Theories of Everything with Curt Jaimungal - Jacob Tsimerman: He Won Math's Highest Prize. Then Announced the End

Episode Date: August 10, 2026

I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE Ten days after winning the Fields Medal — math's highest honor — Jacob Tsimerman joins to explain why he's leaving academia temporarily for OpenAI's AI safety team, and why he's grieving even as he does it. The conversation covers why math is one of the first fields being radically reshaped by AI, whether a proof still counts if no one can understand it, what mathematical "understanding" really means, the ethics of elite access to frontier models, his disagreements with the Leiden Declaration, and his advice for young people weighing a career in pure math in an age of rapidly advancing AI. This is an exclusive first podcast with Jacob Tsimerman. FOLLOW: - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Substack: https://curtjaimungal.substack.com/subscribe - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - Crypto: https://nowpayments.io/donation/TOE - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Fields Medal and Grieving - 00:05:38 - Canonical Human Cognition Patterns - 00:10:40 - Prompting the Mathematical Future - 00:15:40 - Pure Math and Physics Loops - 00:21:00 - Epistemic Black Boxes - 00:26:00 - Rigor Outgrowing Intuition - 00:31:20 - Cognitive Mechanics of Understanding - 00:37:00 - Gödel and Working Memory - 00:42:10 - Mathematics as Improvised Art - 00:47:30 - AI Power and Meritocracy - 00:52:50 - Math on the Chopping Block - 00:58:20 - Unrestricted Optimization Risks - 01:03:40 - AI Safety Manhattan Project - 01:08:50 - Training for Post-AI Careers - 01:14:10 - The Managerial Shift - 01:19:40 - Cognitive Offloading and Adaptation LINKS MENTIONED: - Jacob's Website: https://www.math.utoronto.ca/~jacobt/ - Jacob's Publications: https://www.semanticscholar.org/author/Jacob-Tsimerman/3130599 - Quanta's Story On Jacob [Article]: https://www.quantamagazine.org/jacob-tsimerman-wins-2026-fields-medal-for-andre-oort-conjecture-proof-20260723/ - André-Oort Conjecture: https://www.ams.org/journals/notices/202410/rnoti-p1307.pdf - Canonical Heights On Shimura Varieties And The André-Oort Conjecture [Paper]: https://arxiv.org/abs/2109.08788 - O-Minimal GAGA And A Conjecture Of Griffiths [Paper]: https://arxiv.org/pdf/1811.12230 - Ten Advances In Mathematics And Theoretical Computer Science: https://openai.com/index/ten-advances-in-mathematics/ - Thoughts About The Leiden Declaration: https://gowers.wordpress.com/2026/07/26/thoughts-about-the-leiden-declaration/ - Tobias Osborne LinkedIn Post: https://www.linkedin.com/posts/tobias-osborne-601830a5_farewell-to-the-conjecture-prover-several-share-7487777959299276800-mxsa/ - Math For AI Safety: https://mathforaisafety.org/ - Charles Fefferman: https://en.wikipedia.org/wiki/Charles_Fefferman - G-Functions, Motives, And Unlikely Intersections [Paper]: https://arxiv.org/abs/2501.09867 - Tobias Osborne's QFT Lectures: https://www.youtube.com/playlist?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS - AISI Website: https://www.aisi.gov.uk/ - Sebastian Jaimungal: https://sebastian.statistics.utoronto.ca/ - Edward Frenkel [TOE]: https://youtu.be/RX1tZv_Nv4Y - Roger Penrose [TOE]: https://youtu.be/iO03t21xhdk More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices

We're living in crazy times. It's not going to be business as usual. This is an exclusive, Jacob Zimmerman's first podcast. Ten days prior to filming this, he was awarded the Fields Medal, Math's highest honor. That same day, on stage, he announced he's leaving, temporarily, to open AI and AI safety. I'm definitely grieving. I think he's going to hit math. That medal was for oh minimality, taming some monsters of geometry and analysis. Partially, this is the territory I explored with Edward Frankel on the Languans,

program. Since most other interviews will dwell there, we decided to talk about something different. Part of me thought it would be in academia forever. On this channel, I, Khrjai Mungal, interview researchers regarding their theories of reality with rigor and technical depth. We talk about so much in this episode, such as how AI is revolutionizing math, potentially to its own death. What advice Jacob has for students graduating in fields where AI may be displacing them? And along the way, we bond over our shared comedy past, my stand-up and his improv, and of course, the University of Toronto. I think I'm leaving to do what I think is most important.

You're grieving. Yeah, a little bit. I've talked about how math is changing. You know, there's AI is affecting many different things about our world. One of those that's happening quicker is mathematics. That's a little bit counterintuitive, I think, to many people. including me earlier on, because one would sort of expect what humans find easier to be affected more quickly. And math is generally seen to be one of the harder topics to approach. But because math

is a closed system, you can sort of think about math with just your mind. You don't need experiments. You don't need materials. AI has been very good at it. In fact, just, I think two days ago, OpenEI released the solution to 10 more conjectures. I don't know most of them very well. One of them non-selfic groups, the construction of those, is a very big deal.

So yeah, there's something about you know, math itself is going to go through a very exciting time, hopefully, because you're going to be able to do it in a much more powerful way. But mathematicians, such as myself, are used to a certain working style,

and a lot of my working identity is tied to sort of having year-long projects, decade-long projects sometimes, working at the edges, slowly figuring things out, having those aha moments. I think that's going to go away. So there's something about that that I think I'm definitely grieving. Are you concerned more for mathematicians than mathematics? Yes, at the moment. I think mathematics is going to have to change, but I do think we'll navigate that change. At the moment, I think as far as the field is concerned, more the people, especially the young people, who are going in, sort of looking to do a PhD, and to go about their business as usual in terms of the profession. And I think that's

being upended. So what's going to happen to math in four years? Is there going to be an AI field's medalist? No, there's two things about the question. One is that four years seems like an insanely long time to me. AI is changing so fast that even speculating two years from now seems very, very difficult. So I don't know is the main answer. And I don't know how society will react because often I, when I've been saying these predictions of mine for a while now

that AI is going to become robustly superhuman at the act of doing mathematics as we do it today, people often label me a pessimist or the infer certain values I have about math. And really all I'm saying is that I think this will happen. And how society chooses to react is both a harder question and it's also not set in stone.

We have the power to decide. So I'm involved in certain workshops, the fact one next week, where bringing together mathematicians of various levels doing various types of work to try and figure out how to restructure the field

what it's going to look like going forward. I mean, it's so hard to speculate because when you speculate about the future, you're almost always wrong. But within that, I think it's going to be a transitionary period where we're going to have to deal with the fact that AI is going to produce results faster than we know what to do with them.

We're going to need to figure out how to categorize them. We're going to need to figure out where to point, you know, this immense power we're going to have. And then I can't imagine that we don't have something like an automated machine or an AI system just running math all the time, at least one. You know, looking, making conjectures, solving problems, categorizing them, running them up,

picking definitions, just talking it away, and just working at making math better and better. There's probably other parts to it. But, yeah, hard to say. Did you watch The Odyssey? No, I didn't. I know what happened, but please, no spoilers. I'm the same.

I won't even see the poster. I don't even want to know who's in it. I don't want to know the genre. If there's a film that I like, I just want to see it. No spoilers at all. But have you seen Epic the Musical? Have you heard Epic the Musical?

Oh, I recommend it. It's a purely audio version of The Odyssey. It's very, anyways, it's very, very good. Back to your question. Well, apparently the Greeks around the time of Odysseus, or maybe 400 years after it, I forget. They thought that the relics that they see around were so grand, it couldn't have been manufactured by man.

So they thought giants created much of what they saw. Now what I'm wondering is a lean proof that you can't understand, that no mathematician can understand, is that a proof? Or is that the same thing as just it's being created by beings beyond us? There are sort of very interesting questions with AI around consciousness, for example, and around the nature of self and stuff like that. And that's a very important and interesting conversation.

I feel like it's being too tied in to the question of capabilities and concrete technical work and advancements, the sort of scientific process. So in terms of the proofs, one thing I'll say is it just has not been the case that the machines are writing proofs that we can't understand. They're all building off of human work, very much so. Like, they never come from scratch so far. And all their ideas, while clever, are very much things that we're sort of used to seeing. They're a bit more disorganized.

So, you know, the AI system so far don't write out math work as well as humans. So there's a substantial process in rewriting. But there's this question, like you said, if somebody solves Riemann, you know, and the proof is a billion lines of technically correct, but impossible to decide. for code, what do we do? Mm-hmm. I don't know in that case, but it's just not the world we're seeing. In fact, it seems like, it's so hard to say definitively,

but I feel like what we've seen should be a slight Bayesian update towards the idea that human cognition is not as arbitrary as you may have thought. It seems like the patterns that we notice and the way that we choose to approach subjects maybe just is sort of the canonical way to think, or at least in part. Now there's counter arguments because the systems are also trained in our language and our whatever. Nonetheless, I feel like there's a slight update there. So if they start printing out incomprehensible proofs, I think it depends very much on what that looks like. For the moment, though, it's just not one of the issues.

