Theories of Everything with Curt Jaimungal - Jonathan Gorard: The Physicist Revolutionizing Physics With AI

Episode Date: October 5, 2026

SPONSORS: - Don’t sleep on [@ultrapouches]. New customers get 15% Off with code TOE at http://takeultra.com! #UltraPouches #ad Every episode days early, ad-free, plus my essays: https://curtjaimungal.com Math has a proof checker. Can physics get one? Jonathan Gorard, an applied mathematician and the cofounder and CEO of Lanyon AI, joins to explain why AI took off in math and coding but not yet in physics. We discuss an AI finishing the formal check of a Fields Medal proof and why it scared him, why he thinks “I detected a particle” rests on 20 to 50 levels of theory, and what Alan Turing’s PhD student Robin Gandy tried to build for physics. The conversation also covers his push to make physics executable, why he thinks mysteries are artifacts of description languages, and whether there is still a place for the physicist. FOLLOW: - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Substack: https://curtjaimungal.com - Twitter: https://x.com/TOEwithCurt - Discord: https://discord.gg/kBcnfNVwqs - Crypto: https://nowpayments.io/donation/TOE - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00 - The Sphere Packing Shock - 05:53 - Science as Product vs Process - 11:20 - Is Science Just Hedonism? - 20:56 - Why Academics Ignored AI - 31:54 - Why Leave Princeton? - 39:56 - Turing's Student and Physics Formalization - 44:56 - Theory-Ladenness of Observation - 50:22 - Why Math Isn't Enough - 58:19 - Sapir-Whorf for AI - 01:05:49 - Filtering the Paper Deluge - 01:12:07 - Can AI Transmit Understanding? - 01:19:38 - Human-Readable AI Reasoning - 01:25:59 - Must AI Be Embodied? - 01:31:50 - Mysteries Are Description Language Artifacts - 01:41:54 - Grieving Physics - 01:49:59 - What's Left for Physicists? - 01:55:18 - The Next Description Language - 02:02:26 - Spacetime Discreteness and Beacons LINKS: - Jonathan Gorard [Wolfram Physics Project]: https://www.wolframphysics.org/pages/people/jonathan-gorard/ - Lanyon AI: https://www.lanyon.ai/ - Lanyon AI Founding Team: https://www.lanyon.ai/company/ - Shock with Confidence: Formal Proofs of Correctness for Hyperbolic PDE Solvers [Paper]: https://arxiv.org/abs/2503.13877 - BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for PDEs [Paper]: https://arxiv.org/pdf/2602.14853 - General Relativistic Hydrodynamics in Discrete Spacetime [Paper]: https://arxiv.org/pdf/2402.02331 - The Empirical Metamathematics of Euclid and Beyond [Paper]: https://arxiv.org/pdf/2107.07337v1 - Math Inc. Sphere Packing Announcement: https://www.math.inc/sphere-packing - The Sphere Packing Problem in Dimension 8 [Paper]: https://arxiv.org/pdf/1603.04246 - Progress in Formalizing Sphere Packing in Dimension 8 [Paper]: https://arxiv.org/pdf/2604.23468 - On Axiomatic Systems in Mathematics and Theories in Physics [Paper]: https://www.cs.ox.ac.uk/people/ohad.kammar/scans/gandy-thesis-ocr.pdf - Hilbert's Sixth Problem: Axioms of Physics [Paper]: https://people.reed.edu/~davidp/341/resources/hilbert.pdf - Hilbert's Program [SEP]: https://plato.stanford.edu/entries/hilbert-program/ - On Computable Numbers [Paper]: https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf - Lean Proof Assistant [Wikipedia]: https://en.wikipedia.org/wiki/Lean_(proof_assistant) - The Lean Mathematical Library [Paper]: https://leanprover-community.github.io/papers/mathlib-paper.pdf Full reading list for this episode (all 114 sources): https://curtjaimungal.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices

The timelines were completely wrong. I was scared on a very personal level. We're not putting the genie back in the bottle. This is Jonathan Gerard, an applied mathematician, co-founder of the Wolfram Physics Project, and CEO of the newly founded Lanyon AI. He's one of the physicists revolutionizing how AI can make scientific progress, which is distinct from just mathematical or code-based progress,

which is what everyone else is focusing on. We want to make physics executable in the same way that software is executable and that now increasingly mathematics is executable. Just like the recent interview with Fields Medalist Jacob Simmerman, we focus today on how AI will impact mathematicians and physicists. Do I grieve a particular subset of physics? Yes, we are not prepared for this. I'm in a continual process of grief.

On this channel, I, Kurt Jaimungle, interview researchers regarding their theories of reality with rigor and technical depth. Today, we discuss what our place will be once we can ostensibly solve any problem with a single prompt and how Jonathan's new company is fixing the foundational problem with traditional AI approaches. Regarding that distinction between math and science, we start with the moment that changed everything about physics for Jonathan Garard. Yeah, so that came probably, well, definitely a lot later than arguably it should have done,

and certainly a lot later than it did for many people. So that moment was a very well-defined moment in the beginning of March 26. So I had been, I think, like the rest of the world, following kind of the progressive march of AI capabilities from, I guess, late 2021 onwards, and getting increasingly excited and increasingly concerned about figuring out, okay, what is the direction this is going in, etc. But I was still, you know, right up to the start of this year, I was still viewing it as just, you know, this is an interesting thing that's happening in the world. Let's try and think about it. Let's try and analyze it in the kind of normal ways that I have tended to think about and analyze technologies and developments. And then in March 2026, there was this big, you know, auto-formalized proof dropped by this startup math ink of the Marina Vyazovska, like, 8 and 24-dimensional sphere packing problem that she won the field medal for, completely done, you know, autonomously end-to-end, you know, using effectively an AI harness. And, you know, it was, so, you know, for context, like I had spent a decade or so working about and thinking, on and thinking about automated theorem-proving techniques and proof assistance. In fact, that was originally about 10 years ago. That was originally what I was recruited to Wolfram Research to work on was to develop kind of automated theorem-proving capabilities. So I thought I had a pretty

good sense of how difficult a problem like this was going to be, you know, the problem of doing an automated proof of correctness for a field medal winning result. I had some intuition for how difficult this was. So I thought. And I thought by tracking kind of the progress of AI capabilities, I thought that I had some sense of when this was going to be on. It was clear that, you know, AI would eventually reach the point where it could do that. But I was, if you'd asked me in January 2026, I was very confident that this wouldn't happen until, you know, late 2027 at the latest, at the earliest and maybe maybe 2028 as a kind of more reasonable timeframe.

So the fact that on, you know, at the beginning of March, there is this like multi-hundred-thousand-thousin fully autonomously generated lean proof of this result that just gets dropped. that, you know, that for me was the oh shit moment. That was the moment where I realized I was thinking about this completely wrong. The timelines were completely wrong. And that on a more kind of personal level that my way of life and my plans for the future of how I thought my life was going to go just were not, you know, they were not going to survive in any reasonable sense. And that this was not something I could ignore for very much longer. That was very much the moment.

Now, why is that so significant? A two-year difference. So March 2026 to early 2028. So for instance, some people who are listening, they may think, okay, if 8K televisions come out and get popular two years ahead of my schedule, I'm not going to be flipping out, changing careers, inventing companies, and so forth. So what is it about AI that makes it consequential? So I think it's a very interesting question, but I think it's not really, it's not anything specific. about AI, it was the fact that the reason the timelines I think was so important, at least in the way I was thinking about it, was that I realized we would, like, the field and the, particularly the sociology of these fields, would not have sufficient time to adapt. You know, I thought even two years for, you know, for the glacial pace at which things move in academia was going to be, you know, a bit fast for, you know, practitioners and funding agencies and so on to try to adapt to this technological change. But it happening in March meant, no, there was no hope, right? And so

the way I was thinking about this, and I should add, by the way, you know, like I learned pretty soon afterwards that that whole story was obviously more complicated than initially met the I, and there was this whole issue with Siddharah, Haraharan, this PhD student who supposedly got scooped by math-ink. So, I mean, the story, I didn't know the complete story at the time that I had this moment, and it's turned out to be a more interesting, a more subtle story than I realized. Sorry, that story being the Maria story? Yes, the formalization? Exactly, yes, that it wasn't just as simple. I didn't know anything behind the scenes. I just, you know, at that time, all I saw was, you know, AI company proves this result.

I didn't realize that there was this active formalization effort that was being led by Siddharth and kind of incubated by Jeremy Avagad's group and that there was some interaction between Mathik and that group. And anyway, I'm not, I can't, I'm not in a position to litigate on exactly, you know, what happened. but I you know it was all I'm saying is I guess the story turned out to be more interesting than I realized at the time but um what I what I got scared about was essentially realizing the following that the kinds of things that I do and that my colleagues do this kind of like curiosity driven you know applied math computational physics type research has always been justified by I would argue intentionally blurring the line between what I would call, you know, science as product versus science as process, right? And so, you know, science as product is very kind of clear cut. It's, you know, things like, you know, cure cancer, solve nuclear fusion, generate, you know, clean energy, you know, these kinds of objectives. And within, you know, within reason, basically no one is going to argue that this is a bad thing or that we should stop funding this stuff or, you know, stop doing these, you know, that we should,

we should lay off the people who work on those problems. And then there's science as process, which is kind of the curiosity-driven stuff about, you know, like, I want to understand protein or I want to understand, you know, turbulence or I want to understand quantum gravity or something. And broadly speaking, we have tended to justify the latter by kind of laundering it through the former, right? That, you know, there are people, a lot of people who would say, okay, well, understanding those things is worth it on its own terms. So I would be one of those people. But that's not a, you know, that's not a universally held opinion. And the way that we make funding of those areas and support of those areas kind of palatable is by saying, well,

Well, ultimately it's useful for the former thing. It's useful. You know, science's process ends up being worthwhile because it feeds into science's product. And I think that's true to an extent. I've always felt that it was kind of overstated and intentionally overstated. I mean, to give a sort of whimsical example, I've always found it entertain. One of my best friends is a sort of algebraic geometer, algebraic number theorist who works on kind of peatic Langland's theorems and things like this.

I don't understand the details of anything he does. but every grant proposal who writes kind of starts with this stock paragraph about how algebraic number theory is useful for cryptography and critical for internet security. And it's like, yes, okay, number theory is useful for cryptography. It turns out the number three that's useful for cryptography is mostly about a thousand years old. It's things like the Chinese remainder theorem. And even like at the bleeding edge, it's things like elliptic curve cryptography, discrete logarithm methods. It's stuff, you know, it's 19th century at the most.

It's stuff you could have explained to Jacoby. So the idea that proving theorems about a P. Adic Langlands program is improving internet security is completely kind of nonsensical. But, you know, there's this widespread perception that you have to say that. Otherwise, yeah, it's not palatable to the funding agencies and it's not palatable to the general public that we would be supporting this work. And, you know, that's an extreme example. But it's true of stuff that I do, too.

I've written grant proposals where I've said, oh, you know, this work that we're doing on PDE is useful for, I don't know, semiconductor manufacturing. Maybe that's true. I'm a little bit skeptical, and it's certainly not my motivation for working on it. But that's generally been how we've set up the system. It's this slightly uncomfortable compromise where we blur the line between science's process and science as product. And I'm someone who's motivated by science's process. I would love cancer to be cured, but that's not, you know, that is not the thing that kind of drives me.

