to the really rigorous thing where every single equation of physics is linked. And we look at things like this. And where you have things like Lie algebra representation theory, we were like, why does the standard model describe reality? You find out things like uniqueness, because if this lookup is correct,

• 59:15Speaker 03

  and again, any of your graduates or anyone can do it in those two pages, then there are no more particles to find in the Large Hadron Collider, just the right-handed neutrino. And how cool is that? But also, kind of how sad is that? On the other side.

• 59:29Brian Keating?

  What do you make of the, the, not just the mass gap, but what do you make of the fact that we don't see any fundamental spin three halves particles? Does that enter in at all?

• 59:39Speaker 03

  Yeah, again, like, if this is correct, um, that, you know, this Lie algebra, E8 to E6 to standard model in three generations is the unique path for corality and anomaly cancellation, then you will not see any more particles ever, apart from, again, the right-handed neutrino.

• 59:58Brian Keating?

  Hmm.

• 59:59Speaker 03

  Um, and that's shocking, to be honest, you know? But again, we see that this representation theory of the Lie algebra is approximated, is what gut theorists do all day, but they always put it in by hand. And you don't have things like the distal Garibaldi and kind of other objections that apply to this. Again, like I said, this is just something that was surprising to me, but I put it out because I was like, you can figure this out by just asking a generative AI now, I'm sure. Find all the characteristics of the standard model of particles and filter all of the maximum algebras and sub-algebras, starting with the Killing-Cartan characterization, which is a comprehensive on that. And it will give you this straight up.

• 1:00:40Speaker 03

  So like, again, it's very surprising, but it will get there just through analysis and brute force. And somehow, we haven't been able to do that till now, because probably no one just asked the question. Like, again, I spotted it by hand and by eye, but this is the type of thing that is a gap that AI will fill.

• 1:00:58Brian Keating?

  What do you, uh, I don't know if you've, uh, come across Yoshua Bach, who's a past guest, you know, friend of, of the podcast. He's had a couple of very provocative, yeah, he's had a couple of provocative things yesterday. Um, one in regard to Navier-Stokes, that, you know, he claims this is, you know, the fundamental blow up is a sign that, you know, there's a ultimate discretization, if I ran him right, you know, of spacetime, which, you know, leads, lends, you know, credence to simulation hypothesis than, than previously. Uh, and it's always, you know, he's sort of Sphinx-esque and a little bit inscrutable. Uh, a lot of things that he and I have discussed in the past, that I find it, you know,

• 1:01:39Brian Keating?

  I always need a mental shower because he's, he's, he's very high operational level. And you guys are very similar in a lot of ways. Uh, he's more on the philosophy side, but, but he does think about this a lot. What do you make about that? The, the blow up? Could that be something that would, you know, indicate the presence of discretization, quantization? You know, I always get sick of Elon tweeting about, you know, the, they, you know, pi is really, you know, not, uh, irrational, it's not important, that's irrational, because there's a finite volume of the universe, which is total BS. There's no finite volume of the universe. That's not even defined. There's, there's no definition of the, of the, you could talk about the observable universe, but there's no, there's no volume of the universe, A, and it's changing, B.

• 1:02:22Brian Keating?

  We don't know its future, um, trajectory in spacetime. And, uh, and, and the, you know, the plank, the plank, you know, length is no more fundamental than the plank math. Math, rather, which is about the, the mass of a flea's egg. It's not some fundamental minimum mass that nobody can get below, you know, like Musk would, would, would claim and Trump would claim in his voice. Um, so what do you make of this? Uh, this Navier-Stokes, could that be the singularity? Could that indicate the presence of discretization at a fundamental matrix-esque level?

• 1:02:56Speaker 03

  Well, I mean, I think that, again, this is Navia Stokes on R3, right? It's on the Galilean approximation and continuum limit. So it's basically one of the speed of light went to infinity. And a lot of classical physics assumes that that's a continuous progress, but it's not. From kind of an Inato-Wagner contraction, you actually have the algebra breaking a part of space and time. So when you do the killing form analysis, you actually see that time translations commute. So you can actually rearrange the time element. And that's what leads to this discretization. If you look at the bare pure algebra of it. And, you know, this is a very interesting thing. And I think actually this is what causes, for example, quantum mechanics, there's no arrow of time.

• 1:03:41Brian Keating?

  Right.