I think a bigger issue is that they'll start turning out in principle comprehensible proofs, but it'll be much faster rate than we can keep up with. Like, even now, I mean, you know, I've been a professional mathematician for 20 years. I know my little corner pretty well these ten proofs open the eye released, I can't understand any of them. Not because it's magic just because I can't understand

most math proofs that aren't in my field without devoting a lot of time to them. So if I picked one of them and I spent a few weeks and I really digested it, then I probably could. But it takes time. It takes work, it takes effort. Right now, humans have this huge division of labor because math is so broad

that we're experts in our own little corners. And it's funny, within my field, if somebody proves something outstanding, they can communicate to me the main idea in maybe five minutes. Right. Like, if somebody solves Riemann right now, and it's using anything like the usual methods, they can probably talk to me for like maybe 20 minutes, and then I'll be able to reconstruct the proof. Because the language and the ideas are so shared. On the other hand, if somebody solves something in another field far away, we've got to spend a long time sort of bridging that gap. So we're kind of spread very thin mathematicians

across the domain of math as we know it so far. So I think what's going to likely happen is that AI will just start doing what humans would have done eventually, but so much faster that it'll look like, if I want to understand the math, I'll be like, okay, well, there's like, you know, 10,000 results in this field, which became five other fields, and there's 500 results here and there.

If I want to send any one of them, I can. If I want to get summaries, I can. But I just don't have the time. So then I have to start thinking, how do we organize this? You know, how do I get the main ideas? And I don't know what the answer to that sort of looks like. So we both have a background in comedy. And Seinfeld said when someone was asking him,

hey, what's it like to perform at a club versus at a stadium? So 100 versus 10,000 people. He said, when you're treading water, it makes no difference if it's five meters deep versus five kilometers. is deep. There's just some threshold beyond which it's beyond you. Yes. Currently on the archive, even on your own, in your own subfield, I'm sure it's just beyond you to keep up with your own field. So what is it then that AI is going to do that makes it much different? You have to start categorizing. Yeah. So it turns out that

that could be the case, but it's not. So I basically know all the work being done in my, you know, few little fields like unlikely intersections. I don't know everything, I'm on an expert, and everything, but nothing will surprise me. If I see a paper, I can look at it and be like, okay, they're doing something like this. I've got to all categorized. Number theory is wider than that. So there's definitely work in number theory that is less familiar to me.

But even there, I kind of have a sense, I feel, of the main projects, you know, what they're doing, how they're coming at it. So it's just not the case right now that I'm overwhelmed in my field. If that starts happening, Like, I think what might start happening is, how should I say? I got my award for basically two lines of work.

The Andre Oort Conjecture and the Griffith conjecture. Okay, that's two problems. Andre Oort I spent about 12 years on, maybe, 13. Griffiths I spent about five years on, and that's, you know, I imported some work that I had done before. So if you count that, then maybe 10 as well. So that's two probably I spent 10 years on. and I had those 10 years to basically get oriented, you know, kind of spread my arms a little bit,

take my time, really get to know what's going on. If projects start speeding up to the point where something like that takes, you know, a month or a week, then I have to reorient every week. And I just, I can't do that. I don't have the skill. I know you said predicting even two years out is difficult, but we can imagine that GPT6 is going to be

slightly higher IQ or whatever is the don't. domain that you measure it by for map and for whatever other domains. So let's imagine GPT6 comes out one month from now. Let's imagine next year we have GPT7. What does that look like for mathematicians? I mean, that part is fairly, I don't think I'm saying anything controversial by saying GPT7's coming out. Sure.

One year from now. Sure. Yeah, I think, so I certainly think what's going to start happening is that, I don't know exactly which GPT it is or clot or whatever. But I think we're going to get to the point where there'll be a brief period where mathematicians solve problems in large part by prompting LLMs and then probably also adding our own expertise to it right now. Like I've worked a bit with LOMs throughout, as it improved the past two years.

Recently, I had a proof and LLM found a mistake, but it couldn't fix it, but I could fix it. So there was like a real collaboration there. I think that will change pretty soon. I think my part is going to be very small. And I think there will be a period where we try to get the LOMs to answer our favorite questions, to finish up our research projects, to explore more, beyond we've explored. And then I don't know.

There will be a lot of tumult, I think, because a lot of our systems are broken. Already now, you know, how do you assign credit for something an LLM does? That's not the most important question, I think, but it is an important question, and it's causing a lot of havoc. What do you teach your PhD students exactly? Because the problem-solving skill, and people are unhappy when I focus on problem-solving so much,

but you know, problem-solving skill, the theory-rebuilding skill, the furnishing-making skill. Why are people happy? There's a sort of a... I'm more of a problem-solver. I've always come at math through having a concrete sort of mystery and trying to figure it out. math is not just that.

It's often trying to categorize things the best way, come up with the right definition, ask the right question. I'm of the opinion. Those are all more or less interchangeable skills. Or do you mean to say that the definitions are in service to the problem solving? Yeah, I would say there's sort of a cycle there where to solve something, you look for the best definitions. The best definitions, you make them to sort of address the mysteries that you want solved.

There's sort of a variety of perspectives, and some people think there's a bigger division than I do, and that problem solving is like people have said, and I don't know, it's on Twitter or, you know, an organ, it's hard to get a pull of actual mathematicians, but I've heard it said that quite often that problem solving is a pretty small part of math. You know, mostly what we do is try to understand,

and problem solving is sort of an ancillary part of that or something. I disagree. I think problem solving is pretty central to make. that exists right now. But regardless, whether they're one thing or whether there are a few different skills, I think to be the case that for a while we'll start being like, after the phase where they get better than us, you know, we collaborate and they get better than us at that, so we just promise them and then we decide what we once solved. And I think people will start, you know, asking, well, I don't know, is this connection true? Is that a connection true?

Was the right way to think of this pediatric homology theory, you know, was the right way to think of these class of number theoretic questions or whatnot? And then we'll, we'll, we'll, we'll, sort of keep zooming out, like, cool, now that we can make theories super quickly, do we want to make a meta-theory, do we want to understand where it's all leading? One thing I'm excited about potentially is tightening the loop between pure math and applications. Because right now, you know, pure math sort of does its thing for aesthetic considerations mostly. Like mathematicians want to solve mysteries for the sake of mysteries. It's curiosity-driven research, pure mathematicians. Most than at least. And then the idea, and then practice this happens,

though you can argue about how much. Down the line, and it's often decades, one math theory that was very much pure and just for its own curiosity's sake, it was explored, becomes applicable to something practical. You know, this happened with like information theory, entropy, it happens with physics now and then, you know, physics is some theory

and it imports something like Kalebiows or whatever else. Sure. That takes decades right now, or at least years. That could happen much faster. It could start being the case that physicists are like men something's not right, and the AI is like, oh, cool, you need a math theory for this. Let me go and do it. Even now in our world of GPT and Claude and the AI investments, what I'm saying, sounds like science fiction.

And many people kind of dismiss me when I say it, because it's unreasonable. But I think you've got to get used to the fact that sort of science fictiony elements are going to start happening faster and fast. Not all of them, but a lot of them, yeah. Chess didn't collapse when Deep Blue came out. I mean, there was grieving in the community of chess, but chess is still going strong. So what's the parallel here? What's the difference between chess and math?

Chess was always fundamentally about human ability. It's how good are humans at chess. Let's appreciate the sort of brilliant moves. I play chess well enough to enjoy watching all these tournaments, though I'm not well enough to appreciate them truly. And by nature, it's competitive. By nature is competitive. And solo.

it. It's, I think it's debatable how solo it is, because even though the players are trying to win very much, they're sort of creating these beautiful works of art in these chess games together, and sort of competition is the medium through which is brought about. But, you know, a lot of my friends like just looking through chess games and me too, like when you get fun, interesting positions. It's fun to appreciate. So one can debate how solo it is. In math, though, that's sort of not primarily how we think of math. We think of math as we have these mysteries, and we want to solve them. And look, I shouldn't have said that.

I sort of... I actually am averse to when people say that math is fundamentally for this or that. And mathematicians do math because of this or that. I think there's many reasons why we do math and it's different for different people, and they're all valid. You know, however you choose to approach the subject

is useful and valid. Society, of course, wants math for a certain reason. That's a can't understanding, and we shouldn't lose track of that. But mathematicians have many different things they get from it. But I think it's unviable as a position to say that all we want for math is to see who the best mathematicians are. I mean, we definitely value mathematics for the theories we generate, for the understanding we gain from it, which was never true for chess. Chess was always a game for humans and exercise for humans.