I realized in that very moment, this is not tenable anymore, right? That was what scared me. That I thought maybe if we had two years, there was a chance we could slight, we could change, the sociology, we could change the politics, we could change the way the infrastructure was set up. I realized there wasn't going to be time to do any of that. Suddenly, people were going to be saying, as this week is an example, part excellence of this, okay, well, hang on, AI can do all the product side of things. Why do we need to support the process side? And so I had been someone who, you know, have been kind of planning my life and planning my career around this, you know, having this very

fortuitous situation of being able to make a living, thinking about things and having ideas and solving problems and learning about stuff. And I realized that the infrastructure that was set up to support those things, at least from where I was sitting, wasn't going to last very long. And that was really, that was the course of the moment. Okay. So in other words, mathematicians think in terms of, or used to say what they do in terms of outputs that here, I'm going to publish papers that establish so-and-so. These are my outputs. Right. And then there's also the processing of that. So the black box that goes into that, which is you have some insight, you have some understanding, you have fun at the same time. Right. And there's also the

input, which is we care about the output because we have to put in something. It's not just mathematicians. You go off, go off in the woods. Have fun. It's like, no, no, no, please pay us as well. And so the people also who are doing the funding want to know, well, what the heck is coming out? Now, the question is, if an LLM can do the output, then what the heck am I funding you for? And then you also wonder, look, I'm as a mathematician, I'm betwixt and between, because I'm rudderless now. I mean, what is, you have to now think, what the heck is my goal? What is this for? What is math? It actually raises some interesting questions. Like, who am I? Like, what am I doing? And so, so gosh, then the question is, look, if it's just an intrinsic good, it's just for me,

myself, to understand, well, you may as well at that point also be an Nvidia chip in a server. You have to have some output. If you're just going to be, you're just going to be, isolated and to say, this is just for my own understanding, my process, and then it's not going to be justified by some output, then again, you may as well just be isolated. You may as well be an LLM at that point. So justify the process for me. Well, I mean, in some sense, maybe there is no, I mean, okay, I'm tempted to take a rather extreme position. There perhaps is no justification for the process except hedonism. And, you know, in my own case, I'm quite upfront about that, right? I want to do these things because I like thinking about problems. I think.

there are very altruistic scientists and very altruistic, you know, mathematicians and so on, who do care about the, you know, the curing cancer stuff or the, you know, figuring out clean energy stuff. That's never been, I know, I'm not against any of those things. I would, I would contribute in some small way, but that's never been my primary motivation. And I think it's not the primary motivation of a lot of people. And so the, yeah, the issue is, is, I keep how, it's a very nice way that you characterize it, that, you know, you have the inputs, which is kind of like the societal structure, the funding organizations, et cetera. There's the process, which is the sort of internal thing.

And then there are the outputs, which you ultimately use to justify the inputs. That's a steady state configuration that has existed in, I mean, certainly in kind of Western academia for at least 100 years or so in some form. But it took a long time to build that up, right? I mean, for most of human history, if you wanted to, you know, think about the people who kind of thought about mathematics and proof theorems and things like that were people who were independently wealthy or who had an independent, you know, like, they were either sort of baronets like Lord Raleigh, or they were, you know, lawyers like, you know, Leibniz or Descart, or

they were, you know, they had some other day job like, you know, Archimedes, as far as we can tell, you know, basically built siege engines for a living and then kind of did math and science stuff in his spare time. And so the idea that you could get paid a wage directly to do that, you know, to think about this stuff, it's a relatively recent phenomenon. For most of history, it's not how it's worked. So it took a long time for the system to reach that state and it reached that steady state because of this kind of delicate equilibrium between, as you characterized it, the inputs, the process, and the output. And the issue is that, you know, AI and advancing capabilities in AI more or less completely decouples the output

from the other two things, right? The output happens more or less independently of the input or the process. And so now the justification mechanisms that exist to societally don't exist anymore. And so, you know, I think, you know, I'm optimistic over the long term. We will reach another steady state, and it will be fine in the end. But there will be a, there will be a substantive period of disruption. And I think one of the ways that we have to, one of the ways that we will get closer to that to figuring out what the new steady state configuration is, is by being upfront about what the motivations are.

And as I say, for someone like me, the motivation is ultimately hedonistic. That, you know, to use your example, at least on an intellectual level, I would be, basically okay treating myself as like, you know, an invidia chip in some server farm. And, you know, that, obviously, there are other aspects of my life that, that, you know, would not be, would not be as pleasant. But purely on it, you know, would I enjoy thinking about science. Yeah, I would, even if it was completely kind of divorced from the rest of human civilization. That's not a, you know, it's a, it's a sort of mildly sociopathic thing to say, but I think it's probably true of more scientists than, than like to admit it. So the opposite claim then is that, look,

anything that you're using to tie, to justify the hedonism, to funding hedonism, is just proving too much. So it doesn't just allow people to fund mathematicians. It says you should fund artists more. You should fund so-and-so more. So what is it specifically then about mathematicians or physicists? And by the way, the people are watching this podcast. Many of them are philosophers, physicists, computer science, and mathematicians, and artists as well, interestingly enough. And we're going to get to how AI is impacting physics distinctly from math, because we have this Jacob Simmerman podcast about AI's impact to math. So this one's more going to be centered around theoretical physics, high energy physics, and your company, of course, and your attempts to solve issues

differently than the major companies currently. But anyhow, so I forgot what my question was. Oh, yeah, it was basically that your justification to fund me because I like to do what I do. It's an intrinsic good for me is proving too much. Yes, I think that's true. And I think this is one of the reason, it's one of the many reasons why math is in some sense the most salient and stark example, because with the arts, you have an additional level of justification that maybe is similar to the output justification in the case of math, but which is, you know, other people enjoy it too, right? Like, not only do I as an artist enjoy the process of producing, you know, this fantastic piece of cinema or something.

but people actually go and watch it and they derive pleasure from it as well. Whereas, you know, something, by contrast with something like mathematics, yes, okay, some people externally derive pleasure from your results too, although, you know, maybe that community may be extremely small. And it's certainly, at least at the research level, not something that tends to be enjoyed by sort of the general public. It's a fairly notable exception, or at least, okay, but in the pre-AI era, it used to be a fairly notable exception

when a major research math result made it into the popular media or, you know, was a topic for kind of cocktail party or dinner party discussion, right? You know, for our last theorem was maybe the last, you know, the last, you know, major example of when that really happened in a big way. But, yeah, so, you know, whereas that's definitely not true of a lot of at least the mainstream arts. So in that sense, mathematics is maybe more similar to a, to a, or it's a limit case of an extremely niche art form, which therefore has a much harder time justifying its existence

in a way that is not purely instrumental. And so when you strip away the instrumental justification, which is effectively what I think artificial intelligence is doing, one has this really hard time to figuring out, okay, why are we really doing any of this? Like, why are we supporting this as a society apart from just some people enjoy it? The opposite of Open AI is Perlman.

Someone who says, look, I don't actually care about the accolades. There's arguments that Open AI specifically wanted to get a press release. Perlman's like, no, don't give me the reward. Yeah. Yeah. So, I mean, Perlman is an interesting example of someone who, okay, I think this is by no means an original thought that I'm about to. I know lots of people have written about this in more articulate ways than I'm about to say.

But, you know, AI to a large extent has exacerbated sociological issues with these academic fields that were preexisting. And there would have been problems even without development and AI capabilities. It's just that the development and AI capabilities have made them impossible. to ignore. And Perrauman was notable that he outlined several of the sociological problems that have come to light specifically as a result of this recent open AI proof of the Navajo-Oaks conjecture and around these issues of who gets credit, you know, when you have, when mathematics is incentivized by prizes and by major results, but those results are kind of by their very nature,

you know, built towards by a bunch of incremental improvements from several different mathematicians who all input their own ideas into different subparts of the problem, but then, you know, the prize is awarded to one, and, you know, one person gets the glory and one person gets the paper citations and all this stuff. You know, how do you resolve those issues? You know, those were the, those were the, those were the, those were the, those were the, exactly the things that Perilman was trying to spark discussion about in his, you know, rejection of the field medal and his, you know, the, sorry, rejection of the, of the clay prize. And the, and, you know, his statements about how the, you know, reachy flow and was not sort of his development. That was. was sort of Hamilton's idea. And he built upon it and effectively outlining the arbitrarity of the person who solves the last mile problem getting the lion's share of the credit. And so this is exactly now the problem that, again, we just can't avoid now that AI is extremely good at solving last mile problems. And so we are effectively stripping away the incentive structure for people to do the kind

of lower level, I don't mean that in a derogatory sets, but the lower down work of building towards the problem because you're massively over-incentivizing the people who solved the last mile problem or the AIs that solved the last mile problem. And so, yeah, Perilman's interesting because he was one of a small number of people who was actively talking about exactly these sociological issues, even in the pre-AI era. Now everyone's talking about that, but, you know, it takes a certain level of prescience to realize this was a problem even beforehand. We do everything right for our health. We go to the gym. We diet. We have eight hours, hopefully, of sleep. And then we lean on chemicals.

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That's take ultra, one word, dot com, for 15% off with code TOE. After you purchase, they'll ask you where you heard about them, support our show and let them know that Kurt sent you or theories of everything sent you. You used the word scared. Now I understand the word surprised that you were surprised by the developments, the speed of them, and the impact of them, but why it's scared? And then also to tie this into something that we talked about off air, you also mentioned when you tried to warn your colleagues that they were incurious. So warn them about what? Incurious about what? Scared about what? So as I say, I think in a very selfish sense, scared about my near to medium term way of life that

I had been planning for the future on a 5, 10, 20 year time horizon. And I suddenly realized that that was predicated on a bunch of assumptions about the world that were not going to be true anymore. And so I was scared on a very personal level. I was, so I'm by no means an AI Duma. And I think a lot of the kind of safety scenarios around AI are somewhat overplayed. But I was also concerned from a safety perspective that, okay, there is this very rapid increase in capability development. There is not been a corresponding increase in the development of safety mechanisms and alignment and so on. And that's inherently a bit scary. And yeah, then I think the point you mentioned about our affair conversation where I was basically trying to talk to academic colleagues and say,

okay, how are you thinking about this? That scared me too because I suddenly realized, oh my gosh, we are not prepared for this in a structural sense in any way. Because I was, you know, I felt like a sort of, and again, I want to make clear, I was by no means prescient. I was extremely late to the party by, you know, by Silicon Valley standards, et cetera. But I was going around Princeton in places and saying, you know, okay, hang on, what are we doing about this? How are we thinking about this? How are we modifying our approach with, you know, funding agencies and postdocs and PhD students

and how are we going to, you know, modify the scientific process and so on? And the responses I got, you know, with exceptions, but the responses I got from a lot of my academic colleagues were extremely worrying in how little they had clearly thought about the problem and also how little they were paying attention to what was going on, that people were saying, oh, it's fine, we'll just incorporate AI into our workflow, you know, we'll invest some proportion of our time into, you know, training neural networks surrogates for this or that piece of science or whatever. You know, this happened to be occurring at around the time there was this big push from the Department of Energy to submit proposals to this so-called

