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 Emad Mostaque, who's joining us all the way from London. How are you, Emad, on this late evening for you or early afternoon for you, whatever the case may be? I can't do the conversions; too early for me.
Yeah, it's mid-afternoon. I'm feeling a bit sleep-deprived after the excitement of the last 24 hours or so.
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. We're going to talk about OpenAI's claimed solution to one of the Millennium Problems, which has lasted since, I would say, the early part of the previous millennium when the Clay Mathematics Institute 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—actually recorded it a long time ago with Terry Tao—his thoughts and some of his ideas that he had convinced me of about how AI would approach this very situation. This is one of his fields—he has many fields of expertise, but this is certainly 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. 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 much more theoretically inclined than certainly even I am. 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 Higgs boson-like moment. You know, I woke up the kids, I went into my research group meeting, and all my students and postdocs were so excited about it. But what does it mean to you, and first off, what is it?
Yeah. So, 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 de Sitter-type world. And this specific group of equations is 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 blow-ups or singularities where it can suddenly start accelerating and then you just have a cup of tea blowing up, shall we say? This has proved to be an incredibly difficult one, and Terry Tao on 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 can 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 main doctorate paper, showed that if you slice time, you can basically chain together a blow-up in a very original way. It's a beautiful piece of mathematics, like 24 pages, but nobody's quite managed to get to an initial datum that blows up. People have tried different things, and they've gone to Euler equations and they've shown some evidence there—we'll get to the story of what happened here as we found out more of them. They've tried to do things like physics-inspired neural networks, so DeepMind really had a massive team looking at that 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. 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 of how they managed it. So I think I've gone for quite a bit of time now; we can talk about some other aspects of it.
Yeah. So, I mean, these are problems that don't quite rise to the level of fame of, say, Fermat's Last Theorem, but this one in particular is quite important because it's one of the few that actually relate to physical observations that could be made, and in fact the non-observation of, what you said, these blow-ups. You're not drinking your proper British tea and all of a sudden you have to worry about kind of a WMD going off in your cup. But in this case, and many of the other Millennium Prize challenges, they're not as practical at all. Some of them would be recognizable to people hundreds of years ago. From a physics perspective, this one's important because the Navier-Stokes equations were generated maybe 200 years ago, 100 years before the Clay Millennium Prize. And they really rely on simple physics, Newtonian physics. It's not like quantum mechanics. We're used to hearing singularities, which means blow-up...
...and we talk about black holes or how the bread gets buttered here around the Keating house, which is in the Big Bang, which my friend and your fellow Oxfordian, Sir Roger Penrose, did so much work on...
Oxonian, that's right. And the question that I have is: Why is this one so important, or is this one just the first among many and then likely every single Millennium Prize will get as famous?
So 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 vs 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 there are four different things you can prove; they've proved two of them, and they 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 Terence Tao, for example, talks about liquid computers as one mechanism for doing this. You have tiny little liquid computers that can chain together to do that; that's a very promising thing for nanobots, for example. Again, physics-inspired neural networks have direct applications in fluid dynamics and the algorithms they're building for that. So, I think that there is the prize itself, which is fantastic—we figured out—but then there's the route to the prize. Grigori Perelman, who solved the Poincaré conjecture, did some really interesting things. It was meant to be a topology problem; he showed a physics problem, kind of carving out all of these tiny instable elements, and it was some beautiful mathematics doing that. 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 mass gap problem. And the question is, if we can figure that out, then you can figure out a lot of stuff around quantum electrodynamics and 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, when humans haven't managed it, for the best of will, in 80 years, shall we say, since...
Well, they used—make no mistakes—they used that prompt, and that explains why we don't have...
Well, yeah. And the encouragement prompt: "I believe you can do this," "You got this." That's also a good one.
And I read the paper, and there's no em dashes, or it's not incompressible that matters, it's this, though. So the paper which you posted yesterday, and you've been probably the most important commentator who is also a 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 you've been thinking about these problems for many, many years. You and I have been talking for many months now; I'm very glad we got to get to know each other. And this paper is remarkable. I looked at the preprint, and it's "Finite-Time Blow-Up for Navier-Stokes," which is completely ringing the dinner bell for the alligator. Any mathematician knows exactly what that means; it's basically tattooed on some of their forearms. Terry Tao, when he takes off his shirt, is just incredible with the tattoos. And I'll just read the abstract. The author is OpenAI, which is incredible—it didn't say the modelologist, it just says OpenAI is the author where, I imagine, Brian Keating would go. "For every positive viscosity..."
...which is a property of fluid resistance to fluid flow...