So I think there's important differences between the two. I think it's going to hit math. My understanding is the chess community was hit a bit in how they prepare and stuff. The nature of the game changed. but by and large sort of business as usual, you know, you still train, train a bit differently, and then at the board you still have your skills and all that stuff. I think math is going to change in a more radical way.

So something just happened recently. The economist sat down with Elon Musk, who told them that AI will surpass human intelligence within five years, and then in 10, humans won't be running the world. It went viral, and I recommend you check it out. See, the economist is more than a magazine. Actually, I subscribe to the Economist's annual subscription. Their science and AI coverage is among the best that I found anywhere.

And I say that as someone who reads plenty of it, they even covered how dark energy may be weakening with time. If that holds up, it completely changes our understanding of the universe's fate. Those are exactly the kinds of questions that we explore every week on this channel. Now, the Economist is, of course, known for global affairs, both political and economic reporting. Interestingly and flatteringly, Toe is one of the only podcasts that they're the Economist partners with. So as a Toe listener, you get their summer sale 50% off the annual subscription, but only until August 17th, 2026. That's not a deal they have just anywhere. Head to

Economist.com slash Toe to subscribe. That's Economist.com slash TOE for 50% off the annual subscription. Someone asked, is a proof, almost like a tree in the forest? Is a proof still a proof if no one understands it? Suppose it has a lien certificate. I think it's one of these cases where in a sense yes and a sense no. It's sort of, you know, what is a proof? If you, I mean, there's a sense in which yes. A proof is a statement, you know, a theorem is a statement in first sort of logic or DFC or wherever you want to formalize it.

And the proof is a sequence of deductions that lead you to get there. So in some sense, I think a sense that's very much alive, the answer is yes. I think pretty soon we're going to have proof no one understands and they're going to underlying mathematics and based on mathematics, other things are going to work. So, you know, does a train run even if no one understands the mechanics by which it runs? Yes, it does.

I mean, you can look at it run. So I think that's going to happen. A proof also definitely plays the role of conveying understanding to the community and, you know, facilitating a shared understanding. And from that perspective, it's a more complicated question. Now, already now, I mean, a lot of my theorems that I have proven, I don't understand all the steps to. Meaning that you couldn't recapitulate them on the spot, but if you were to go back.

No, meaning more than that, meaning that I have used other theorems that are very much accepted by the community, to which I usually know the main ideas, but not even always. I mean, oh, minimality, you know, this thing from logic and model theory that I've used continuing traditional. why are people using it, is something which are very comfortable using. I kind of know loosely how they prove that tourism structures are or minimal, but I definitely don't know the proofs, and I definitely couldn't recreate them. Like, maybe I could if I spent years on it, but it would take me years. It's not like it's something that I can't do on the spot.

I just can't do it. I rely on other people who have done it as a step. So does that mean that I don't understand my own work? I mean, in some sense, I understand the pieces of it that I contributed. You know, there's bits that I really thought hard about, which I understand very, very well. But do I understand it from first principles? No. So we're already living in this world where, like, what is understanding?

Typically, if we're a working mathematician, you take a problem and you try to isolate the parts of it that people are actively working on. And the background, you just kind of accept this background. I mean, you slowly, over time, want to keep adding to your sort of repository of knowledge. actually, Charles Fefferman, a very proud mathematician, he came to see me when I was an undergrad to talk to me a little bit. It was very kind of him.

I really appreciated it. And I asked him some question like this. I was like, so do you know, you have to know everything from scratch? And he was like, no, no, no, look, there's always stuff that you know fully from scratch. There's stuff you've kind of heard about and know roughly how it worked, no other details.

And there's stuff you've sort of heard about maybe can name some words, but you really, you know, you can't flesh it out at all. And he was like, those are all always going to exist. And it's fine to have them all, as long as that first one keeps growing. The stuff you know from the beginning and, like, super well, you have to keep having that increase. You don't want to rely too many black boxes. So it's already the case that, like, you work on the things that need working on

and understand the things that need understanding. This is going to become much more prominent in the world in a few years, the world of the mathematics. but it's definitely something that's already here. What are some of your ideas? About categories. About categorizing not category theory. Uh-huh. About categorizing math.

Oh, categories of math. First of all, I want to start saying, like, I'm really not, and I'm not being, you know, this is not full humility. I am like not the best person to think about this. It's just not what I'm trained in, and it's not what I spend my time thinking about. the way I think about it now, and this is really from thinking about it quite recently

in terms of like what mathematicians are going to do and what math is going to be for is there are sort of two, I think, roles that math plays. One is identifying interesting structures that exist in the universe, sort of, you know, just in pure thought. A lot of math. Matt is really fun for mathematicians, for me.

I think math's really fun because by nature, you study the things that are most interesting. Like, is the study of puzzles and which puzzles do you work on? The ones that have the most structure, the ones that have the most mystery, that bring about the most fun, the most aesthetics. So, you know, other fields like physics and chemistry, and they're wonderful fields, obviously,

and they interact with the real world, and there's a huge benefit there. They have their own pluses. But they are limited in terms of bringing your creativity by what actually exists in the world. And math is only limited by what makes sense. So part of math is just trying to figure out, you know, what structure can exist in the world.

Now, part of math, another part of math, is trying to explain, make concrete notions which we only sort of fuzzily have understood thus far. Topology is a great example of this, right? Topology is like, you understand the shape of something, but you don't really want to care about stretching or bending. You want to just know the shades, what does that mean?

We've actually come up with, you know, we play with definitions. One of them works better than others. We use open and close sets. And that brings to light a whole bunch of tools. And you know, you know what theory is successful? One way of knowing a theory successful is when the rigor

outgrows the intuition. You have justified the intuition and the rigor is so solid that you can use it to test your intuition against and refine it and throw away bad intuition. That's when you've really achieved something. So in terms of categorizing math in the future, like how we organize it, I think there are these two divisions. There's divisions by applicability. You know, there's a big physics right now is a big open problem in many ways. Like we've achieved so much, but I'm talking beyond my expertise here,

But my understanding is, theoretical physics at least, is going through a rough time to some extent. We have all these theories. We have a hard time testing them. We have a hard time making the math work out as economically as we want. So that's one place where we'll see. Like right now, it's not clear if AI can help with that, but I suspect it can.

There's many different, like what we do in general, we think about the things that seem tangible and practical. You know, like in chemistry and physics, there's many problems we don't attempt mathematical precision for because it's too difficult. This year, actually, one of the fused metals Udang won his prize for, I'm going to get this a little bit wrong, but he derived a global property of behavior

from a statistical, sort of rigorously, a statistical limit of the underlying interaction between the particles, the Boltzmann equations, which is really cool. And in the past, that was too hard. We sort of kind of assumed we had like heuristic ideas, but we didn't actually know how to go from one to the other. So if we could do that to a much larger scale, we might be able to approach more fundamental questions of physics

and maybe tie quantum mechanics and gravity and have engineering applications. And again, I'm talking way beyond my expertise here. But stuff like that, I think, becomes in reach. A tricky part about physics compared to math and computer science. most people think physics is reality. We say, okay, well, this is a physical object, and so the bare metal of the world is physical.

And then you think, well, why is it the case that if someone hands you a theory, a physics theory, they're like, here's my theory of everything. I've solved quantum gravity or whatever it is. It requires an expert to go through. Why is it different than, say, math? Math requires just a lien certificate for these AI proofs. One thing that you learn very quickly about lean is

if you formalize a lien proof, you have to check that the statement is correct because you know you have theorem and you'll write

some lien code and meanwhile we want to know that whatever all all broxins are schloxins you know there's a conjecture

and then somebody writes some some symbols down and it's up to us to check that what's written down really does say that broxins or fluxins

are not something else and that might seem trivial but it's not as trivial it seems. You can only check that what is in the program is correct line by line, but human has to certify that what's being modeled

by the code that we're interested in. In physics, it's kind of is the same idea that we have a physical world we want to understand. And so before you can input it into math, which ultimately, you know, once you have a theory, you can. It might be hard, but in principle

you can. You have to make sure that you're modeling the right thing. So if someone gives you physics theory, you, I think, have to, it depends on what they're sort of giving you. Are they giving you intuitions, which they argue are extremely plausible and correspond very well to the kind of mysteries we're seeing the phenomenon we're seeing? Are they literally taking a model of physics, an underlying theory, and deriving some consequences? If they're doing the former, then we have to think of it's in the latter, then you can plug it into Lean and see what happens. Yeah. Oh gosh, okay, so earlier you mentioned something about intuition versus rigor.

He said, okay, we can rigorize some intuition and then we can do some sort of have some feedback loop and refine our own intuition. Now, if intuitions are blurry and ill-defined, then how do we know we've properly defined this cloudiness? We don't. I mean, we don't and it's not clear there is something to it, right? Like intuitions are higher order heuristics. and practically what happens is you try a bunch of formalizations. Eventually you get one and it feels right. And you sort of test it on all your different intuitions

and hopefully all of them either get formalized in a way which feels satisfying or get contradicted in a way which feels satisfying. You know, you might have some vague ideas. You might formalize it, get a counter example, and you can get two reactions to that at least. One reaction is like, that kind of example is silly. It's not really what I'm talking about.