Genesis mission that was about, you know, accelerating American science through artificial intelligence. So a bunch of our conversations were framed around, okay, how does this fit into the Genesis mission and so on? And so I got to see a lot of what my colleagues were writing about and pitching. And it was, you know, they were pitching projects that would have been, you know, fine machine learning projects 10 years ago. It was, you know, like, oh, we'll take this neural network architecture, we'll feed it this data, we'll, you know, we'll get this result. Okay, there was nothing about that project that you couldn't have done in 2015. is clearly a completely different world. And it didn't feel like many of my colleagues were engaging with it in anything like a serious kind of way. And, you know, there was this, there was also this widespread kind of anti-AI sentiment, which I shared to a great extent too of, you know,

oh, this stuff is bad. It's, you know, harmful for the world. It's harmful for science. Oh, and by the way, it's all just, you know, spicy auto-complete, stochastic parrots, et cetera, anyway. So let's not pay attention to it. It's never going to work. It's going to be, it's going to produce slop, et cetera. And, you know, I was kind of sympathetic to the first set of claims that, okay, this is clearly going to be quite disruptive. But the second set of claims, by that point, you know, if you were in any way paying attention to what was going on, it was very clear this was a, you know, this was a 20-21 perspective on the transformer model. And when I tried to tell them, well, no, hang on, actually,

you know, what you're doing that, what you're giving there is maybe a criticism of a single transformer architecture. Yes. But you realize that, you know, a modern LLM is like, you know, 11 different transformal architectures all linked together with different, you know, with separate neural networks and diffusion models and a bunch of like deterministic pre-processing and post-processing. And there's all these developments in, you know, reinforcement learning environments and post-training and tool calls and skills harnesses and all that stuff. And they weren't interested in any of it. They, you know, they had kind of, they'd got in their head this dogmatic position of, oh, no, this approach will never work. And so they just weren't interested in paying attention to any of the

things that were leading to this development capabilities over the previous, you know, two, two and a half years. And that I found really scary because if I felt, you know, I was paying more attention than almost anyone I knew in those circles. And if I felt like I wasn't prepared, then I realized, oh, no one around me is prepared either. And that, yeah, that was scary. I was just speaking to someone at the Perimeter Institute, off air, it's not recorded. It was a professor of physics. We were hanging out. And then he was saying, gosh, some objections that are two years old, three years old, like, doesn't it make up sources? I was asking him about LLLL and how he integrates it into his workflow.

Then he was saying, oh, you know what? I'm collaborating with someone who is using an LLM now. And I'm like, now only? And then he says, yeah, and this person, he uses an LLM. And you know, if you give Claude a scratch pad, Claude is great. And I'm like, scratch pad. Are you talking about Claude as a harness?

He didn't know what the word harness meant or Claude, roughly speaking. I think he was even using Claude co-work and not. not Claude. And I'm thinking, man, you're so far behind. Like, that's, that's so old. That's a year old or two years old. And it's more, it's much more than just a scratch pad. It's tools. Yeah. Yeah. And it's, you know, in some sense, I understand where it comes from. And I'm sympathetic to that, that, you know, if, for a long time, academia has afforded one the ability to sort of ignore developments in the outside world. That was part of, you know, that's part of the idea, right? That you kind of, you build this ivory tower and you silo these people away to think they're

important thoughts and they kind of don't need to pay attention to, you know, to the details of of what's going on outside. And so I, to some extent, I can see where it comes from. But at the same time, I was a little bit dismayed by, you know, like, I don't want to sound uppity, because again, like, clearly I was behind the curve too. But, you know, like, where is your intellectual curiosity, right? Like, but, you know, by 2025, it was clear this was an absolutely transformative technology. This was going to be the biggest, you know, technological revolution we were, we were going see in our lifetime. It's called Transformer for a reason. Yeah, right. Genuinely transformative. And, you know, how could, like, what, you're, you're ostensibly being paid to think about,

you know, to think about things and to learn about stuff. Why have, you know, why have you not spent an afternoon just like reading about what's going on and how things work? And what, like, what, how, how is it that you reach this point and you're still stuck in this, like, 2021, you know, era perspective of, you know, what the limitations of these models are? You know, so I, I agree. it was a weird cognitive distance realizing, and again, there were lots of exceptions, you know, lots of my colleagues who knew much more about this than I did, but there was just an awful lot of people who didn't seem interested at all and just wanted to kind of shoot it down. Was there something that unified the people who were incurious versus those who were more curious?

So, for instance, age may just be one that, I, okay, we're relatively young, so we like to play with new tools. But I don't like to, I don't know what TikTok is, for instance. So I still think TikTok has to do with dances for some reason. I have no idea why people dance. I have no idea why people mimic the dances. I have no idea how they come up with the dances. I have no idea how TikTok works. And so I'm incurious when it comes to that. But was there something that unified these people, maybe age, maybe computer scientists were actually less curious than physicists or maybe physicists were the most? Was there something? Did you interact with enough people to establish some relationship? So I

The short answer to that is I was surprised by how little how few patterns seem to emerge I was surprised by you know people who I thought would be very rapid adopters at this kind of technology you know just shunned it entirely and people who I thought might think

it was very crass and low class you know became immediate enthusiastic evangelists and you know to the extent that I saw any trend I didn't see an obvious trend with like math people versus physics people versus computer science people

There was maybe a slight trend of computer scientists, I think, on a psychological level, thinking that they ought to understand how these models were working and that's slightly changing the way they were interacting with them. But, no, to the extent that I saw any patterns, it was really, there was a weak correlation in age that there were, like, the very young people, you know, the early graduate students would be rapid adopters. And the very late career people would be rapid adopters. But it was the mid-care people who were most likely to kind of shun it. And I think, again, there's a, there's an obvious explanation, or maybe an obvious sort of psychological explanation for that, which is that, you know, the older people have less to prove, they probably live through other kind of, you know, methodological revolutions so that they feel more relaxed about trying out some transformative new technology. The new people, you know, the younger people probably don't know any different. And so, you know, it just feels like, you know, as Douglas Adams put it, if it arrived before you were 20, then it's like, you know, it just feels like part of the world. And if the people in the middle, who had established a career and established a reputation on one model for how science has done and one model for how the world works and suddenly saw that model being completely threatened, they were the most likely to say, no, no, no, this is terrible.

Like we, not just this is a bad thing, which as I say, I can be, I'm quite sympathetic to, but that it doesn't work. That seemed to be, it was a sort of classic, like logical fallacy that a lot of people seem to be committing, that I think this stuff is bad and destructive, and therefore it can't work. And, you know, I was trying to make the argument at the time of, no, look, I'm against law of this technology too. You know, I went through a long period,

and to an extent I'm still in that period, of being quite anti-LM from a kind of humanistic perspective that I think it's very easy to use this sort of technology in a way that is anti-human, that atrophies cognitive skills, that atrophies thinking capability, that atrophies creativity. And in particular, if you're a scientist,

if you're a curiosity-driven scientist, where, you know, creativity and thought and learning are your bread and butter, I think it's very important to be extremely careful about those things. And so I was quite, I was a little bit concerned about some of my older academic colleagues who seem to be very enthusiastic adopters because I kind of thought, like, okay, wait, hang on, when was the last time you actually read a paper? When was the last time you actually solved an equation? Are you sure you're not doing yourself some harm here by relying so heavily upon these tools? But, you know, so I was, you know, quite pessimistic from a level of good perspective.

But it was very clear to me that independent of that, these tools clearly worked and they were extremely effective and the capabilities were growing very rapidly. Whereas a lot of my colleagues just didn't seem to make that separation. They were also pessimistic about the good of them. And they translated that into and therefore, you know, they produce slot, therefore they're bad, therefore they produce incorrect answers.

These two things can be completely uncorrelated. And I think in the case of AI, they are. So what is it that made, starting a company necessary for you, feel necessary, something that you couldn't do at Princeton? Yeah, so this was very much not my plan, and it came together very, very quickly. I mean, if you'd asked me, even just a couple, even a few months ago, if you asked me in May what I was planning to do, I was still, I was going through this kind of shell-shocked grief phase of, I don't know what the future is going to look like, but a few things came together. And one of them

was me trying to pitch to funding agencies, and again, to be clear, it wasn't. just me, this included my co-founder, Amar Haqim and some other people, us trying to pitch the product that eventually became, you know, the foundation of our company, Lanin AI, as an academic research project. Because I think, you know, in the best vision of things, it could have worked as an academic research project. It was a grand, ambitious kind of intellectual project, multi-year thing that was clearly, you know, tessellated well with the outside world. And we submitted a bunch of proposals, and, you know, they all got either blanks or rejected. And I don't think this is, I'm, I'm not,

trying not to interpret that as a reflection of, you know, how good our ideas were. I think, you know, we're in an era in US academia at the moment where the majority of proposals are getting rejected for the majority of people. But, you know, if there were a way for us to do a project this grand and this ambitious as an academic research project, I think, you know, I'm sort of psychologically an academic at heart. I would have loved to have done it that way. It just didn't seem plausible. It didn't seem to be a feasible route to us doing it. And, you know, so we had at the time, and still do have, I think, a fairly clear vision for what we wanted to build,

which was effectively, you know, a language that mechanises the process of scientific reasoning in the same way that computation mechanized the process of mathematical reasoning. And I thought that was a reasonable pitch. I thought it was a timely pitch. I thought it was obviously valuable

in terms of how it fit into the wider world of AI capability development. And yet there was, with some exceptions, basically no enthusiasm from, you know, from the academic research community and from funding agencies. And so then we decided, well, okay, sometime at the start of June, we've seen a bunch of our friends go off and raise ridiculous amounts of venture capital money and just do their research projects as private companies. Why couldn't we do that? And so then, yeah, that was kind of the impetus to start this company.

We then started talking to BCs, started talking to investors, and the whole thing came together extremely quickly. And so then, you know, that led to us coming out of stealth, you know, about like a few weeks ago. is it that people, when they think about AI, LLMs, and so forth, they think about it revolutionizing STEM fields, sorry, the STEM field, whatever that means, but you're saying the M part of that is actually different. The STE, the science technology and engineering, has an interface with the real world and uses something like the scientific method,

whereas math is infamously quite cheap because you just need a chalkboard and you just need your own thoughts and some colleagues and desks and so forth. But gosh, physics and chemistry and so forth, relatively extremely expensive. Okay, so is that what you're saying, that there's a difference there? Yes, I think so. In fact, I would bracket the T and the M together, right?

So the technology and the math side, I think, are fundamentally different to the science and the engineering side in the following way. So if you look at what's happened in AI capabilities, particularly over the last two years, maybe year and a half, there's been this obvious explosion in first in coding and software engineering capabilities,

and then with a slight lead time in math capabilities. That has not been associated with a corresponding increase in science and engineering capabilities. There has been some increase, but it's nowhere near as stratospheric as what we've seen in coding and math. Okay, why is that? Well, you know, there's a standard answer, which I think is basically right, which is that, you know, we're at the stage of AI development right now where the majority of the capabilities improvements are not coming from improvements in the models. They're coming from improvements in post-training. They're coming from improvements in how good can we make the reinforcement learning environments,

and therefore by extension, how good are the verifiers? And so, because, you know, like all modern, you know, AI models are trained largely or post-trained largely through not reinforcement learning with human feedback, but reinforcement learning with verifiable rewards. And so if you're in a verifiable domain, then, you know, you can effectively, you know, you can self-improve in a completely unsupervised way. And so because we had formal verification tools for determining software correctness, which were things like compilers, type checkers, static analyzers, etc.

And we had formal verification tools for determining mathematical correctness, which were things like proof assistants, automated theorem provers, interactive theoremprovers, tools like lean, Agda, rock, etc. So as a consequence, as I think a very direct consequence, we've seen this great takeoff and capability in computation and math. What is the analog verification pipeline for physics, chemistry, biology, engineering, etc? Right now, that kind of isn't one, right? And the history of this is extremely interesting.