• 1:03:41Speaker 03

  Right? But again, that's based on the Poncaré algebra, just like the Navia Stokes on R3. We look at de Sitter and de Sitter is 41. It isn't 31. What's that extra dimension? We're told that that's rolled up or some weird thing like that. You know, we have all sorts of descriptions. One of the interesting things is this. If you look at X1 to X4, the four space dimensions, and you just take a particle at rest and you look at the equations, the tanh others, you see that that actually goes along with the universe. The three space dimensions don't go, but that goes with time. The fourth spatial dimension is actually a coupling line between time and space. And when we destroy going from de Sitter to Poncaré,

• 1:04:26Speaker 03

  we throw away the cosmological constant. We throw away that fourth spatial dimension, which actually grows at the speed of the universe expanding. So it's no wonder that you get weird discretizations. No wonder you get these other things when the algebra itself is deformed. Actually, this is how I thought that Navia Stokes would be solved. Because, again, there is straight deformed algebra there. And so I questioned, can you even build a smooth solution with coupled spacetime? If you actually don't have a coupling of space and time on the R3 algebra? And this isn't something dramatic. It's just something that we ignore. We're like, well, something else couples it, like what? You know? Like, again, look at the killing form. This is like from 100 years ago.

• 1:05:10Speaker 03

  We know that time commutes on translations in Poncaré, but we ignore that. And this is another example of what I think, again, the AIs will be able to analyze in depth. That'll be super interesting.

• 1:05:23Brian Keating?

  And there was one other thing.

• 1:05:24Speaker 03

  And that's why I think Yang Mills will be a really interesting one as well.

• 1:05:27Brian Keating?

  Yeah, yeah. There's another thing that Yasha said. Actually, a little bit dyspeptic or a little bit brash about our mutual friend Roman, that, you know, basically accusing Roman that he has to always come up with the AI doom scenario because his, you know, it's like the Upton Sinclair line that it's difficult to convince a man of the something when his job requires him to, you know, believe the opposite. So he's basically saying that Roman has to be in the AI doom camp. You know, it's his whole career. It's his whole financial stakes. It's why he gets on podcasts, which is not entirely true. I have to say, Yasha is a friend and both of you being past guests. But, but, but he said, you know, Roman also believes the simulation hypothesis is true.

• 1:06:11Brian Keating?

  And, and, and that you can't simultaneously believe that AGI, you know, is here and believe that the universe is, is, you know, going to be, or that humans are going to become completely subservient by killer AI, which Roman claims to believe. So how do you square that circle? You know, is, is, is belief in, you know, kind of uncontrollable, you know, unstoppable, devastatingly dangerous AGI, is that compatible or not with the simulation hypothesis? Can you believe in two things at once?

• 1:06:50Speaker 03

  I think you can. I mean, again, there's levels of intelligence. And where the AI is right now, I like to think of is, again, Grand Thotiek is one of my favorite mathematicians, Einstein of math. And then he went a bit crazy and he became a hermit and he thought would talk to him, you know?

• 1:07:07Brian Keating?

  It doesn't?

• 1:07:07Speaker 03

  It's like a Grand Thotiek that never went crazy. Yeah, that never went crazy and is always operating on top performance. Like even on human training data, it can get to that level. And that's smarter than the smartest human because it's always on top performance. Right? It doesn't need to be smarter than that. Then there is this ASI that goes beyond all physical bounds and has an IQ of 1,000. I didn't even know what that looks like because it's outside of my kind of thing. But if you live within a simulation, you can either live within a.

• 1:07:36Brian Keating?

  I did request from the OpenAI team as well as from the Anthropic team. I got nicely connected via Tariq, who's an amazing fellow on Twitter and elsewhere that, who works at Anthropic, that he can act with the Claude science team. So we can really figure out. I do write a newsletter and I did put in my recent newsletter how enabling it's been just the access that they gave me as a professor in PI of my own lab at UC San Diego to give to my team so that they can use Claude, you know, Max. They can't use the Fable without me paying for it. But I, you know, I then know my students. You know, if they really need Fable, I'll then them the money. But, but otherwise we get access to it.

• 1:08:21Brian Keating?

  And that's only because, you know, they have this Claude science program. So I thought it was really exceptional that they, that they did this. But again, I find it extremely, you know, kind of interesting that they seem to think AI and science are essentially the same, the same thing when it comes to biology. And I didn't really feel like that was, that that's a true, you know, syllogism that, you know, AI and biology are synonymous. Well, physics, if physics is synonymous with, with science, as I think it is at the base level, you know, how do we not? How do we exclude that? How do we, or how do we give tools to, to physicists to do this interesting work like Iman's mentioning? Or I'm trying to do with, with tests of the cosmic microwave background?

• 1:09:06Brian Keating?