I think we have the wrong definition. And another one is like, oh, crap, yeah, I was wrong. Like, my intuition is misplaced. And now upon sort of integrating this kind of example, I have updated my intuition. So intuitions are one way to think about them, but they're sort of pointers, hopefully, towards actual, more well-defined theories in the world. And we've properly realized them when it feels like we have,

when the copyright understanding we have sort of matches or intuitive sense. Maybe this is a foolish question, but let's imagine someone's explaining something to you, some proof, doesn't matter, some concept in that, and then you say, I don't quite get that, can you explain this, what about this, and blah, blah, blah, blah. At some point you say, ah, I understand. Okay, what does understanding mean? Yeah. Now, I say it's foolish because I imagine you could say, it depends, I understand it enough for

this purpose, but not for so-and-so, or it's a matter of degree, but there seems to be a moment where it clicks and all of a sudden you say, I understand. Yeah. Seems like a step change. Yeah. This happens all the time. First of all, we use shorthand, you know, hyper-aggressively when discussing math. We don't stop to properly ground everything because there's not enough time.

You have to find short-hands to think about things. So often when someone's explaining something, like a collaborator explains some idea, they will use few words. aren't all the detail, they're just a few words, and I literally don't understand. I'm like, I literally don't know what you mean, and they'll literally, they'll say things like, no, no, no, X is a variety.

It's not a sheaf, and I'd be like, oh, okay, now I get it. So a lot of it's actually getting the, sometimes for me, I carry around, I'm sure many mathematicians do, but I'm hesitant to say all, but many of us carry around toy problems, toy examples, in our heads. Like, what does it mean to understand?

We use the word understanding a lot, but it's a very complicated word. It's a very complicated concept. What does it mean to understand something? You know, some teachers worry that students would be able to compute any integral by memorizing, but they haven't really understood integration. And I sort of challenge that notion. If you can integrate any function, surely there's some kind of understanding there.

I mean, there's no magic to understanding. So I think a concrete way to measure. understanding is can you apply a certain concept to various situations of interest. So algebraic geometry, hodge theory, number theory, representation theory, we all carry around examples on their heads of sort of mathematical constructions and universes where we can quickly test out what's we know that in this one example that I have proving some result is true. tricky. The world has decided that it is tricky, and

if you're going to give me a method that can do something more generally, then I'm going to test it out here. And if it can work here, then I believe you that something you just think is happening. And if it can, then I'm skeptical. So one thing that's happening when someone's explaining something, like I don't get it, is me trying to take what they're saying and apply it

to my internal picture. And then when I say, I get it, it's like, okay, I see how this bit works. And then I've decided that I got it. It's very rare, at least for me, I think for other mathematicians as well, but it's very rare for me to fully work through the details

of something until you get to the actual writing stage where you write the paper. It's just not how you work. It's also not a convincing. Like being able to do something in generality, in practice ends up being, again, for me, a worse test of understanding

than if I can do my four favorite examples. Sorry, what's the worst test of understanding? Being able to write down some proof in general, or some concept in general terms, because you're likely to make mistakes there too. You're not seeing as clearly. When you're a student, often you think more general equals better, and you're seeing deeper and further

if you're using tools that are more abstract and scenarios that are more abstract. And then, you know, there's some truth to that, but there's a lot of truth too also. There's a lot of benefit just sticking to your favorite examples and being able to test things, literally on cases you can work out by hand. So we went to the same university for undergrad,

Correct? UFT? Yeah. So there's Matt 308. I don't know if you remember that. It's a logic. Logic course. Okay.

And at least when I was there, the final exam was you have to prove Gertil's Incompleteness theorem from scratch or whatever scratch means. That's right. I didn't find that it gave me much. I mean, it actually did give me plenty of intricate understanding of Gerdl's theorem, or theorems, but I don't know if that was the most efficient way. Incompleteness theorem.

So if a theory can prove its own consistency, it's inconsistent, that one. Yeah. That's the second one. Yeah. The first one is. is the statement that there exists on truths with your outside of provability? Yeah, I don't know what to say about that.

There's like, there's a couple things. One is that sometimes the intuition is clear. You have to formalize it still, and you look for formalizations that are as neat as possible, but they don't super exist. So like girdle encoding and girdle numberings, the clean recursion stuff,

it's not my field. I've worked at it. It's not my field exactly, so, you know, I'm probably not the most proficient person in it. I've never found a formalization that I've been super comfortable with. Even though I feel like I understand the big picture ideas, my intuition about the big picture behavior is pretty good. Working with a nitty-gritty of it, I'm just not so comfortable with. And so that's one way in which actually working through like the complete proof and writing it down doesn't feel like it's super satisfying corresponding intuition. So that's one way.

Another way is, another thing I want to say is that, like, math is big, even little parts of math are big, and it's just hard for us humans to remember a lot of things at once. So there's various proofs that I just can't keep in my head at once. And I think Gerdows and completely the theorem is probably one of them. Like, I can definitely write it down. You know, if you give me 20 minutes, I can write it down or whatever. You mean the theorem or the proof? The proof. Like a sketch of the proof for the full.

proof? No, probably a sketch. I mean, a sketch, but a sketch that's enough to, you know, satisfy people. But I don't feel it's a different exercise to do that and to sort of have it all loaded up into your head at once. And I think that's actually a pretty important differentiator between some of the really top experts in subjects, is they have some of these proofs really loaded up in their head. These concepts are really short for them. Whereas, for me, for me, me or other, you know, my limitations that aren't proficient, it's more of a workman-like sort of process where you sort of pull up the right, you go your flipbook and you go step by step.

Yeah. Okay, so I was going to ask you if that was particular to model theory, or if that also applies to, say, unlikely intersections, do you also not know the nitty-gritty details, or is it also just a facet of the nitty-gritty details being tedious? And so all you have to do is verify it once, and then you get the gist, and then you move on. and you actually don't like the specific details? It depends.

The work that I actually have done, I think I understand very, very concisely, like very well, I would say, for the Unluck Interjecture stuff in particular. There's newer work now, like the field doesn't stop. You know, you solve something, hooray, but then people move on super quickly. And if you don't keep up, then you get left behind.

Right now, there's a bunch of work being done with G functions. Like something Andre of the Android conjecture wrote about way back, which now is really being developed into a much powerful method. And I haven't, like, I've kept, I've had students who know it a lot better than I do now, actually, which is great. That's always your hope for a student. And I kind of understand it, but I definitely have not put into work. Like, I'm sure if I sit down and spend a month and really go through it to the point where, like, I want to use this, I would sort of go over proofs again and again. I would try to make examples they can't fail.

I'd be like, why does this prove X but not Y? They really need this step, all this stuff. And I'm sure I would shorten it a lot more. And I would need to do that in order to work at sort of a top level in the field. Earlier when I was talking about chess and I was saying it's a competitive sport and it's not as much of a community as math. Would you say that, oh gosh, where was I going? Okay, well, see improv.

Let's go here. Okay, all right, let's do this. Let's do this. See, I like stand-up. I like stand-up because I used to do stand-up, you do and used to. There's a joke from Mitch Hedberg that said, I used to do drugs. I still do, but I used to do. Yes, yes, yes.

So improv, you do and you do and use to do. Yes, yes. Okay. Well, anyhow, I like stand-up for the reasons that Colin Quinn, I don't know if you know who that is. He's a stand-up comedian, that he likes it. It's solo. He said it's like Mike Tyson in your shorts and shoes, and that's it. Yeah.

And math is a community effort, or some people say it is, and improv is definitely, you're not supposed to be as selfish. Standup, you're just purely selfish. In fact, I think Larry David said he liked stand-up because, I mean, sorry, he killed at improv, but he wasn't liked by the other people there because he can kill at the expense of other people. Yeah, right.

And make you look brilliant. You don't want to do that. Yeah, yeah. You don't want to do that. That's interesting. I find myself thinking about what he just said about math being a collab. Math is like both, in my opinion, very collaborative and also very solo in some sense. Like, your confusions are your own.

And your friends help you resolve them, of course. But there is some, yeah, I don't know. There's something very solo about math as well. I came from a very, like, I came from math competitions. They played a big part of it with medical development. I think they taught me a lot. Very grateful for the experience of having had them. And that's, again, like, you train.

together with your friends, but you're there alone for like four and a half hours working. And so I came from a very competitive perspective to it. Definitely my math career, I started out being more solo, and now I never work alone. I always work with somebody because it's more fun and it's better. It's just, it just works better. As far as improv, I definitely love the fact that improv is collaborative. That was a huge draw for me. When I started doing it, it's like, man, this is great.