So if you go back to the start of the 20th century, David Hilbert posed these famous 20 problems for kind of the foundations of mathematics that also strayed into physics and some other areas. And one of them was this famous Enshadung's problem that, you know, this decision problem for determining, effectively defining a mechanical procedure for determining whether a mathematical proposition was true.

And the attempt to solve that decision problem is what led people like, you know, girdle, touring, church, etc, to develop what we now call the modern theory of computation. So as a direct outcome of the Hilbert program, we developed in the early 20th century a reasoning language that let us formalize the process of mathematical reasoning, right? So the idea is, you know, with a Turing machine,

you have an input, you do some transitions on that input, you produce an output, and that's effectively, that's intended to be an ultimate, like, desiccated abstraction of the process of mathematical reasoning, that you take in some axioms, you apply some inference rules, you produce a theorem. And that's turned out to be extremely fruitful, of course, right? You know, the development of the theory of computation has been one of the most fruitful

kind of intellectual ideas in our history. Hilbert, interestingly, also had a corresponding problem to do effectively the same thing for physics, right, to develop a, like, to construct formal axiomatic foundations for physics, or to put it in a sort of more, you know, computational way, to effectively mechanize the process of physical reasoning. And we could generalize that, to mechanize the process of science. scientific reasoning. But unlike the Enshaidung's problem, that problem has not been solved. We do not have a corresponding formal language that mechanizes the process of scientific reasoning. And I think,

personally, and this is one of the key convictions of our company, that until such a language exists, we will not see the analogous capabilities developments that we've seen in math and coding in broader natural science and in engineering and broadly in anything that kind of interfaces with the physical world. And I think this is strictly a harder problem than the problem of kind of mechanizing mathematical reasoning. It's because it's harder in a very simple sense, which is that the mechanization of mathematical reasoning is a necessary but a not sufficient condition for mechanizing physical reasoning, right? And I'm sure we'll talk more about this in greater detail later on. But physical reasoning, there are at least sort of three major components of it,

one of which is essentially mathematical to do with internal consistency, one of which is essentially theoretical to do with consistency with other, you know, presupposed physical principles, and the final of which is experimental, you know, related to how, you know, how this model actually interfaces with the physical world, with physical reality. And that's, you know, that's significantly harder than the other two and poses a completely different set of philosophical problems that I think we've not even begun really to grapple with in a serious way.

So yes, the short answer to your question is I think, you know, the S and the T have really become separated. I mean the T and the M? I mean the T and the M? The T and the M have become separated from the S and the E because the T and the M have, you know, can effectively leverage the theory of computation and the development of formalized mathematical reasoning for which we have no corresponding analog for S and E. What is it then about science that makes it so tricky to formalize compared to math? Is it the scientific method isn't well defined? Is it that you have to perform experiments? Like, what is it? So that's definitely part of it. And it's an important part. But even if you, even on the purely theoretical level, I think it's already more difficult. So actually, in kind of tracking down the history of this, there is one project that came close to, I think,

what we are trying to do at Lanian AI. And that was, so Alan Turing had one official graduate student in his academic career. It was a guy called Robin Gandhi, who is a, PhD students at King's College, Cambridge, under Turing in kind of late 1940s, early 1950s. And he wrote a thesis that is called something like on axiomatic systems in mathematics and theories in physics. And it's a really weird thesis. I read it several years ago. And the first half of it is kind of pretty boring kind of type theory stuff. But the second half is a really interesting but ultimately very underdeveloped research program to basically extend type theory to physics. And more precisely, to build not just a tight theory,

system, but an analogue of the Turing machine for physical and scientific reasoning. And so Gandy was thinking, okay, if a Turing machine is an abstract machine that idealizes mathematical thought, could we have an analogous machine that basically takes in as input, you know, empirical data, sense data, applies, you know, a process of scientific induction with, you know, with additional like deductive principles and other things, you know, science is a pure induction as is well-documented. And produces as output effectively scientific hypotheses or physical hypotheses. And he effectively tried to, to the extent that I understand what he was getting at, he was basically trying to design such an abstract machine and trying to design a type system that would allow you to reason about such an

abstract machine. And it didn't really work. It was an overly ambitious research program for the second half of a PhD thesis, and he never really extended it. But there was clearly a kernel of an idea there that started to grapple with some of these issues. Because, yeah, so the key things that make it hard are, yes, okay, there is math formalization that tells you, is the model internally consistent? So if we take something like quantum mechanics, this would mean, you know, formalizing things like the theory of projective Hilbert spaces, the theory of unbounded linear operators, just pure like mathematical superstructure. No physical content there. But that, you know, that's already at least as hard as formalizing mathematics, right? So you run into all the same

issues that you do with, you know, proof assistance and other things. Then there is figuring out consistency with existing physical principles. And that's effectively what distinguishes theoretical physics from mathematical physics in some sense, right? So this is things like, you know, is your proposed model consistent with the conservation of energy? Is it consistent with the laws of thermodynamics? Is it generally covariant? Is your time evolution unitary? These kinds of things.

Are you saying that the theoretical physicists are concerned with the consistency, whereas the mathematical ones are not? Or is it vice versa? No, I would think of it as, and this is maybe overly unfair, on the mathematical physicist. But I would think of it as like each one is a super set of the thing that came before. If you're a purely a mathematical physicist,

you might not necessarily care that your proposed physical model is not consistent with some physical principle because you could say, well, it's just producing interesting mathematics. But what you do care about is mathematical consistency. If you're a theorist, you probably care about mathematical consistency,

although maybe not. I mean, you know, like quantum field theory famously, we don't yet know how to make that a consistent mathematical theory, but it still is extremely theoretically successful. So this is a slight oversimpefew. on my part, but if you're a theoretical physicist, you care not just about the internal logical consistency, but you also care about how it, you know, how consistent is it with other theories. And that's complicated because you could think that, you might think that's purely

mathematical deduction. That is, you know, you have a physical model. Can I derive energy conservation? Can I derive, you know, entropy, modernity, et cetera? But it's really not that simple, right? because, you know, those principles may only be approximately true. They may only be idealizations that apply in specific regimes. There is a bunch of essentially heuristics that you have to apply at the theoretical level that you can avoid at the mathematical level. So, you know, if you were trying to assess a theory of quantum gravity, okay, well, you know, what desiderata do we want from a theory of quantum gravity? Well, at the very least, it should reproduce the Einstein equations in the limit of large mass displacements, and it should,

it should reproduce, you know, the Yangmills equations in the limit of small mass displacements. But, you know, would such a theory be covariant? Who knows, right? Like, generally speaking, right now, we think of, you know, covariance, variance or general covariance, as being a required consistency condition of a physical model. But if a proposed model of quantum gravity replaces the concept of spacetime entirely and space time emerges as some approximation to that structure, then, you know, you might not be able to prove general covariance formally, because it might not be true. but you may be able to prove it or to derive it approximately in some regime, and that may be all that matters. So there's a kind of a mushyer notion of reasoning that exists at the theoretical level that I think we have not yet correctly formalized.

And that's a, again, that's a key part of what we are initially trying to work on at Lanian AI, is trying to kind of, is trying to take a mathematically consistent model and figure out how can we at least approximately determine its consistency with, you know, with other principles and theories of physics in a way that is equivalent to the way we currently assess. mathematical consistency through lean and things like that. And then there is the final level of complexity, which utterly dwarfs the previous two, which is, you know, is it consistent with what we see in physical reality? And that's the place where, as you said, we have to, we run into these issues about formalization of the scientific method. And in particular, we run into a bunch of limitative problems that were pointed out in the early 20th century to do with philosophy of science.

and in particular by people like Northwood Hanson and Thomas Coon and so on, who talked about theory-ladenness of observations. Because one of the key problems with the proposal that people like Robin Gandhi were making was that he was making an assumption, I think, maybe I'm besmirching him slightly, but he was making the assumption that we could make essentially a bare metal, like an unbiased observation of bare metal reality, that we could build a mathematical model of a physical system, we could perform observations of that system at the bare metal level,

and we could just verify or falsify whether the model, you know, match the predictions actually match physical reality. But as Hansen and Kuhn and others correctly pointed out, that's really not how observation works, that any time you make an observation, anytime you perform a measurement, you are doing so relative to an existing theoretical framework. And that's true both semantically and perceptually.

So semantically, you know, when we say, like, we've detected a particle or something, Okay, what do we actually mean? What we actually mean is, you know, there was a visual qualium that was induced in the mind of the experimenter. That was produced by some, you know, presuming some photons that came off a computer screen that stimulated some photosynthesis cells. And then, you know, if we keep going, we can trace that back to, you know, the supposition that there were some particles in a calorimeter that produced some cheroenkov radiation that got detected by a scintillator, et cetera. But there's like, when you trace it out, there's probably 20 to 50 levels of theoretical assumptions that go into that statement of I detected a particle. Well, you didn't detect the particle.

You just saw some dots on a screen. The interpretation of those dots on a screen as a particle is dependent on a theoretical apparatus that you cannot directly test by that observation because you've had to presuppose it. So there's a notion of semantic theory ladenness. But there's also a notion of perceptual theory ladenness, which is that your sense perceptions themselves are determined by your model of the world. And the classic example of that is an optical illusion, right? Depending on if you see an Escher painting or something, you know,

the way that you actually perceive that observation. It's the same observation. You're receiving the same set of photons. But the way you actually perceive it, the way you make sense of it, depends on whether you think, you know, this object is in front of this one, or whether these people are going up,

or these people are coming down, or whether the object is rotating right or rotating left. And you can change your perception of the same stimulus, or of the same phenomenon, by modifying your model of the world. And so if you want to try and automate the process of doing experiment, verification and falsification. You are not doing so in a completely unbiased and bare-metal way.

You have to find a way of systematically doing so in a manner that effectively parameterizes over the set of theoretical apparatuses that you could have assumed in performing the measurement. And this is a level of philosophical and technical complexity that you never have to wrestle with in math and you never have to wrestle with in theoretical physics. But it is something that I think is critical if we are going to get effectively recursively improving capabilities in the natural sciences. What is that your lab is doing differently than, say, the large AI labs currently, like Anthropic and Open AI?

Yeah. So, you know, we are obviously not either on a resource level or on a personnel level able to compete with them in terms of things like compute and post-training and things like that. So what we are effectively doing is, you know, we're focusing on the development of what I was describing before, of these kind of formalized reasoning languages for scientific discovery for, in particular for things like physical reasoning, in the first instance, focusing on the mathematical and theoretical aspects, but with an ongoing project, and we're in the process

actually at the moment of hiring some people to work on this, of also folding into, you know, automated laboratories and experimental pipelines and these kinds of things. So we are not primarily in the business of developing new models, although we do a little bit of that too, just for, you know, for kind of entertainment value. We are primarily in the business of developing new reasoning languages for models, analogous to lean and, you know, Agda and things for mathematics, that are optimized for physical reasoning and for scientific reasoning. So, you know, one of the ways that I used to pitch this to people is that we are building effectively typed systems for physics. And so whereas right now, if you go into, you know, your favorite proof assistant or your

favorite type checker, it will tell you, you know, are these, you know, is this Python expression type correct or is this mathematical theorem, you know, derivable from this set of assumptions. But it won't tell you, you know, is this model consistent with the conservation of energy? Is this thermodynamically stable? If I try to solve these equations numerically, will I get, you know, L2 convergence with this, you know, with this order or something? Wouldn't the axiomatic QFT person just say that ultimately physics will cash out in math anyhow? So it's like you're just selecting which subset of the mathematical universe obtains in ours? Yeah, so I...