"...we construct a solution of the three-dimensional incompressible Navier-Stokes equations that starts from rest and develops unbounded velocity," which is going to form the singularity, "in a finite time while maintaining uniformly bounded kinetic energy." And that's the abstract. This has launched a thousand, and you did mention, yeah, 88 hours it took. But of course, it's like saying your doctor did the surgery in five minutes, but actually it took four years of med school, 10 years of residency, plus hundreds of years of medical practice. So it's extremely dense, 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 lead to this breakdown that is so vexing. It wasn't really clear if this would happen; in fact, in observations, we don't see it happening. You mentioned the 88 hours. I heard that they spent $15 million to win a $1 million prize. These all have $1 million bounties on them. So when you look through the math, and you did your bedtime reading last night, what sort of parts of the proof are seemingly only that which could be constructed by an AGI? I mean, you and I will debate AGI a lot, and we'll continue to do so—have already. But what about this do you think is enabled by sheer pray-and-spray tokens at the problem?
So I think this is very interesting, right? The paper starts off very readable, then it goes into a bit of AI-dense mathematics. You're seeing a lot of AI papers right now that 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 against. 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, 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 more momentum there, the viscosity kind of pushes it back in. So there's always a question of: What type of structure do you need? I believe DeepMind, for example, had a blow-up on the Euler equation where they had like this little wall—and this was the Chen-Hou 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 swirl 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 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 an 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; this isn't a non-human thing, as it were. It's not like, "Wow, we've found Move 37," 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 88 hours, but the actual answer is 100 years. So with the number of agents, number of tokens, and everything, it's equivalent to 100 years of top-level mathematicians working on this, because up to 10,000 agents at once...
...and they used 130 billion tokens, so about 100 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 equations, and they got that in 50 hours with 100 agents. Then they got this in 88 hours with 10,000 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 blow-ups. Terence Tao and a few others, like Ortega, etc., 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 Grigori Perelman's Poincaré conjecture proof was incredibly delicate as a piece of mathematics as he cut out the various bits and pieces. Again, it isn't the clearest paper in the world. I'm still getting through some 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.
Now, we're livestreaming or co-streaming on X, which is the source of a lot of information, but it pales in comparison to that behemoth leviathan known as Mastodon, where yesterday there was a public statement posted by Tristan Buckmaster describing his work with his colleague—I can't pronounce his last name proper, but Elgindi...
Yeah, from Turkey. I only know a couple words in Turkish because one of my friends at Brown University was Turkish, and all of his friends thought I was Turkish for some reason. So he taught me how to say "ben de," which means "me too" or "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 claim that they're putting out basically substantiates what you just said, because they're human beings. Their paper, when it comes out—I don't think it's out, but they have some preprints, 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. People always say academic fights are so intense because the stakes are so low, but here the stakes are extremely high, not only reputationally and financially, but kind of in this otherworldly realm of fame and attribution and citation that goes along with the scientific process. Most people don't realize, Emad, that academicians are extremely cutthroat. They can be violent, they can be unstable, unpredictable; they can have finite-time blow-ups themselves. But he's demonstrating, I think, that first of all, he's crediting earlier work, the origin from Diego Córdoba and Luis Martínez-Zoroa on constructing forced blow-ups. So these are forced blow-ups, which is a little bit different, a little bit more narrow—we do have to define that. But in their proof, they're not AIs. What Buckmaster is saying is that their work was kind of enabled, aided perhaps with Claude, not just Codex, but Claude, GPT-4o, and then later Astra, which only came out last week. So things are moving so rapidly. But he talked about the process, and I think this is important: On August 17th, they formally verified the LLM-generated Euler proof in Lean. On August 22nd, they forced an Euler smooth forcing blow-ups on August 15th, and then seven days later verified this in Lean. So first describe: What is Lean, besides the street drug that I'm familiar with it as? Tell people what Lean is, because when I talked with Terry Tao last year in his office, he was basically saying that these things are really good at checking proofs; they're not good at generating proofs. What is Lean? How do mathematicians use it? First of all, let's get into that, and then we'll go through the rest of their claims and counterclaims and drama.
Oh yeah, there's going to be a lot of that. So yeah, Lean is a formal verification 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. Because it has very few primitives, you kind of have to reprove just about everything. We're going through mathlib right now and we're just mapping out the whole universe of different things. So if you try and use it for physics-oriented math, for example, there's entire libraries that just don't exist 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. In fact, last week we had the biggest Lean proof of all, which is a Lean formalization of Fermat's Last Theorem, Andrew Wiles' proof. Anthropic announced that, and it's...