No one's competing. We're fully trying to be empathetic with each other and listen and make each other look good. I also loved how off the cuff it is because math is so slow. You know, you'll think about the same example and the same theorem and the same thing you're stuck on for like years, sometimes, certainly months.

And there's a joy in that, but there's also, you know, there's something you're not experiencing. There's a lack there as well. So improv, going off the cuff and just sort of living in the moment and not having homework. I really like that part of improv. It's just not a chore at all. And I love math, but there is a lot of homework in math.

You constantly have to go and read papers, make sure that you understand this, make sure you're on top of that. So that was a big draw for me, which is why I don't feel the same way about stand-up. Like stand-up is both alone, as you say. it's not off the cuff. Like stand-up, you have to get... A lot of the providers do stand-up, and they're like, oh, I see, I'll never get good at this, because you have to do the same set over and over and over again.

As an improviser, most of the time, and people vary, of course, but most improvisers, they tell some jokes that work, and they're like, great, now I'm going to tell new jokes. Right. And like, no, no, no, no. You have to tell the set again and again and again until it's perfect.

And that part of it doesn't give the same off-the-cuff feel. And also, it's not... it's not as fun in some ways because, again, it's homework. It's a chore. You have to memorize your set. You have to memorize your reactions. But you'll find fun various, but I'm not trying to just stand up at all. I'm just saying from my perspective why I was so much more into improv.

In a way, it was a huge break from math for me and continues to be. It's very dual to how I work. What I said, somewhat recently I quoted and I really like, to me, it feels true. like in math, I'm constantly trying to gain as much control as I can. Like, I really view math as like I'm trying to conquer a sort of a branch of mathematics. Not in the sense of proving everything, but like make everything as simple as possible. I want it to be no mystery left. I want to be able to handle every concept, to apply every technique.

And in improv, it's so much about giving up control that it was sort of a nice missing ingredient for me in my life. Okay, let's have some fun. What am I missing? I went to one improv class and then I was expecting it to be like how Steve Correll is and you go on stage and you have some fun but then they did some they said okay we're going to go like this

and then you say I don't know what it was I just remember I remember feeling like a fool and I didn't like it but what am I missing what about that exercise do you know that exercise is that a standard one? Sure Zib Zabs up or name there's a lot of clapping exercise in improv well first of all I would say you should probably try few more classes

If you want to get into improv, I have a big believer that anything you want to learn. I think that things require effort to find the fun and join them. So if you try something once and you don't like it, you know. I didn't give it a fair shot. I mean, fair is fair. No, I'm not saying you have to try improv, but I think there's a good chance if you kept going back, you would find it.

In terms of looking silly, it's definitely true in improv that if you don't like looking silly, you're going to have a hard time at the beginning. A lot of it is about shedding your ego. and... Yeah, we had to pretend to be some animal. Sure. Chose different animals.

Embarrassment and shame are like the death of comedy is what they say. So, you know, improv, people think improv is about this scene, and I think it's about being very quick-witted. I mean, it helps, certainly, everything, but improv is much more about being empathetic and fully present and listening. If you really listen to your partner

and react to what they're saying, honestly, the scene usually goes very well. You don't have to be super clever. But yeah, it definitely encourages vulnerability and openness and empathy. In terms of what Steve Carell and people are doing, it's funny, you say, like, Steve Carell looks silly all the time, doesn't he? Oh, yeah. I mean, he does that, yeah.

I'm not sure I answered your question at all. That's fine. That's good. This improv. That's right. Okay, so let's stick on this competitive aspect of Matt. Sure. Even though there's a community, there's also a competitive aspect.

Yeah. It's something that I see when a new model gets released. They say, oh, and we've been working, by the way, with 10 other mathematicians or something like that. And then I wonder, how do other mathematicians view this? Because, look, the difference between Opus 4 and Fable 5 is quite large. So suppose Opus 4 was out and you had access to Fable 5 and you're one of the top mathematicians. That's why Anthropic in this case came to you and said, hey, do you want to test out our model?

Doesn't that give you an advantage? And then if you're already at the top of your field, why do you need that advantage? Do other mathematicians look at others and say, that's not fair? Look, what the heck are you doing? You're giving someone the most brilliant graduate, a thousand brilliant grad students for two weeks or sometimes a month. Yeah. And unlimited tokens, unlimited compute.

Sure, I've heard people say that. Or again, I've read on Twitter. No, I've heard people say that. Sorry, that's legit. That's perfectly fair. I think it's complicated. I mean, it's already true that, I mean, if you do good work or you're seen to do good work,

you get to go to the best places. the best places have the best people. So now you're collaborating with people who are typically more proficient or have had more success, more ideas maybe, and you're going to keep doing better. So it's always been the case, I think in every field,

like in other fields more than that, if you're doing well in physics, you'll get experimental physics, you get more grants, you can have more experiments, you're going to keep doing better. So it's always true that success begets more success. I'm not saying that's how it should be.

I'm not advocating anything. thing. In terms of a policy, policies are hard. It's much easier to point out the flaws in how to do things than come up with a good system.

There's something I find a lot, actually, about the AI discussion in general is, I'm glad people are worried about AI and that they're thinking about it very critically. I think that's a very good thing. But I see

a lot of comments, both again, on social media and also talking to people, sort of criticizing you know, oh, AI is being controlled by this group or that group and it's being used in this way and that's not fair and that's not fair. Whenever you have something new coming into the world, you have to decide where the power goes. You have to decide how to disseminate it amongst whatever your society. And where does it go?

Well, go to companies, but companies have profit incentives. Go to government, but government can become authoritarian. they can enact much deeper abuses than other members. So where do you want sort of the power to go? I'm not saying I have the answer, again, but I see a lot of sort of negative comments of the form, well, you can't do this because that has this side effect. And this idea of like, again, I'm not even criticizing that

because it's good to point out flaws, and whoever's winning should have a critical eye towards that. them. But I think people often don't think through the alternatives and they kind of imagine that what's happening now was terrible. If we just changed, things work super well. AI is a very difficult problem. I think there's a lot of low-hanging fruit to be improved,

and I hope we improve that. But even if we all, in the best case of all of us working together with full cooperation and stuff, it's hard to decide how to handle it well. So to come back to your question of how to use it well for math, yeah, I don't know. Right now, it's being given to the best researchers. Why is you going to be as to reachers?

I don't know. I'm not involved with that at all. I would assume part of the reason is, you know, for whatever resource limitation, it's hard to give to everybody. And so they pick it to give it to, and how do you do that? But we typically do things meritocratically, and what's our best approximation to meritocracy? It's the research is doing well right now.

Does it give them a further leg up? Absolutely. Should we stop that? and instead make it available to everyone or some rotating system, maybe. I don't have a strong... I should think about it more before talking about that. Have you found that your colleagues are more skeptical of AI

than you think they should be with concerns that you think are not concerned? So, for instance, when I was speaking to Roger Penrose, he was saying, AI, oh, yes, it couldn't get strawberry correct. Yeah. And I was saying, yes, that's true, but that was many years ago. Yeah. But that was enough to turn him off.

And of course, skills are difficult to acquire it. as you're older and he's 95 now. Yeah, he's a pretty amazing person. So sharp. Crazy. Holy moly, man. He's very sharp, yeah. Okay, but anyhow, are you surprised at the slow adoption

of your colleagues with AI or no? It definitely has been the case. I mean, I've been talking about this publicly for at least about two years. And, you know, I wasn't, for two decades, I've had friends around me. Like, I've been near and, like, observing. And I had friends who were in the AI community,

AI safety and the rashless community and stuff, people talking about AI. And I've been sort of dismissive about it for a while. So I don't feel like I have, I'm not criticizing anybody. It takes you, however long it takes you. But 2016 is when I started coming around. And then soon as Chad GPT came out, I actually called a friend of mine. And I was like, you're right.

I was wrong. This is going to be the big deal of our lifetimes. Yeah, I still think people are being overly skeptical of it. I don't know. It's hard, right? Orienting in the world is hard. I try to be compassionate to every. I don't say that drugatorily.

I mean, I make mistakes all the time. It's so easy to jump down someone's throat, especially like when someone's wrong in retrospect, you can be like, well, you should have applied this heuristic. Like, well, okay, in this circumstance, but how many times if somebody said X or Y would be the next big thing and they were wrong? Right.

Right. It's legitimately hard to judge this stuff. I do think there's some amount of motivated reasoning stemming from the fact that like, if AI becomes, for example, super good at math, I guess we started with, you know, very, very flashily. We started with the fact that I'm grieving. And I think there is a lot of degree there, and more than that, people are worried about their jobs.