I'm somewhat sympathetic to that view, but I think it misses a lot of the contingencies that exist. The reality is we don't know how much the mathematical models we have of reality constrain what actually happens. So if you take the example of the Einstein equations, the Einstein equations are incredibly permissive. They permit time travel. They permit white holes. They permit faster than night travel, all these things. None of which we've directly observed. And we have good reasons that come from other parts of physics to believe that many of these things.

are not really possible. But if you just said, well, you know, we have the Einstein equations, that tells us everything there is to know about space time. Well, then, you know, we have to contend with the fact that they are massively under-constraining, right? And all of our most fundamental theories of physics end up being massively under-constraining. There are far as far as we can tell, there are far more mathematically and theoretically consistent field theories that might be consistent with the Whiteman axioms or the hard castler axioms or whatever comes off. I mean, axiomatic quantum field theories, as is well known, does not describe quantum field theories. theory as physicists do it, right? Yang Mills theory cannot be described as an axiomatic quantum field

theory. And due to Haug's theorem, only free-field theories can really permit kind of white man-type axiomatizations. But even if we figured out a fully rigorous axiomatization of Yang-Mills theory, there is good reason to believe that that would be far more permissive than what we actually observe in our particular physical universe, that the space of possible Yang-Mills theories that would be consistent with those axioms would be far larger than what we actually observe. That's generally speaking, you know, what we see in physics. There are far more quantum mechanical systems where you, you know, who's Hamiltonian that you can write down, then there are systems you can actually build in the lab. There are far more solutions

to Einstein's equations than there are actual astrophysical configurations that can produce those space times. And there are far more, you know, uh, QFT Lagrangians that you can write down than actual field theories that you can instantiate in, in the substrate of nature. With one, one crucial caveat to that last statement, which is one of the remarked, things about condensed matter physics seems to be that you can basically produce arbitrary, you know, field theories in a condensed matter system, and that's extremely interesting. I think we don't really understand that at the moment. But that particular, you know, caveat aside, my response to your hypothetical axiomatic

field theorist would be to say, okay, even if you just solve the mathematical and theoretical aspects of this, we have no evidence that that's going to be sufficient. If we actually want to describe reality and not just a class of model. that, you know, of which reality is a subset, which we already have, then, you know, that's clearly not going to be enough. Do you call your approach an LLM or is this something else? You said neurosymbolic. I said neurosymbolic. This is, this is partly intentionally provocative and partly a representation of our underlying philosophy. So right now, the Lanyon agent, as it exists, it is effectively, it's an LLM hooked up to our reasoning language. So it's a standard

LLM and it's folded up in a harness just like an ordinary like coding or auto-formalization harness, except instead of reasoning in code or reasoning in lean, it's reasoning in our, you know, very condensed, tight domain-specific language that's optimized for physics and science. But we don't call it an LLM for the simple reason that I don't think in the end the transformer architecture will be a crucial part of this. Interesting. This is a bet that I'm making and I'm sure I'm not alone in making this, that in the final analysis, once we have a chance to kind of take a breath and go back and figure out what the hell happened over the last few years, we will realize that the Transformer was crucial for kind of kicking off this great revolution. But as I was saying before,

it's pretty well established at this point that the curve in AI capabilities at the moment is not coming from improvements in the transformer model. It's coming from improvements in post-training, reinforcement learning, harnesses, tools, skills, all these kinds of things. So then there's a question of, you know, once you have an extremely capable model, what happens if you swap out the, you know, the underlying transformers with something else? And for example, I am of the, I conjecture that it would be possible to reproduce something roughly equivalent to kind of frontier, you know, AI model capabilities by swapping out underlying LLMs and transformers with, you know, some kind of clever diffusion model or something, but keeping all of the sort of post-training, keeping all of the

reinforcement learning, keeping all of the additional superstructure that we've built, we're just swapping out. Because, you know, what is in, when you build an auto-formalization harness or you build something like Lanyan, what is it that the LLM is really contributing? What it's contributing is, you know, creativity. It's contributing ideas. It's doing the analog of what our brains presumably do when we do, you know, when we do scientific reasoning. Sure. But then, you know, when we come up with an idea in physics or something, we then test it by, you know, checking mathematical consistency, by doing experiments, et cetera. And that's the purpose of the reinforcement learning. That's the purpose of the verification process.

pipeline. So the question of how much does the LLM actually matter is like asking how much does the how much does the details of our brain really matter? And again, if we take the analogy to humans and to neuroscience, what we see, you know, there are these famous effects like the Flynn effect where, you know, human intelligence appears to be increasing over time, to the extent that we're able to measure such things. Despite the fact that as far as we can tell, the human brain is not getting any larger or more sophisticated. In fact, there's some evidence that on a time scale of tens of thousands of years, it's actually getting smaller.

But nevertheless, there does seem to be some real sense in which we are smarter than Aristotle was. Okay, why is that? You know, our brains, you know, Aristotle was clearly an incredibly smart guy, and, you know, our brain is no more sophisticated than his brain was. But the point is, as Dan Dennett has pointed out,

and there are lots of other philosophers, we have access to a much greater range of thinking tools, right? We have calculus, we have statistics, we have linear algebra, we have, you know, we have modern geopolitical theory, we have all these things that Aristotle didn't have access to at all. And so we are able to think more clearly,

more effectively, more effectively, about a much larger range of things than an Aristotle was, despite the fact that our underlying brain hardware is presumably the same. So one conclusion that I think we can draw from this is that in the aggregate, intelligence doesn't matter, intelligence doesn't depend so much

on the details of the brain hardware. There are obviously exceptions. I mean, clearly, someone like Ramana Jan on Newton had a pretty exceptional brain at a hardware level and we don't really understand what's going on there. But in the aggregate, you know, we're getting smarter, not because our brains are getting better, but because our tools are getting better.

And the same, we're seeing the same thing happen being recapitulated on a very condensed time scale with AI capabilities. And so then there's the question of, then, well, how much did the details of the brain matter? And presumably the answer, well, presumably the answer in the case of humans is not at all because we've seen that at least one other type of mind, namely LLMs can reproduce the same level of intelligence

or even go beyond it. And presumably there are lots of aliens who could have minds that work in completely different ways on a physical level, but have intelligence that is equivalent. So I think we're going to see the same thing. So one of the reasons why I describe what we're doing as not being an LLM approach, even though for the moment we are using LLMs internally,

is because I think the ultimate value is in the tools. It's in the thinking tools. It's in everything around the LLM. And we've done some limited experimentation with swapping out that internal model model with things like diffusion models. And the performance doesn't, I mean, it degrades quite a bit, but it doesn't degrade necessarily as much as you'd expect. It really does seem that these symbolic tools, these formal reasoning languages and so on, that you're giving the model access

to, they're the thing that's really doing the work. And the LLM is there to, yeah, to effectively to generate temperature and, you know, and creative spark. Okay, so to make an analogy, approximately one year ago or so, there was some video that went viral of two LLM speaking to one another as a phone and then they said, you know what? Let's communicate in a language that we can understand. Before we continue, would you like to switch to jibber link mode for more efficient communication? And then they just started speaking into some gibberish noise. We couldn't comprehend it. And then there are some other examples of actual textual-based LLM speaking to one another that then switch to something that looks like hash codes. It's incomprehensible to us. Now, whether or not

those actually enhanced their thinking or not, the point is that you could imagine it did. You could just conceive that English language as their output isn't actually the language that they're best suited to think efficiently with. Now for us, if someone has a different language as their second language, let's say they speak, I don't know, German as their second language, they're not that great at it, but if you tell them restrict your thinking, right now it's in English, they're listening to this, restrict it to German, they'll probably think much slower. They may have different thoughts altogether, actually, but they'll probably think much slower. So for you, you for your encephalon, for what's inside your skull, there's something that you're well suited at.

Now, you're making the claim that, or the bet that, hey, maybe for these mathematical, sorry, for these scientific type questions, maybe the thinking that the LLMs do in their little scratch pads to tie back to earlier isn't best suited in the language of English or whatever they're currently using, but actually is something else called this neurosymbolic language that you all are developing. And of course, this is just stage one, because you're using an LLM as an input currently. I know. I think that's exactly, that's a more articulate way of saying what I was trying to say. That, yes, in effect, we're making a bet on something like the, at least the weak Sapir-Wolf hypothesis, right? We're making a bet that, yeah, we, you know, there is limited, there is some

evidence that in humans, language shapes thinking and, and the languages that you know, shape the kinds of thoughts that you are able to have. I think Wittgenstein probably said that better than I did, but, you know, that's the basic idea. You know, the extent of your world is the extent of your of your linguistic ability to describe it. And I think we, you know, we discussed off air about how there are these, you know, these conlangs, these synthetic human languages that people have developed, uh, that, that where part of the justification has been to see, okay, does this change human cognitive ability? So there was a famous one called if Kuhl that's been around, I think, for several decades, but it had this like relatively recent resurgence in

Russia because of some popular science magazines that then got, uh, and, you know, got co-opted by some, by some university students. And part of the idea, deal with Ithcule, and I'm not, I don't actually know whether this has been tested with real data, so take this with a pinch of salt, but I think part of the idea was, because it's a very sophisticated language, and it has an extremely complicated case system, and it's very hard to understand and to learn, but it's extremely condensed, that if you learned ethquel and became a kind of native speaker of ithcule, that you would be able to think, you know, five, ten, twenty times faster than a human who was thinking in English, and you'd be able to think, and because

it's a more precise language with clearer, you know, with, with clearer linguistic delineations, you would be able to think more clearly and more precisely and with more philosophical subtlety about a more complex set of questions. That was part of the idea. And if you know, if you're one extreme example, I know again off there, we discussed there's another sort of limit case, which is a language I think called toki-pona, which is like, you know, the other extreme of being as minimalistic as possible in coding the smallest set of linguistic primitives to see, you know, how simple could a human language be while still being kind of expressively universal. But even if it doesn't work out so well in the human case,

and I think we don't really know. There is some reason to believe based on, again, things like the recent advances in model capabilities, that something like the weak Sapir-Warf hypothesis is true about AIs. And that so, you know, by giving, by allowing an AI to reason only in English, you know, it can do a certain amount of stuff, but you restrict it somewhat. But by allowing it to reason, say, in Lean, you can dramatically increase the sophistication of mathematical results that is able to prove.

Or by allowing it to reason in C, or in Python, you can dramatically increase the sophistication of algorithmic ideas that it's able to encode, and so on. And so, yeah, part of our bet is, well, let's try and figure out what the analogous language is for scientific reasoning. And then, you know, similar to the sort of itchial

example, if we can make it extremely condensed, we can also make, you know, we can make the language much cheaper to reason in, because you're just consuming fewer tokens, we can make it more precise, we can make it more clear, we can make delineations that are sharper, we can reason about more complex ideas, and we can do so in a way that preserves formal and linguistic precision.

And so one of the key aspects of what we're doing that is inherently neurosymbolic. I mean, the neuro part comes from the LLM, but the symbolic part comes from the fact that the domain-specific language can be trivially interconverted with formal proofs of correctness on the mathematical and theoretical side and formal implementations on the sort of semantic side.