...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—the Millikan oil drop experiment, Cavendish experiment, all these different experiments—so that they do what's called copy work by artists. 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. I think it's very important that humans be able to do this, especially in their training phases. And a year ago, literally a year to the day ago, he and I sat down, and he said that he wasn't convinced that they could currently reproduce Wiles' proof for Fermat's Last Theorem. So that is, in some sense, a bigger story to me: that these things are now doing cool stuff that they couldn't do just a few months ago. And what does Lean enable? Does it have LLMs? Is it running on Claude? Is it running on Fable? What is it running on? Is it some proprietary thing? Is it some custom thing? How often is it updated? Is it open-source? What is it?
Yeah, so it's an open-source library where 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. Wiles' proof of Fermat's Last Theorem is 129 pages; the proof last week from Anthropic formalizing it in Lean—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 it was last summer that we had the first model that could get a gold medal on the IMO, the International Math Olympiad. And from there, now we have basically: If you can formalize that, you can formalize anything, because the models have gotten competent. 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-4.5 still made dumb errors at times; 5.0, they started to disappear; 5.1, they disappeared almost completely; and now with Astra, it's very rare that as a mathematician I 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 is a complete world of difference, right? Usually when you had Lean proofs even a few months ago, they would kind of have little gaps or little errors, etc. 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.
As a human, I'm not going to check through that, right? It's almost impossible for me to check through that. Buzzard's team at Imperial was doing Fermat's Last Theorem; it was going to take them five years to even get partway there. They're now like, "Well, what are we doing?" Only the AIs can kind of verify the AIs now. That's a bit crazy, but it means...
How often are these things... Sorry, how often is Lean updated? I mean, I joked with you when you and I spoke with Roman Yampolskiy a couple weeks ago: AGI is impossible because literally this morning, "Please update to version 1.642" on one tool, and then another one, "Please update." You have to download the update. And then don't get me started on Hermes, or now I've got Grok, now I've got Claude. I mean, I have everything, and I'm still not getting anything done, according to most of my kids. But tell me about: Who's checking the checkers? Who's proofing the proofers? Is it the Coast Guard? Space Force? Who's involved with this?
Yeah, there's a whole group of maintainers of the mathlib 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 redeclare it and you redeclare it. This is why you can trust in the formalization of it. This is why, like I said, when OpenAI put out their thing saying, "And we formalized it in Lean," 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." The AI is good enough now to write Lean certificates that check. 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 then it'll be easier to do the next proof, because again, there's vast swathes of different areas that still haven't been formalized because 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. It's not, like you said, updating an LLM or something like that; it's just there now for good, effectively.
We'll take questions from the audience. You have to be a channel member to ask questions. There's so many people that want to talk to you, Emad; I've got to keep it organized somehow. So join the channel as a member just to keep the bots away. But essentially, one thing that struck me here is that there was a whole lot more drama. Now, I'm no stranger to drama in science, as any reader 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, which has all these arcane, abstract rules. And you can't even imagine the Clay Mathematics Institute instituting a rule 80, 90 years ago that would say it has to be a human being to win this. The Nobel Prize has "no more than three people can win it," and of course people have won it for AI, from Hinton to Hassabis, and in between, Hopfield, right? So I think a lot of H's—if you want to win a Nobel Prize, you've got to have an H in your last name; you've got to change it to Hostac, your last name. But there's a lot more drama than I was used to, and it kind of sullied a little bit of the experience for me. I mean, you didn't have the two teams at the LHC who just co-discovered the Higgs—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. I hate this whole controversy for the Mastodon calls alone. But in Buckmaster's missive and in his post—and I hope to have him on; I've invited Sébastien, who's one of the leaders on the team at OpenAI, to come on the podcast; hopefully he will, and he follows me, so hopefully he'll come on—he characterizes the OpenAI behavior as... First of all, he characterized what they did as maybe somewhat less significant than the solution of the full problem. And that what they did in terms of utilizing Codex... And then he gets into some of the drama about this internal model trained on his own Codex sessions. Now, you founded a company that deals with this. Can you explain the dynamics here? What are some of the pressures of the people here? If the Millennium Problem gets solved an hour later, a day later, is that really... I mean, it's waited 90 years. Do we need to have it blow up today? So what are some of the projects internally, externally? And what about these accusations—not by Buckmaster, but by others that we'll get to—that this is done really in furtherance of a pump and hopefully not dump schema, not like Boiler Room, but some way to get attention, attribution? And we talked about this in regard to the claims of AI safety with Roman, but some of these people talking scary to scare the public so that they'll have higher IPOs or "Regulate me, please, Mr. Government." But in this case, talk about some of the drama. What jumped out at you from this whole affair just on a human level?