People are worried about their sense of meaning. You know, these are serious issues that I think, I see people being dismissive all the time of this concern or that concern. Like, mathematicians, some of them are legitimately, like, worried. They're posting, like, you know, what am I going to do? I've been doing this my whole life and now what. And some people, a lot of people respond sort of vitriolically

with like math was never forced. you. It was for everybody. And, you know, who cares about mathematicians doing their job. This is what's important. It's like, it's so important. I mean, we all orient life the best way we can, and this is a big loss for the mathematicians currently exist.

Should society not do something that's better for the majority of people because mathematicians will lose their jobs? No. That's not a good enough reason. But does that mean as to respond with vitriot and not compassion? I don't think so either. Do you think mathematicians would lose their jobs or that less would be given new jobs?

I don't know. I was speaking a little quickly there. I don't know what will happen to jobs in general. Jobs is a complicated question because it's not going to stop at math. Other fields are being automated. It would be automated as well. Like math is one of the first of the chopping block in some sense.

But it's going to continue well beyond math. I don't know if they'll lose your job. I just meant that they'll lose the job in the sense of like what they're doing right now. And I think what we, like, we all identify with our work. Maybe not all, but a lot of us, you know, for better or worse, a lot of us identify with what we contribute towards society or what we achieve. And that's a big part of the sense of meaning that we all get, right? We all want meaning.

And like, the meaning mathematicians have gotten, the way the oriented around that, this a lot of us, is going to shift. It's going to radically change. And it's hard. It's hard to adapt. that. So Tobias Osborne is a physicist. Many people who watch this channel may know him from his lectures on QFT or conformal field theory. He has some great lecture series on there on YouTube. And he wrote a LinkedIn post recently where he said that some of the low-hanging fruit in quantum information theory, people are sending out swarms of agents to actually check for open conjectures,

maybe solving one to five of them per day, just spending maybe $10,000 a week or so, just sending out some swarms. So as Tobias was saying that there's an inflationary area, what he means is, when the Spanish galleons flooded Europe with the silver of the Americans, of the Americas, Spain didn't get rich. It got inflation. So abundance changes value systems. When everyone knows your paper was generated in an afternoon with a single prompt, no one's impressed any longer. I felt this myself. After producing a master's grade result with an accompanying lean proof in a single weekend last November, I instantly devalued the contribution. So a weekend of work is not six months of concerted effort. Honestly, how much credit do you assign someone who's prompted a chatbot to

prove conjecture X? Try hard. Don't stop until you're done. Then he says the new equilibrium is this. That given that it's easy to launch agent swarms, it's ridiculously hard to craft clean, compelling definitions that organize a rapidly growing field. Value will shift to theory builders, people who absorb vast amounts of discordant information and create clarity through organizing principles and definitions that agent swarms can build on. Then I commented, I just want to know what you think. Well, my immediate reaction when I hear that is like,

he might be right, but, and I don't know this, I don't know this person, so you're saying, I don't mean to be able to get a critical, but like anybody claiming that, like, was a new equilibrium, value will shift to X, I just find it strange that they're so confident that AIs won't also be able to do X. So what did he say?

Like, value will shift to organizing this into good definitions that are easier to digest. You just feel like the immediate question. Why won't AI is able to do it either right away or through training? Because once they get there, like right now they're hard to practice, but once A.I. get to the point, like, he's claiming they will, and I agree, of rapidly solving conjectures,

you get more information. We can then start training them, and distilling it into a good format. how long will that new equilibrium that he's suggesting left? I don't know where the confidence is coming from. I left a comment also, which pretty much agrees with yours. I said, thank you, Tobias. I'm curious. So what happens when interesting conjectures, compelling definitions, becomes

promptable, also promptable in an afternoon? I think the concern is that whatever we place in the new equilibrium, it seems that soon, relatively shortly will also be promptable. Anyhow, I think that's what people are thinking about. Yeah, exactly. Like, I feel like there's a lot of people saying, well, here, the role humans will play and there's the role to play. It's a very difficult question for whatever role you think humans will play,

you can just ask yourself, why won't AIs be able to do this as well? Tim Gower is actually recently wrote a pose that I really, really liked, responding to the Leiden Declaration, which he didn't sign, and he explains his reason for not signing it. And he's not adversarial at all, which I strongly approve. I don't think being adversarial, but I don't need to be adversarial just now, about to buy his comment. I just meant to say my reaction to them.

But I really agree with his thoughts. He really grapples with the difficulty here, Tim Garvers does, of understanding where a stable equilibrium exists, because it's very plausible that for whatever role in humans doing, AI will supersede their ability. Now, maybe humans will start playing roles at which they are not the best,

at which AIs would be better, but we want to organize societies such that humans have this role. I think that's fine. I think that unrestricted optimization is not going to be a sustainable strategy going forward. I think we're going to have to impose

other restrictions on that. I think, you know, uncontrolled, just continuously making the AI smarter and ceding control to them. the moment they supersede humans and ability, I think it's a very risky proposition. I think it's something we're going to have to grapple with very strongly. So, yeah, that's sort of a question.

I don't know the answer. That's something that I want to see more people thinking about, both in terms of like what a feature looks like when AIs are better than us at more and more, more and more tasks at more zoomed-out level of abstraction, and we find it hard to find a role for us that the AIs can't become better on, so a role that we should occupy purely based on ability.

And also for sort of what a potentially responsible social policy looks like in that world. How do we want to structure society? Where do we want the limits to be? What do we want human roles to be? Not just because, you know, of capitalistic sort of concerns where like we're best at this, of course we'll do this, but just because, well, we're,

humans and we're making a world for humans to a large extent. And how do we structure that? Almost any question about the future, it's so uncertain as we started this conversation about four years from now the field's metal. And even two years from now, like, who the heck knows? Sure. But there's got to be some meta answer that is, okay, we don't know. So then the answer is that we first need to gain awareness about that this is an issue and then number two maybe debate or something like that. Without having an answer, the answer is, well, we all, actually come with our own answers and fight it out or something like that. So what is the meta answer?

No, I completely agree. I think it starts with everyone talking about this more and proposing their own answers. And I think we're seeing this now a bit, but we start seeing think tanks or other corporations show up with proposals and the government appoints some sort of group to think through it themselves. The meta-entry, like you say, is all of us trying to think through it now before it hits us like a train because we won't just naturally fall into a good equilibrium.

It'll happen. It's more likely to happen if we sort of, even like you say, even though it's hard to figure out now, we scope out what it might look like, we hedge our bets, and then as we get closer and we start seeing what the world looks more, looks like more and more, and then we sort of tailor it towards something that we went.

You know, like even now, I mean, everyone forgets, I think, not everyone, but a lot of even forget how crazy this world currently is from the perspective of 10 years ago. Like, we have magic systems. Five years ago. Five years ago, we have genius

that can do not everything, but so many things that we would have thought to be impossible, would have laughed at broadly in society 10 years ago. Again, not everybody, but most people. Kurt here, note that if you'd rather listen to Toe, we're on Spotify, iTunes,

Everywhere with a podcast catcher, you can just search my name or theories of everything. And also, remember to hit subscribe. Can you explain what the Leiden Declaration is for those who are unfamiliar? So, Latin Declaration is a group of mathematicians sort of got together to think through the implications of AI and math. And they put forward sort of a statement for, I forget exactly what it says, but sort of for how to use AI responsibly in math and where they think some risks are going forward. And incidentally, like, there's a... I have a lot of disagreements with them, but I think what they say about the potential risks of AI and math

and the potential safeguards we put in place, I think is very important. I think they run in the money as far as that's concerned. But Jacob didn't sign it. I actually wasn't invited. I never had the chance to sign it. I would not have signed it, though, no. I disagree with too much of what it says.

Ah, okay. Because the IMU signed it, and they gilded you. They gave you the fields, medal and you're saying I wouldn't sign what you which you proved but please I'll thank the Fields Medal. I'm not, all my opinions are my own. If you're suggesting

that I can't accept anything from anybody unless I agree with all their opinion. I am suggesting that you took some of my food and you don't agree with everything. I respectfully disagree and I'm happy to leave so it's nice okay so the Fields Medal says apparently it says on the front and the back something like I had my sister-in-law

translated. I forgot no one was one be better than you were yesterday something like that Yeah, that's right. And then the next one is Master of the World. It's like transcend the world or something. Yeah, it's pretty cool. Which one's easier?

Well, I think improving yourself was probably easier than transcending the world. That one seems like a big pill to swallow. No, but I mean, I mean what you're getting at is the Fields Medal is awarded to encourage future achievement. That's partly why it's under 40. And of course, the reasons for awarding it were decided 100 years ago, and they're sort of naturally morphed to their own thing. the Fields Medal now is not what it was intended to be way back, and that's due to some interesting historical coincidences. But as far as furthering future achievement,

I'm definitely trying to use, you know, this opportunity. I'm very grateful for it to work on what I think is the most important problem, which is AI safety, and that's not. I think I don't think that's a particularly innovative or weird, unusual take. I think many people have realized long before I have that AI safety is, is the most or one of the most important problems over time, and I think many others will realize it shortly. I want to encourage mathematicians.