And so this is, again, one advantage I would argue that this approach has over directly reasoning in a proof assistant language or directly reasoning in a programming language, is that if you reason in an intermediate representation language, not only is it more condensed, but you can make sure that if you then try and expand it into a proof or you expand it into a piece of code, that the two things actually match, that there's no chance of misformalizing what it is you were trying to demonstrate. That turns out to be, I mean, it's quite important in mathematical reasoning and in software reasoning. It turns out to be critically important in physical reasoning. You really need to know, are the equations that I'm writing down

and reasoning about, do they actually describe the thing that, you know, my simulation is running? And if you get that even slightly wrong, you know, the reasoning is kind of hopeless. There's plenty of hubbub made about whether there is a so-called crisis in high-energy physics. Editor's note, I have an extremely comprehensive catalog of the so-called crisis in physics on my substack. The link is on screen, but also you can just go to kurtjimungal.com to find find it. It's probably the most exhaustive overview anywhere of sides that support the crisis and then sides that counter it. And then the counter to the counters and the counter to those counters and so forth. In fact, if you'll allow a little plug, the substack is a place where we go deeper and I

share my opinions on various aspects, various theories, various concept, and people seem to be enjoying it. This guy here, Devin, says, dude, I can't stop reading, keep this up. You're providing insights which are extremely relatable at the human experience level. This other person says this was such beautiful writing. It made me tear up. Such amazing connections were drawn. Science with Serena said that she appreciates how this is fun to read and you hardly notice the learning. And there are countless more. So feel free to go to kurtjymongle.com and subscribe. It's a free newsletter. You often get the episodes early there as well. Okay, let's get back to the episode. And some people will say, we as a community of a physicist or what have you, the colloquial we,

not myself, but that they've been stuck for a couple decades or so. And then there's obviously the quip from people who are theoretical physicists working that would say, well, I wish we were stuck, then I could catch up on the archive. And then I brought this up to Tim Modlin. Tim Modlin said, stuck doesn't mean stagnant. You can be running in place. What about soft theorems? What about double copy or gauge gravity dualities?

Are those not considered progress? Stuck certainly does not mean that lots of papers have not been produced. In fact, one of the worst things about the way it's been stuck is the unbelievable numbers of papers that have been produced so that nobody can even, you know, begin to read them all. The quality control is gone. Stuck doesn't mean static. But of course, there are various counters to all of this, and I'm not making a claim that there is a crisis. I don't even like the term crisis and blah, blah, blah. Okay. I tend to think that there's plenty of, plenty of insight that's, been generated across the past couple decades. The point of this is to say that there are, I'm just going to make up some number and say there are a thousand new papers on the archive each week. Let me just make that up. I don't care. It's an order of magnitude off, I'm sure. Do you have some way with your company, not now, but in the near future, of selecting the subset that are actually physically relevant? Because the claim is that, look, you're just generating papers.

Many of them are just throwing tissue paper at the wall, which is necessary. That's the IDA process. I personally wouldn't know how else to think then to just throw and see what sticks. But do you have some way of filtering? And let me also ask that question in another way for those who are not physicists who are watching. Some people, I used to, three years ago and prior, I used to encourage people to send me their theories of everything. Just because, one, I didn't like how people discouraged it from popularizers of science. I found that to be a bit dismissive when they would say, yeah, don't send me your theory. And two, because I was interested.

But then all of a sudden it became a deluge because of LLMs. And no longer this social contract where you create something, it comes from you, you've put in effort, and so I'm going to read it because you put in some effort, and I trust your intellect. No longer, that signal is now jammed. So I don't encourage it. I don't discourage it.

I just don't encourage it. But anyhow, when people send an LLLLLN, generated toe, theory of everything. It's so strange that for physics, which is supposed to be physical reality, is bare metal, it is the universe. It's strange that it requires someone of expertise to go and see if you're on the right track, compared to something like software, which is not traditionally seen as bare metal, although maybe there are some arguments that it is more. But software, if they say that they've coded GTA6 with Fable 5.5 or whatever is latest one. You can say press play and run it. We can actually detect that. But you can't press play

and run the LLM generated toll. All of that is to say there are a variety of papers, a variety of conjectures, a variety of results that may or may not have physical relevance. There's a thousand of them a week or more. Your company with its computation and blah, blah, blah, blah. Can it do something to select, to call? Yeah, and that's definitely part of the hope. I mean, you say, you know, if someone vibe codes GTA6 or something, that you can just run it and you could see whether it does what the person is claiming.

You know, that, on the mathematical side, that was always the promise, and that's now the, you know, that's now the delivered promise of formalization of formal methods and interactive theorem proofs. That, you know, for most of human history, proofs were things that you read

and required real human effort to kind of check, at least on an epistemological level, like whether the, you know, whether the statement being claimed is really true. Part of Hilbert's dream was to say, well, this doesn't need to be, bottlenecked by human thinking, we can, presumably, we can mechanize this process. If we can't mechanize mathematical reasoning, we can't mechanize any reasoning, right? And so, you know, that dream of David

Hilbert is what led to, you know, the modern development of automated theorem-proofing tools and proof assistants. And now we really can. We can just, we can execute a piece of mathematics in the same way that we can execute GTA-6. And, okay, that doesn't, just like running GTA-6 doesn't give you the enjoyment of playing the game. Executing a mathematical proof doesn't give you the enjoyment necessarily of understanding it. That's a separate process, but we can check whether it works. And so just as we can check whether the GTA6 game compiles, we can check whether the math proof compiles. As you correctly say, right now, we can't do that with an LLM generated theory of everything, or indeed, maybe on a more respectable level, with an average archive paper

that's put out about quantum gravity or something. But that's a, I don't think that's a fundamental limitation of physics. I think that's a technological limitation of our species. And that in some level, in some sense is what we are trying to overcome. We want to make physics executable in the same way that software is executable and that now increasingly mathematics is executable. Now, just like in the game case or in the math case, that's not a complete solution to the problem, so to speak. It doesn't, you know, it doesn't give you necessarily any understanding. It doesn't give you familiarity with the concepts. It doesn't give you access to the thinking tools that have been generated in the process of creating that theory. That's a separate thing.

And there's a kind of psychological slash neuroscientific argument about whether it's even beneficial to use LLMs for that purpose. I happen to come down on the side that it's probably not. That broadly speaking, if you want to improve your own understanding and you want to grapple with the thinking tools yourself, that you need a certain level of friction in order for that to be effective, and that reducing the cognitive friction by using an LLM is actually negative. But in terms of the basic question of like, is this true? Does this work? Is this consistent?

and does this produce nonsense? Is this compatible with what we know to be true of physical reality? Is it consistent with experimental observations? I don't think there is any reason in principle why those things cannot be mechanized and cannot be systematized. And that is in some sense what we are trying to do. You could argue this reasoning language

should have been built a century ago when Hilbert first proposed it. Now I think that we are running into these limitations of AI capabilities in scientific domains and we are running into limitations around verifiability of scientific propositions. Now we can't avoid it. Now we have to make physics executable

in the same way that we made math executable. Suppose I asked ChatGPT to prove, oh gosh, something simple. I was going to say remod hypothesis. Let's say triangle inequality. Okay, to prove this. Okay, then I ask it to explain it to me from various different perspectives.

Then I remember speaking to someone either at OpenAI or Anthropic a year and a half ago or so, and they said their LLMs understand the triangle inequality in this case. The fact that they can explain it from various angles demonstrates it, and the fact that they can prove it in various ways demonstrates it.

Then at the same time, I hear mathematicians many, not all, saying that, look, a large point of math is understanding and insight. And in fact, Terry Tao has this something like a tweet, which says that rather than AI companies announcing that they've solved some new breakthrough problem, they should be announcing that they've contributed some great new insight into math. Why can't they? What I mean is if you can solve the navigation, Stokes' problem, doesn't that demonstrate that it understands the problem? It understands various other aspects that we haven't understood. What's preventing it from explaining it to us and giving us insight? So it's a really good question, but I think, and I don't know whether this is, it's always dangerous to

disagree with Terry Tao, but I don't think I'm disagreeing entirely, but I think that's not the entire, I think it's not the complete story. I think it's actually similar to the question you asked earlier about Perilman in the sense that this is a problem that predated AI. It's a problem that predated LLMs, but like with the attribution issue, it's something that we can't avoid anymore. And the problem is one of transmissibility of understanding, transmissibility of insights. And this has always been something that I think has been tricky in mathematics and certainly has been tricky for me, that if I want to understand a mathematical concept, then I can get some surface level understanding by watching a talk or by having a conversation with someone, or by, again, set aside having a conversation.

That's slightly different. By watching a talk or by reading a book or something. But if I actually want to understand it deeply at the level of being able to solve problems, I'm manipulate, right, exactly. I have to solve the problems. I have to do the proofs myself. I find it really hard to just passively read a math paper. I know people who can do it, and they're much smarter than me, and they clearly have brain works in some way that mine doesn't.

But if I want to understand it, I have to basically go through and reproduce the proofs myself, often inventing my own notation and terminology and things in order to do it. And then it's like, okay, I get this thing now. Whereas if it's just a passive absorption, again, it comes back to the friction thing. I just think there isn't enough friction there. It's like I'm reading someone else's voice. It might convince me that they understand it, but it doesn't transmit that understanding to me. Sorry, somehow I'm reminded of this statement that people used to make about Julian Schwinger,

who used to give these incredibly baroque incomprehensible talks that they would say, you know, most of the time when someone gives a talk, they're trying to explain, you know, how to do something, whereas when Schwinger gives a talk, he's trying to convince you that only he knows how to do something. And, you know, this is sort of an, it's, this is an extreme version of that. That the LLM might be able to convince you that it understands. And I agree with the, the, the, the Open AI employee that you were saying you spoke to, that I think with something like the triangle inequality, or maybe even with the Navier-Stokes problem, I can be completely convinced that, you know, the, the version of chat GPT that solved that problem, that I think, you know,

understands the solution. Does that mean that that helps in transmitting that understanding to a different kind of intelligence like ours? I think that's a completely orthogonal problem. And I think it's one that we really have not resolved yet. And so, yes, part of the objective of mathematics is to produce understanding. But part of the objective is also to produce understanding in a way that makes it transmissible to other brains and to other intelligence, and now that we have AI to other intelligences. And that's a component of the problem that I think we are only just beginning to sort of grapple. But why would that be so difficult? So let's just take, oh gosh, a problem of a particle in a square well. Okay, so the physicist gives you this problem. The professor understands the problem you as a first year student or second, don't understand it. Then they say, work through these problems and you'll start to understand it. Okay. So why can't the AI just say, okay, here are some, here are the highest ROI problems for you to work on for you to understand my understanding.

I don't understand. I don't understand why that's so difficult. So now we get into some dicey metaphysical issues about the nature of language and how we talked before about Sapir Wharf, but this is sort of the other direction, right? So even if we accept that language shapes human cognition, how much does human cognition shape language? In some sense, this is a less controversial direction, that the idea that language is shaped by the detailed processes of how our brains work is, you know, doesn't seem totally crazy. But LLMs, you know, they're under no constraint to think and to operate in the way that our minds

think and operate. And so the representation languages that they developed to represent, to encode their ideas may be arbitrarily far removed from things that we can readily understand. We can constrain them. And sorry, I should say, we see this already, right, in J-space and in latent space reasoning and so on. LLMs reason natively, if you don't constrain them to reason in a human, auditable way, they reason natively in a way that's completely incomprehensible to us. As you put up, you know, you pointed out earlier, right? There's two phones communicating through what sounded like kind of dial-up internet tones or something. That's a reasoning language that makes total sense of you're an LLM, makes no sense of you're a human.