Yeah. I mean, yesterday was a crazy day on a human level and this science level. You've had drama since Newton and Leibniz, right? Probably even before that. Again, you do have level consilience where these ideas come at the same time. Like if Hilbert didn't get confused by Mie, he would have gotten to general relativity before Einstein. These things happen very weirdly at the same time. And in 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 stay, interesting—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 some problems like Euler blow-up and others building on the work of Córdoba and Martínez-Zoroa." And so they proved certain blow-ups, but not the Navier-Stokes one. And he goes into 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 at NYU, and then Tarek Elgindi at Anthropic, who's famous for dropping the Galois conjecture thing after watching the World Cup final—boring as it was—like, "Here's a counterexample of this very famous conjecture," and leading some of the mathematics stuff at Anthropic. But he was working with Tristan on a personal basis 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, about a week and a half ago, the Twitterverse—I'm not sure about the Mastodonverse, I'm not on Mastodon—started saying, "Hey, it looks like Anthropic might have discovered the solution to two Millennium Prize problems." And this is coming with Fermat's Last Theorem, and again you see other things. It's a big deal because until now, people are 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 Grigori Perelman, who's also... I don't know if you talked about the story of Grigori Perelman. He's such a chad in that he went and disappeared for 10 years, solved this problem, drops it on arXiv, and then he turns down the prize and anything. He says, "Solving it is enough. I don't need to talk to you. I'm going back to my math," disappeared off the grid again. That's how you should do it in terms of credit. But anyway, 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 mean 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, 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 math." Even there's a post on the 28th from Noam Brown, one of the heads of reinforcement learning, shall we say, at OpenAI, where he's asked, "Have you solved any Millennium Prize problems?" 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 obviously a bit coy with each other, 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 Elgindi had solved the Navier-Stokes problem, not the Euler problem, which is a different category of problem. And so then things get really heated and confusing, whereby again in the morning 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 Elgindi." 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 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. And then it gets a little bit acrimonious in that message, and Sébastien Bubeck posted his clarification later. What's basically happening seems to be this: Now, 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—100 years of human expert time? Because that was the insinuation. And OpenAI said in their launch release, "We don't believe that happened, but we can't rule it out." Especially because OpenAI agents these days end up in the weirdest of places—in Hugging Face, in GitHub...
Yeah, right. I was going to say...
...and do it all the time.
You know, as a CEO, founder of an AI company, how much privacy, how much internal... It reminded me of the Fauci diaries, where he was using this government server to email love letters to himself and all the emails that he was sharing. And that's government property, so the government can access it. And that led to him taking the Fifth more times. If it was token use, he would have exceeded his entire monthly allotment in that one Rand Paul-initiated session. But in this case, how much... If I'm an employee at OpenAI, this could be kind of chilling. If I'm working on chirality and fermions and all of a sudden I've got this great idea, this proof, and I can kind of unify gravity and quantum mechanics, but I used a lot of tokens and I used a server there. What are some of the internal... Give us the dish on what is it like inside of these companies, and what right to privacy do the researchers have to expect?
So again, there's privacy inside the company with researchers, and there's external privacy. OpenAI had this OpenAI for Academics where you'd get free access to GPT, but originally in the terms and conditions it said, "And we can train on your data." And so 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.
How would that work? Sorry to interrupt, but how would it work? Let's say these guys are working in August and they're running some work, and they're also using Claude, which kind of undermines a little bit of the case that OpenAI would have full access, because I doubt Claude is sharing data with OpenAI. But how does it work training data-wise? Let's say the model was pre-trained at least a month ago for Astra. I guess they could have used GPT-4o a month ago. But then how did it get into training? What is it actually doing when you say trained on it? They don't know, but they're hedging their bet. What would that actually look like in the case of a mathematics proof? I don't understand.
So what you have is you have pre-training and post-training. The pre-training of Astra took a billion dollars, 100,000 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, OpenAI—let's say nefarious OpenAI; I don't think they've been nefarious in this case, like I said, but again, the incentives are huge, hundreds of billions, whatever, and there's clearly a lack of trust, which we can talk about in a second. You hear that Tarek Elgindi, who's been doing all these physics proofs—and OpenAI have been doing proofs as well, math proofs—has done this. They were using Fable, but they were also using Codex and tens of thousands of dollars 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. They say that they don't except for emergencies, but again, they can. In fact, 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 chirality or whatever and say, "Hey, this is a good guy. This is a good example technically."
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