I have a webpage, actually, if you could link it in your thing called Math for AISafy.org, where I try to make it a little bit easier for mathematicians in particular to go into the field of A.I. safety. If anyone else finds it useful, that's great. It's not meant to be exclusive, but it was written sort of in mind with a mathematician's background because I think that there's a lot of work to do from a lot of different parts of society. Society has to make its own large-scale Manhattan project.

We need more theory work, we need more governance work, we need more social work to sort of navigate this transition. I think if we don't... Again, I think it's not going to fall into our lap. If we don't start doing it now, we'll definitely fall into some kind of equilibrium, but it might not be as good as I think if we give ourselves time to orient.

Are you allowed to say what your job is at Open Air? Well, it's not really anything yet. They haven't started. I'm on the AI safety team, which, you know, AI safety is a broad list of things. We'll see exactly what it is that I end up doing. But, yeah, I think it's important to, again, to have a healthy ecosystem of people working on AI safety. I think the companies are part, the more distributed powers, I think the better. I think the company's part to play. I think I want people working in government work.

Like the UK has a very, very impressive institute called the AASI Institute, the Artifield Intelligence, I believe, Security Institute, maybe Safety Institute, one of those two. They do a ton of work. They foster grants. They have mentorship programs. They work with the American labs. They work with the UK. Incredible work.

And then there's all sorts of groups, sort of independent nonprofit organizations, other companies that are working on understanding EA is better. So we can mitigate them or creating infrastructure, like from a verification, other stuff, to allow us to deal with these things. better. I don't want anybody to go into, I don't want everybody to go into one place. I think, I think diversity is really important here. You mean, you're at the peak of your field. And so some people see that it's almost like curling and it's different, but. Oh, really? It's like firm. I don't feel like it's like for one at all. You're at the top of your field and then you

are leaving academia at least temporarily to go into industry. Yeah. I mean, we're living in Crazy times I think I'm leaving to do what I think is most important Yeah I don't know Do you have a more, I mean yeah To me it feels I'm happy to talk more about it

But if you have a concrete sort of objection Or question or whatever I'd love to hear it I'm still involved Like I still love math I'm still depending sometime doing it Much less now But you know I really care about the problems

That I'm involved in I have a lot of curiosity about them Like, if AI comes in a few years, like I'm expecting it to, and is able to, whatever. Wait, what do you mean AI comes in a few years? AGI, AGI. If the systems sort of arrive in a few years, which are better than mathematicians like I expect them to be. They can solve my problems. I will definitely be very curious to see the solutions and to understand that stuff.

There's a different question of, like, how curious will I be to invest in the next set of questions? Because, you know, there's definitely going to be next questions. Like, math is not going to run out of questions. And AI, even though I expected better than humans, is also going to have its limits. Like, we're going to come up with questions I expect that the AI is going to be stumped by, if we haven't already. But there's something to, like, yeah, how invested do you get in these questions, given that you're not the one working on them anymore? It's a different experience. Was it a large decision to make this transition?

Sure. A huge decision. I mean, part of me thought it would be in academia forever. Like, it's a very... It would be my position forever. It's a very comfortable life being a mathematician. Once you've managed to sort of become a senior professor or whatever, until that's a lot of anxiety. Sure.

But once you're there... Just that small hurdle, yeah. Just a small hurdle, yeah. But once you're there, you know, you never basically have to retire. Retiring is when you get to think more. The longer you do it, usually the more comfortable you are in a field, you sort of... You keep accumulating expertise, knowledge and little pieces here and there. You get to work with young people.

that's very satisfying. If I didn't think we're about to enter a very turbulent transition and I was confident that everything was going to go well, I'd almost certainly just stay in academia. You said something earlier about improv. You went into it because of the empathy. That empathy aspect. And then something I've noticed with you is that you are highly empathetic.

In fact, you said that you no longer are taking new students because you're unclear about the ethics of what are they signing up for? Is there some implicit contract that they have with me where I'm saying, hey, most likely you'll be able to get a job and I actually don't know, I as Jacob, don't know what job market's going to be in two years.

Yeah, I'm not thinking students, I still think students who weren't very AI focused because I think that whatever happens in a few years is going to be centered around AI. It's not going to be business as usual. Maybe not centered around,

on AI, but like involving AI in a very deeply integrated sort of level. And yeah, it's exactly what you're saying. I don't feel, I don't feel confident, pointing them towards a career that will exist and giving them, in the way that I'm sort of, I'm used to training people for, you know, if mathematicians keep existing as a career, which I hope it does, and I think in some ways it does, in some way it will, I just don't think the kind of training that will be useful for it will be what we're doing now, you know? So, yeah, I've been encouraging people to pivot. People have been talking to me a lot about, like, my views about AI and math.

And look, I have a lot of uncertainty. But I think when things are uncertain, you hedge. And I think when a big new player comes in, like AI, you start getting oriented around. I think getting oriented around stuff, something's not valued enough in our in our discourse. Maybe just an academic problem. I'm not sure, an academia problem. But people sort of talk about AI,

like, well, if it gets big, then I'll sort of get into it then. It's like, well, it's hard to just up and engage with something. Like, the AI systems now, I encourage people to engage with them, because even though they'll change and the specific skills that you'll need will probably change a bit,

there's something, there's some sort of generalizable skills that I think will stay the same. So, like, one thing I remember to happen to me, is the first time I used, I think it was cloud code, I'm not sure, one of these coding agents. And I was like, I'm going to try it. I'm going to make a game.

There was this typing game when I was a kid. I learned to type. There were these like aliens descending and they had letters on them. And I had to like press a letter for the lowest alien to make that alien blow up. And in the level, it got progressively faster. You learn more and more keys, whatever, that kind of thing.

And I couldn't find it. For some reason, the typing games have got much worse, in my opinion. Now they're all, the graphics are better. but the game was educational content worse. So for my nieces, I was like, okay, I'm going to make this game, and it'll be fun for me too. So I sat down and I was like, cool, you and I, sort of cloud code,

they're going to think about it together, make a design plan, and then you do the coding. And I typed them off to what I wanted, and it gave me back like 15 files, and it was like, great, I've got the game, what should we do next? And it was overwhelming. Like, first of all, I didn't know,

it was good, but second of all, I was like, I don't know. I need a minute. I'm not used to getting results. Like, I thought we were going to, this would happen on week three or something. Right. And it wasn't perfect.

And it needed, you know, it made some silly decisions that I had to correct. And we collaborated for a bit. But like six hours later, I had everything. And I had the game. It had graphics. It had good sounds.

It looked good. You know, I have it on GitHub, which I don't know how to use. But my AI does. So now I use it all the time, you know. And it's always telling me. me, you know, don't worry, I've organized, I've organized your good, how well. Great. Thank you.

And so the experience of I want to take on a project and getting back results that quickly and having to sort of digest it all and decide what I wanted to next, even though, you know, I started reading the files and I was like, this is pointless. I don't have time to read these files. And like they're in JavaScript. I don't know JavaScript that well. I'm going to, what, learn JavaScript to read these files to make sure it's the way I wanted to do?

Like, it's not practical anymore. And so this idea. of like you have to be a manager now. Like we're all managers to some extent. But the extent which were managers, the level of whose careers is relevant to us all, has really increased. So that's one thing that you will learn now

if you start engaging with AI systems. Like we're with math. Like this will get better, but the experience of here's a problem, oh, you can actually just do this. There are certain pieces to the problem that I can just get back. And the speed at which I'm progressing

in developing this theory is just much higher than before, that's an experience that's worth having. So the biggest piece of advice I have, not that you asked, but the biggest piece of advice of people sort of get oriented, get those experiences as much as you can now,

so that when they become truly necessary, you're not playing catch-up. My biggest piece of advice to you is the next time you tell that story, make sure it's codex, it's not itthropic, I just don't want you to get in any trouble. Okay.

I stay plugged into, the AI news and the AI industry and software engineers. And something that I see is that they say that the programmers, firstly, you don't need to know how to program anymore, which is quite odd that you don't need to know it. And they say that they haven't actually, even Carpathie says he hasn't touched code and quite some time. Now, they say that what they are are more like project managers. Yes. And it's a different skill set. And some of them loved actually going through and tinkering and fine-tuning and coming up with extremely efficient. solutions, but now it's inefficient to come up with some efficient solution. You just ask the AI

and the AI can come up with 10 more features and prototype something rapidly. Okay, maybe I shouldn't say this. I was going to say remanagan with Claude, like what happens. But maybe I should say codex. Sure. Whatever. I doubt everyone's that sensitive about it. But okay. Yeah, so you can't quite know the future. And I guess this question is also about that. But what's lurking in the background is the 19-year-old von Neumann or someone who is a 19-year-old who wants to get into math, maybe physics, maybe computer science, but let's just stick with pure math. Sure. What would you say?