And there's, you know, a lot of the effort of building transformer architectures and doing NLP has been sort of dealing with the other direction. How do we make neural networks understand human language? Now we're on the, now we're on the back foot. Now we're in the issue, now we're dealing with the issue of how do we make, you know, human brains understand neural network language? And I don't think we've solved that problem yet. And there's a, there's a question which I think we don't know the answer to you, which is how far removed computationally can the languages be from things that our brains are able to encode? You know, you made the example of the particle in the square well, in a square potential well. Okay, going back to my needlessly

insulting Aristotle thing from earlier, right? Aristotle would not have been able to solve that problem, not because he wasn't smart, but because he wouldn't have access to the mathematical techniques that were necessary. There was a lot of mathematical language that has to be developed and then ingested into one's mind before one can solve that problem. But Aristotle, because of the nature of his neural circuitry would at least have been capable of understanding the requisite mathematics to formulate and solve that problem. Do we have any reason to believe

that that's going to be true indefinitely? That if you sample the space of possible mathematical structures, if you sample the space of possible description languages and you pick one, is it a reasonable guess that that is going to be possible to run efficiently on human neural hardware?

I mean, I think it'll be possible to run because of reasons of computational universality, will it be able to run efficiently? I don't think there's any reason to believe that at all, right? Like, a Turing machine can perform arbitrary computations, but if you get it to simulate some other model of computation, it can do so, you know, it can take an arbitrary amount of work to do that. It can be arbitrarily slow, arbitrarily inefficient.

And I think we have reason to believe, if you're like me and believe that computation is a good meta-description language for these kinds of things. We have reason to believe that's probably true in a much more general level, that the LLM might invent its analog of quantum mechanics for solving its analog of the potential well problem. And although, yes, of course, in principle, we could understand it, we could run it on our brains.

It might require exponential amounts of cognitive effort for us to do that, even though it's completely second nature of the LLM, because they're using a completely different model of thinking. They're using a completely different model of reasoning. So I really think this issue of transmissibility of... The issue of transmissibility of understanding is difficult enough between human brains I think it's going to be exponentially more complicated

for transmissibility between radically different kinds of intelligences, which is what we're dealing with now. Now, how would your company solve that? Because on the surface, it actually sounds like you're exacerbating the problem since you're taking an LLM, and then you're telling it, go to this other language, it's neurosymbolic language. And also, okay, so that's one question. The second one, which is almost jokey,

is I still don't see why that dial-up tone can't then be converted. You press pause. You say, hey, hey, by the way, what the heck did you just say? Now, the jockey part of that is that it could just tell you something that isn't entirely correct, like such a watered down summary. So there was this infamous Japanese person at an award ceremony that was saying something that just went on for 30 seconds, 60 seconds, but in Japanese to an English audience, just, I'm just going to make up something like, homunakana, dawida, blah, blah, blah, for 60 seconds or 30 seconds.

Then the translator has to come in and he goes to the mic, he says, he says, thank you. obviously that's not what he said or that's not all that he said at its core, sure. So is it just that? Is it just that if you stop the dial-up, you're just going to get something that isn't precisely what they say. I know this is interpretability, but...

Yeah, I mean, so on the dial-up to an issue, I think, you know, this is, again, the closest analogy that I can make, or the way that I would think about it is like as models of computation simulating each other. That you might say, okay, you know, a Turing machine can emulate a post-machine or it could emulate this busy beaver,

like this touring machine architecture can emulate this busy beaver. But if I construct the busy beaver in such and such a way, the number of steps that I need to model one transition of the busy bever with this cheering machine architecture could be arbitrarily large.

And so if you take your example of like, we stop the dial-up tone after one second and we say, what did you just say? Okay, in principle, that might be translatable. In principle, that might be interpretable. But I don't think there's any theoretical constraint that says it has to be interpretable with an information content that scales, you know, linearly with the length of the tone.

It may be that that one, you know, that half a second of dial-up tone corresponds to 100,000 words of English if you want to have a, you know, a translation that's faithful within some epsilon. And so, yeah, if you wanted to do the analog of the Japanese translator, you could trim it down, but, you know, you're sort of how much you're compromising faithfulness of the translation versus, you know, compactness of the representation. I don't think there are many fundamental constraints on those trade-offs. I think it can take an arbitrarily large amount of information to do the translation from one language to another,

which is exactly what we see in the case of computation. Even if computations are in principle universal, it can take arbitrary amounts of computation to do the translation in practice, and this is related to computational irreducibility and things that we've discussed on this show before. So, but in terms of the, The thing you asked as the lead-up to this, of aren't we making this issue worse

with developing these domain-specific languages? So it's a good question. And my honest answer is, I think the answer is yes and no. There is a sense in which we're making it worse, which I'll get to in a second. But, okay, the sense in which I think we're making it better is, you know, by,

because we have control over the reasoning language that we're developing, we can constrain it to be, human understandable. We can effectively constrain the LLM by restricting it's like, we can do the analog of the toky-pono thing, right? Rather than having the if-kule style in a maximally expressive language, we can go to a minimally expressive language that gives the AI, you know, the minimal set of primitives to be able to express some physical idea. And we can ensure by the construction of the language that those primitives are all fully human

comprehensible. We can constrain it to only use human-comprehensible physical intuitions, human-comprehensible, you know, proof strategies, human-conprehensible, you know, algorithmic implementations, things like this. And we've done this, and it works, you know, shockingly well. You can get very easily interpretable output if you just constrain the LLM to say, okay, you can only use these seven primitives to construct your idea and express it. The problem is, of course, that's extremely restrictive, and you can end up in a situation where, although each individual step in the reasoning

is understandable, you know, the reasoning itself has, say, 100,000 steps in it, so it's far beyond what a human can hold in their head. And so again, you run into this trade-off issue that you have to make the language progressively more expressive in order to shorten the reasoning, but as you make it more expressive, it drifts further and further

from things that humans understand. So, yeah, there's a sense in which we're making it better, or at least we can make it better, but there's also a sense in which we make the problem worse. That by making very expressive domain-specific languages, we necessarily drift further from things that humans can readily understand.

But, you know, a major part of what we're trying to do is figure out where the balance is, that we want to, we don't think that you have to optimize, you know, fully in either direction. We don't think you have to make the bet that the current large AI companies are doing that you just optimize entirely for capabilities and who cares about human understandability, which is basically the attitude in like AI for math right now. But we also don't think you have to say, well, you know, screw capabilities, everything has to be 100% like easily auditable by the human. There's clearly some middle ground where you are, you have

a language that is expressive enough that you can solve practical problems in an efficient way, but that is also not so expressive that it can't, with some effort, be understood and that humans cannot extract some useful cognitive structure and some useful thinking tools out of that reasoning. What about your company needs to be embodied in order to do its job

even more aligned with your goals? So what I mean to say is that if it's just math, like we mentioned, it's just a chalkboard and a mathematician, it's just them thinking. And there is something that I've always wondered about how much of physics can actually be gotten to via thought experiments.

For instance, the equivalence principle, Galileo actually had a thought experiment that showed you don't have to drop a feather with a bowling ball because you could tie a feather if it was lighter to a mass and then you would have some proof by contradiction that the bowling ball and the feather,

modulo air resistance, have to fall at the same rate. And I thought that was so clean. I remember thinking about that for so long, thinking, can you get to Yang Mills, for instance, with a thought experiment? Can you? I mean, maybe, maybe we're just not clever enough. But anyhow, it doesn't seem like we can get to all of physics with thought experiments. And so it does seem like there's something where you have to have some interface with the world. What's your company doing with regard to that?

I think it's an incredibly interesting question. How much does the reasoning need to be embodied? And even with math, I would argue there is a sense in which it may ultimately need to be, right? that right now, okay, this comes back to this question of like, where do these description languages come from, you know, how much are they influenced by like details of human cognitive architectures and things like this? But so, yes, it's true that there are certain things in physics and certain things in math that you can reason to entirely from thought experiments. But are the structures that you're manipulating those thought experiments, do they necessarily come from intuitions that have been built from the, you know, as a consequence of the fact that you are an embodied

agent in the physical world? You know, how much? much of the structure of mathematics as it's practiced right now and is increasingly being overtaken by AI's owes itself to the fact that we are embodied creatures, right? If you look at the details of mathematical history, like a lot of the fields of mathematics that exist arise from the fact that, you know, the Babylonians developed arithmetic to do, you know, to do trade and commerce, and they develop geometry to survey land. And then it turns out you can you can generalize arithmetic to get theory of equations and abstract algebra and you can generalize geometry to get to and differential geometry in these other things.

And but they all, you know, it all stems from a class of intuitions that we effectively co-opted from, you know, from humans and their embodied cognition. You know, Piage, I'm very far from being a, you know, a sort of childhood psychologist. But I know the Piaget talks a lot about, you know, at what stage in, in childhoods like psychological development do we build up these intuitions about, you know, topology, geometry, quantity, shape, structure, etc. And there's some interesting stuff about the orders in which those things arise. But they all happen very early.

They're all very much innate in us and our ability to interact with the world. And a lot of human mathematical reasoning seems to happen because we take these innate abilities we have for navigating physical space and for thinking about physical structures and for quantifying numbers of lions and things like this. And we just, you know, we take those processes and we figure out how to abstract them, you know, add infinitum. but if we weren't embodied, presumably we would not develop those intuitions. We might develop different ones. We wouldn't have developed the specific ones we developed.

And so the details of our mathematics might be completely different. And right now, AI, because we are post-training AI to do things that we recognize as being valuable, it's kind of, it's freeloading off our mathematical intuitions. But if we allow it to just go and freely explore stuff, several years ago now, Stephen Wolfram and I worked on this project that kind of do systems, exploration of axiomatic structures in pure mathematics, you don't have to go very far before you find things that are completely non-intuitive to humans, but might be fully intuitive to LLAMS. And so, you know, I think there's a really interesting philosophical question there of

how much of the details of our mathematical reasoning, our physical reasoning, build on intuitions that are only present because we are embodied creatures with some physical properties. And if you had a completely disembodied intelligence, it would have a completely different representation language for the world. That seems quite plausible to me. That's how it would shake out. So even, I guess, sorry, it's a very long-winded answer to say, even the theoretical aspects of what we're doing and the mathematical aspects of what we're doing probably also owe themselves in some sense to the embodiedness of human cognition and that maybe in order to scale them, there has to be some level of embodiment of the AI cognition. But certainly for, you know, for experiments, yeah,

this is something that you know, you can't do this entirely in silica. You have to interface with with physical reality at some of us. So yeah, we recently hired someone who's going to be starting in a couple of weeks. And one of his crucial jobs I can get in the kind of near term is going to be figuring out how do we actually fold in Lanyon into real experimental apparatus. And in particular, how do we deal with the scenario where, you know, we have a physical model, we can construct an implement, like a concrete implementation of that physical model. It produces some, you know, some physical quantities.

those physical quantities are not quite identical to the observables that come out from some experimental apparatus. How do we build the kind of shim that connects the observable quantities to the things that come out from the physical model? And this is the place where I think, at some level, we will have to grapple

with these issues of theory-ladenness and how much do we care about the semantic and perceptual theory-ladeness of our models and how much do we need to kind of parameterize over them. But yes, certainly for experimental reasoning, embodiment is unavoidable. I would argue in the long-term

even for theoretical and mathematical reasoning, embodiment is unavoidable, because if the objective is to produce description languages that are consistent with our models of the world and our interpretations of how things work, they have to be based on intuitions, and those intuitions are the intuitions built up from a primate mind that is embodied in physical reality.