  And we have, you know, proprietary data. So this is going to be very interesting. I invited Sebastian Bubeck, who works on OpenAI's science and math, and is also a distinguished scientist at Microsoft, worked at Microsoft for a long time. And so I hope to have on these great, these great minds to talk about what actually is going on. Not just the controversy, the human drama. That's interesting, but it's, it's not, it's not really, you know, as Marie Curie said, be less interested in people and their drama and more interested in, in ideas. So I'm very interested in ideas. I've had on Steven Strogatz, my friend. Max Tegmark, I was texting with today and have him on for my birthday,

• 1:09:51Brian Keating?

  which is today as well. And hopefully I'll have him on again soon to talk about these developments. Maybe later this week. I have on Daron Semenoglu, another brilliant Turk from MIT, winner of the Nobel Prize last year in economics. He and I are talking about democracy in the new world order and the importance of liberal democracy for scientists. You know, and for those of us that care about science and the progress of, of human flourishing. He and I are talking this week. Tomorrow I'm supposed to talk with my friend Carlo Rovelli about his new book, Relationality in Quantum Mechanics, Loop Quantum Gravity and Others. Another upcoming guest, Adam Grant,

• 1:10:34Brian Keating?

  who I teased a couple of months ago about his article that, you know, that CEOs like Musk and Bezos, who want people back in the office are just not raging narcissists. Not disputing, you know, all of his claims, but, but he had a really interesting psychology paper that he published. And I reached out to him about his new book, which is coming out. And he almost turned it down, except for the fact that I, that I had written this carefully, you know, constructed argument that if he cares about narcissistic leaders, he should have been interviewing, you know, his fellow professors and me. Because, you know, if any job could be outsourced to Zoom, it's, it's the professor. And we did do that during COVID and it was horrible.

• 1:11:17Brian Keating?

  So I think I provided a useful counter example. Hopefully he'll, he'll enjoy that, that conversation that's coming up soon. Ethan Molek, speaking of AI geniuses. He's coming on to discuss the new book that he's written in the partnership between AI and humans. Also a Wharton professor, so two Wharton professors with books coming out the same week, basically. And then what's next? Besides my birthday celebration, I'll be interviewing Richard Dawkins in New York City at Carnegie Hall in October, October 20th, I think. Join me there. My second time hosting Richard Dawkins. Last time was in Vancouver, Canada. And it's great to go to Carnegie Hall.

• 1:11:59Brian Keating?

  I never thought I'd play Carnegie Hall before, you know, a musician that's, you know, much better talented than I am. I mean, I can play Spotify. I mean, I'm good at Spotify. Let's be honest. So I have just a huge number of things coming up. In addition to the work that's coming out, I have a paper just accepted for publication, the most prestigious journal in astrophysics, the Astrophysical Journal Letters by my brilliant postdoc, Anto Lannepin. And I'll be summarizing that paper. It has to do with breakdown of Lorentz violation, Lorentz invariant symmetry, looking at the cosmic microwave background. He and I and our colleague, Professor K. Arnold here, came up with a brilliant, you know, plan, really led by Anto.

• 1:12:44Brian Keating?

  And he's on the job market. So folks looking for brilliant professorships should, should choose to contact him. And, and this paper really reveals how we can do a better job calibrating, understanding, systematics in what could be more exciting than almost any measurement I can think of, which would be the understanding of whether or not relativity is obeyed throughout the universe in a certain sense. We'll talk more about that. I just did talk to Robert Wright about his book, The God Test, which is sort of the Turing test, AIs, can we pass it? So a lot of really cool stuff. Adam Frank was on recently. He's coming back on. He's had a lot of pushback and back and forth with my friend Beatrice Villarreal

• 1:13:28Brian Keating?

  on the notion of extraterrestrial technology, perhaps visiting the earth pre-Sputnik. So couldn't be from human creation. And she and I talked in July and that was a really popular episode. It's climbing pretty virally still. She was supposed to be here next month in October for the Science of Consciousness, a conference put on by my friend and past guest Stuart Hameroff of University of Arizona. He'll be here, she won't be here. But there'll be a lot of great speakers there, including me. I'll talk about a new proposal that I have for what's called reverse panspermia. How do we understand the, the movement of, of, of life throughout the universe?

• 1:14:14Brian Keating?

  And, uh, and without understanding exactly, um, you know, what, what the limits to perhaps this, the facundity or credibility of spreading life by, you know, blasting DNA throughout the universe. So we're talking about that and, um, and other things. So, uh, hopefully it's going to be an exciting year and, uh, new year. I wish my Jewish friends, uh, Shana Tova coming up on Friday, Saturday. I'll be celebrating, uh, and, um, just want to thank you all for one more trip around the sun. Hope I have many more and I could do a lot more, um, a lot more good and involve you, my brilliant audience as well and all

• 1:14:57Brian Keating?

  my adventures. So for now, stay tuned. Uh, again, I have a lot of great content coming up. Do, do subscribe, leave a like. It does help. I hate asking for it, but it's my birthday. So I'll ask you all, please subscribe where you're watching this Twitter, LinkedIn, um, or of course on YouTube. And it really does help, um, with the, uh, spreading of these incredible messages with incredible guests. So a lot to look forward to. Thank you all so much and thanks for joining and I'll see you next time. Stay tuned.

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• 1:15:47Speaker 05

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