You have a daughter who's quite young, so she's not at this stage, but you can even imagine that. She's 19, and she wants to follow in her father's footsteps. What would I say? Well, she's young enough that again. By the time she makes a decision, it will have either a lot more or a lot less clarity. I think more, one way or the other. So that's something I'm putting off for now.

People who are now, who are young, who do ask me this question, look, I always tell people to, even now, like to pursue their passion. If someone really likes math, engage with math, learn math. Now, having said that, how do you engage with it and how do you learn it? So when we say that, like, mathematician will stop doing what they're doing. Most people now who are doing mathematics, we're engaging with it, are not professional research mathematicians. They're kids playing with math.

They're engineers using math for something else. People doing math just for fun. I knew a poet, a writer in undergrad who was doing math because he found it beautiful and he was quite good. And he enjoyed a lot. And like, engaging with math is definitely not going anywhere. And people should keep doing that. In terms of angling for a career and making it your only focus, I would advise them to hedge more. So engage with math.

but again, don't lose, don't sort of close your eyes, put your head down and hope the AI buzz dies down and we'll get back to business as usual. Head your bets, learn about the world, learn about AI, learn about things are changing. I guess learn computer science to some extent. I don't know exactly, but people like all sorts of things that end up becoming not their profession

or at least not their profession by itself in a pure way. and I think pure math is something which is which is very tumultuous now as a field to go into I often like pure math in general has been I tell all my students before I before I do any math with them so they know this isn't a reflection on their ability I tell them that there's a lot more grad

students going into math than there are jobs for mathematicians this is just fact so most people who go into math as grad students do not end up getting a tenure job So that's already true. And you should already kind of be hedging a little bit. Now, it depends, of course. And in order to succeed, you've got to spend a lot of time on math.

So you don't want to, at the moment, you don't want to diversify too much at risk of, you know, becoming a jack-of-all-trade, the master of nine or something, because math requires a lot of focus. At the same time, it's, you know, it's good to keep aware of the facts. I think to the extent it's already been true,

it's going to become a lot more true now. how has AI or LLMs, let's say, helped you learn quicker? I mean, how have they not is kind of the answer now. Like everything I want to, every single time I'm engaging with something new, I go to an LOM and I ask it to teach me. You know, every time, if my sink is broken,

I take a picture and I'm like, what's going on here? Whenever I learn about, you know, I'm going to learn how some country works, some political situation, some history. I ask LOMs everything all the time. It's kind of like asking how does Google help you in Wikipedia? It's my starting point for everything.

Now, it's my starting point, which means it's not the only thing I use. You know, I, especially in the current world, just the LOMs have limitations. At a certain point, it becomes counterproductive, and also you sort of start disengaging your brain. when you use them too much. Yeah, so my brother's at UFT. he's a prof of math finance,

and he said that he's noticed his students that they don't sit with not knowing the answer to something for longer than 20 seconds or two minutes or something like that, and they quickly check what an LLM was known. So it's funny, this is already a problem, like when I've, so I thought about your math class at UFT. And the classes where I had a midterm

the students did far better on the final as a result. What I would always do, they have a midterm, and then the grade for your midterm would be the max of how you did in your midterm and how you did in the final. So if you did poorly, you'd kind of upended with the final. And inevitably, so I start teaching a class and I always tell the students, here's homework.

Now, please, at least for some of them, like put away the book, sit down for 30 minutes, and try it for yourself, just to assess what your actual abilities are, because it's very hard to get an honest assessment and not trick yourself when you're constantly glancing over at the right steps, the right ideas. So just really do it to get a sense of where you are this year,

because you can work on them. And, of course, nobody ever did it. And the midterm happened. Everybody did terribly. Everybody was shocked that it turns out when the book's not there, they do so much worse. But the lesson is learned. And then for the final,

they've internalized it, and now they actually do the step of, you know, taking an hour, going to the question by themselves, they see where they're weak, they work on it, and they get better. This already is a thing in our world. Now, it's worse with LOMs, this particular kind of dependency that can foster

of, like, not sitting with the answer. But I'm probably not so worried about this facet of it, maybe naively, but like, we have very good reward systems and tests. Like, if students start, use the OLMs of the time, then during the exam or some application where they aren't right there, the OLMs, they will do worse. And the signal is very clear when you're looking at an F or whatever it is,

the way you didn't want to get. So you see it as somewhat it weeds people out? I think people aren't, I think addiction isn't as, um, how do I put it? It's a serious problem, but people can resist and people can orient around what they need to do. Like, people are smart. I really believe people are smart. Like, people in math class who do poorly in math class, you know, they're often made fun

of by sort of mathematicians or, you know, teachers who get frustrated and stuff. A lot of those people don't need to do very well. They're there because it's a requirement. And they don't care. And so they do the bare minimum. And they're doing what they need to do. I mean, you know, they have their goals and their lives and whatnot. People who need to do well, take it much more seriously.

And they study more properly. Now, if certain skills actually become useless, you know, like log tables aren't something anyone ever does anymore, and they don't need to. And we don't go around making fun of people for not knowing their log tables. If somebody can't multiply one-digit numbers, that typically does hurt them. Like, it's impractical to go around typing six times eight into a calculator. It will, in a lot of professions, straight up hurt your performance. Right? And so people learn that.

and if it were practical to learn multiplication of two-digit numbers, people would also learn that. But it's not. It's not necessary. People don't need to know it. It's fine. If we don't need to know integration anymore, or, you know, engineers don't need to know their tritonometry or whatever it is,

that would be fine. We'll just actually stop using it. So this particular problem of, like, people will stop using their brains to their own detriment. I don't view it as as big of a problem as I think. think some other people do. Wait, is the reason you don't think it's a problem, some historical analysis that, look, we used to scoff at the calculators, the calculators were going to diminish people's brains, but every technology comes out and we think that it's going to harm the next

generation and it doesn't? Is it because of that or something? That's part of the reason. Other reasons that I think we just have a lot of evidence that people act according to their incentives. and I think if if every generation of people who use LLMs and then need to do a certain task without the LLMs there and it hurts their performance people will notice that and they will adapt

I just I think there's a lot of evidence that people adapt to perform as they need to not everybody of course some people will fall prey to this sort of trap but I just don't see it as as big of a deal as everybody else does I think what are you excited about Boy, so much. I mean,

again, I speak mostly about the risks of AI and the need for AI safety because I think that's what's needed right now. But the promise is enormous. I mean, there's so many practices. Like, I love to learn personally. I love to gain proficiency and skill. I would love to, if I felt everything was good,

just have my own AI tutor explain chemistry to me, for example, to a level that I can sort of, you know, understand the mathematics of chemistry and mathematics of physics, playing musical instruments, I want to play video games designed by AI.

I want to create D&D games that AI really helps with, actually, because a lot of the work gets shortened tremendously. I write musicals, I like writing, I think AI is not there yet, but when it becomes a good writing assistant, some of the fun parts that I,

basically I can get to a world where anything that you find fun you can focus on and you're not going to be bottlenecked by the necessary sort of skill gaps that you have and you have to overcome. Like somebody might find pieces of math fun, but they have to learn multiplication,

they have to practice their analysis, they have to, you know, do all that stuff, and they don't want to, and it's fair. And right now you can't. I like I like playing guitar, but even I'm not a huge fan of practicing my scales and stuff like that. But already in our world, I can compose music

because I go on Logic Pro, just type in the notes, where I play them and whatever, I adjust all the stuff. And it sounds good, and that's the way I can engage. So I think we're going to have so much more surface area to engage on things that were previously blocked off because AI is going to enable us to do that. This is not even talking about potential, show, you know, qualitative improvements in the human experience, which, who knows, are sort of

in the realm of sci-fi, even though sci-fi is rapidly approaching. Thank you so much for coming over, man. Thank you. I appreciate it. We're out. Oh, by the way, while we were editing this podcast, funnily enough, we found this from Tobias Osborne. Have you ever done a podcast?

Never. This is like a first time for me. I'm a complete virgin. So I don't know if you know this guy. He does this theory of everything channel. Yeah. I think he's in Toronto. Yeah, I think he's in Canada, right?

Yeah. And he's invited me way at the beginning of his channel to do a podcast or an interview with him. And this guy's really grown. Like, he's like interviewing serious, serious people now. He still occasionally asked me, do I want to come on the channel? And I'm like, ah, I don't know. Because he also has, he's pretty hard, right? In his interviewing, he dives deep.

He goes hard. And I'm not sure I'm quite ready for that. That was from a couple of years ago. Tobias, just so you know, I'd still love to have you on. Hi there, Kurt here. If you'd like more content from theories of everything and the very best listening experience, then be sure to check out my substack at kurtjymongle.org. Some of the top perks are that every week you get brand new episodes ahead of time. You also get bonus written content exclusively for our members.

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