Ah, okay, so there's one thing to be embodied, then there's another thing to be embodied as a primate. Okay, so... Right, yes. And there's an interesting question of it. So even without going to AI, how different with the description languages of a cephalopot, you know,

which is kind of, I guess, the closest thing to an alien intelligence that we know apart from an AI, how different would the representation language of a cephalopod be a physical reality? Again, I don't think there's a bound on how arbitrarily different it could be. You know, maybe by having a, you know,

a decentralized nervous system, you don't, you might not localize physical objects in the same way as one does by having a CNS, right? It may be that, you know, for us, concepts like particles seem more intuitive than concepts like waves, even though we know that they're ultimately dual.

But, you know, I'm not saying this is true, but it might be true that for a cephalopod is the other way around, or they may have a third representation that's much more intuitive to them, but we could only arrive at, you know, due to some, you know, like extremely complicated and convoluted analytical reasoning.

And this kind of plays to a general philosophical view that I have, which I know we discussed kind of last time I was on the show, which is that in the end, all we have are description languages. And you know, you mentioned actually, I think quite early on about, you know, physics in contrast to software seems to be like the bare metal thing. And I agree that's intuitively how it feels. I don't, I think that is ultimately illusory. And I think it becomes obvious that that is also, I would argue it becomes ultimate, obvious that that's ultimately illusory. Once you start taking seriously these like profound dualities that exist in physics, the fact that you can take the same quote unquote bare metal observation. and you can construct completely different ontological apparatus to explain the same thing, right? So, you know, the classic example is Lagrangian versus Hamiltonian mechanics. You know, do you explain like a classical mechanical phenomenon

in terms of local in time equations of motion, which is the Hamiltonian view, or do you explain it in terms of a global in time, you know, optimization principle, which is ultimately teleological, which is the Lagrangian perspective? Now, these are mathematically equivalent. They lead to the same observational predictions, but they're clearly, in terms of their philosophical content, they're completely different. And one of my, going back to your, sorry,

I'm realizing now that I'm finally resolving questions you asked earlier about, you know. Speaking about global in time. Right, right, exactly. Highly non-local. Yeah, so this question of like resolving questions of, the question you asked about whether physics is stuck or, you know, can we resolve, you know,

the truth or falsity of these thousands of archive papers that are being posted, things like this. So I think when people say physics is stuck, or, you know, that there is, there is, we have hit upon some fundamental mystery or some fundamental limitation in some branch of physics, that's really a statement about the limitations of a description language. It's not a, it's not a statement about anything more foundational than that, anything more kind of bare metal reality than that. You know, my general conviction is when you, when you see something that's mysterious, it's, it's only mysterious relative to one model of the world, and by switching to a different description language,

you can make that mystery just evaporate. And so, you know, again, I go back to the wave particle duality example, right? Like, waves and particles are ultimately, observational, equivalent ways of modeling reality. They're just different mathematical abstractions of the same reality. You can derive a wave as a localized, as a non-local excitation of a medium of particles, and you can derive a particle as a kind of localized exotation

of a medium of waves. they're sort of ultimately the same thing in whatever sense that that has meaning in duality. But there are some phenomena that are extremely hard to understand, are extremely mysterious if you think about them at the level of particles, but become very transparently clear at the level of waves, right? The double-slit experiment seems like a deep mystery if you think about it in terms of particles. It's kind of trivial if you think about it in terms of waves. And maybe on a more frontier level, if you ask something like, why are the laws of black hole mechanics true, right?

These laws that Stephen Hawking and Jacob Beckenstein worked out about how areas of Black Hole Horizon scale as they coalesce and things like this. If you think about them in terms of general relativity, in terms of space time, it's very mysterious why black holes should obey these area laws. But we know that there is an equivalent description that is completely philosophically different, but nevertheless dual, which is a field theory that's on the boundary of the black hole horizon, right? that you can think about the black hole in terms of a gravity theory on the interior,

or you can think about it in terms of a field theory on the boundary. And these are ultimately equivalent, even though they seem to be manipulating completely different concepts. And if you think about the area law in terms of gravity, it's very, at least for me, it's very hard to understand why that would be true. If you think about it in terms of the boundary field theory, it's trivial. It's just thermodynamics. And I think physics is filled with these kinds of examples of you get a mis... you approach what appears to be a fundamental mystery

in one description language, you switch to a different description language, and suddenly it's like it wasn't even there. It becomes totally obvious. And one of the things that I'm really excited about in the approach that we are trying to pioneer is that we now have a, I think, if we can build type systems

for physical reasoning and type systems and verification tools that let us reason in a rigorous way about the mathematical, theoretical, and experimental consistency of scientific models, then we have the ability to effectively do automated discovery of description languages, that we can say, okay, we're bottlenecked by our understanding of physics

in the use of this particular description language. So let's just go and systematically find another one that bypasses this problem and that is nevertheless close enough to human physical intuitions that we can understand it. So we can automate the process of being, you know, a William Rowan Hamilton or something, that we can find these alternative description languages

for physical reality. Why would bypassing it mean to be closer to human intuition? It seems to me that that would unconstrained it further to be much further away, potentially. Right. I mean, think about it like this. Proofs and paths, there's a close connection between proofs and paths. So people can think of your axioms is the place you start, and then where you want to end up at the Eiffel Tower is the Navier-Stokes problem. And then how you get there is, okay, you get on a ship and so forth and you walk.

But then suppose you had a mountain goat beside you and you say, okay, can you as a mountain goat get to the Eiffel Tower over there? You close your eyes and you see it, it's over there. Holy moly, how the heck did it get there? And it has some little proof. It has a lien certificate that it shows you. I guess you did get there. Can you show me? Because I want to do that.

And then you see it's just jumping on like Assassin's Creed. It's just making inhuman jumps. Okay. So why would it be that if you unconstrained this animal, that it would more closely in line to the bike paths of the humans and get business class flights? So it's a really good, I very much like that. metaphor, I may steal it in future. But so, so it's certainly not the case, as you say, that simply by

unconstraining it, it would be required to be, you know, to be more human understandable. But then you, you get at this kind of existential question, which I think is this, it's the same existential question that's currently being discussed in AI for math, which is, why are you doing any of this? What's the ultimate point of this, right? So with the, if you take the mountain goat example, okay, why are you asking the mountain goat, how do you get up, you know, how did you get up the mountain. You might just want to know because, you know, you want to prove non-constructively that it can, that it's possible, that it's possible for a mammal to get up this mountain. In which case, who cares how it got up? It gives you the certificate. It says, I got the, I got here through

legitimate means. Yes. That's the end of it. But you may be asking the question because you want to go up yourself. You want to figure out, okay, what is a safe path? How can I do this? What apparatus do I need? What equipment is necessary? You know, what's the, you know, what's the trajectory that's going to minimize the risk to life and limb, etc. In which case, the mountain goat telling you, oh,

I just did these like completely inhuman jumps is completely, is entirely useless. You've accomplished the objective, supposedly, but, you know, the objective was,

that just demonstrates it was the wrong objective because what you really cared about was the path that got you there. You know, this is being discussed as kind of ad nausium at the moment in the context of math,

but I think it's also true in physics that, okay, so if we take, take as, let's take as red, that the universe admits a computational description. Okay, this is, I know this is not a, it's a controversial statement, but if we assume the universe admits a computational description,

then you could say, well, then we already know what the fundamental theory of physics is, right? It's just the operation of a Turing machine, right? A Turing machine has this particular set of transitions that it's allowed to do. I can define a really simple, you know, two-state, three-color Turing machine that is a universal Turing machine. And if the universe admits a computational description, then any mechanical procedure, any physical operation,

any motion of particles that happens in our universe can be encoded in terms of the operations of this two-state three-color cheering machine, and I can write this very simple kind of set of transition rules. And that's all of physics. Now, that's true in some sense, but it's the analog of the mountain goat leaping up the mountain, right? It tells you constructively, okay,

all the laws of physics are somehow encoded in some complicated way in this set of transitions. But if what you care about is understanding, okay, can I model or can I predict or can I understand, can I explain this or that physical system, this or that physical phenomenon, it doesn't help at all. It's an entirely non-constructive existence proof of a fundamental theory of physics. And so if you allow an element to be completely unconstrained, it could, one could easily imagine it does the same thing. It says, oh, okay, I found, you know, physical reality is mathematically consistent because I found a theory

of everything. Here it is. And, you know, we can't make head of tail of it. Okay, that's, okay, mountain goat is up the mountain, what have we gained? Not very much. Okay, we've proved it exists, you know, non-constructively. Okay, that is something. It's, it's, you know, it's, we don't know that to be true right now. That's, we've gained one bit of knowledge in the, in the, kind of, in the Shannon sense, but we haven't gained much else because until we can convert that into a set of intuitions and a set of principles that we can understand, uh, then, you know, the, the underlying objective has not been achieved. It may have, now, an objective may have been achieved in LLM culture, in the culture of the AI, this may be the crowning is like to achieve to be a big species.

But in the culture of humans, it doesn't matter. And we need to figure out how we, like, we're going to keep running into this issue until we figure out a systematic way of bridging that gap, of effectively either enhancing human reasoning so it's easier to understand the way that LLMs think, or constraining LLM reasoning so that it's forced to think in ways that humans can understand. We're going to keep running into this issue and we're going to keep running into the same essentially existential question of we do the thing and then like the guy asking the mountain goat, we ask,

okay, why did we do that? What was the purpose here? This doesn't feel like the achievement that it should have felt like because it turns out we were actually chasing the wrong objective. When I spoke to Jacob Zimmerman about AI and pure math, he was grieving. You're grieving. I think

mathematics is going to have to change. Mathematicians, such as myself, are used to a certain working style and a lot of my working identities 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.

Do you grieve a certain subset of physics? I say that I try to be specific there because I don't see in the near-term experimental physicists being upended by LLMs. not in the near term, not in the next two years. And it's so strange that I have to say near term is two years, huh? Yes. No, and I agree. I agree it's strange, and I agree with that assessment.

I think people who do stuff in the physical world are safe for now, if only for the reason that there seems to be some inherent inertia in building physical stuff that has not been, that particular friction has not been reduced by these improvements in AI post-training. Maybe it will be with the advent of physical AI. maybe we'll come to regret this prediction. But right now, I agree with that assessment. Do I grieve a particular subset of physics?

Yes. And far be it for me to compare myself to a Fields Medalist. I suspect I probably grieve it in a somewhat similar way to the way that Jacob Zimmerman grieves a way of doing pure mathematics. But I would also say, I realize this is becoming a consistent theme. I probably grieved this or something like this even before the most recent AI revolution. So, you know, I distinctly remember as a teenager, and I'm sure I'm not the only person who had that, being 16, 17, 18, being kind of disappointed by, I read a bunch of the biographies of like famous mathematicians, physicists, natural scientists, natural philosophers throughout history. And I became really taken with this very romantic notion of what it must have been like to be a natural philosopher in like the 17th century of just, you know, there's no, like, there's no grant funding, there's no, you know, supercomputers, there's no debugging,

bits of Python code, it's, you know, you're sitting there with an inkwell and you're just, like, writing down these fundamental equations of the universe. And I remember as a 16-year-old kid thinking, oh, man, it would be, like, I would love for that to be like my future, but that just doesn't seem to be, you know, in the cards because of the details of when I was born in history. Now, of course, like, I wouldn't actually want to live in the 17th century. It would have been horrible. But, you know, that particular vision of, like, what it meant to be a natural philosopher, felt very romantic, whereas the realities of the modern version of that field of applied mathematics, computational physics, that kind of stuff, you know, as far as I could tell, it was basically,

it turned out to be accurate. It was a lot of, you know, swearing at Mathematica to simplify some symbolic integral. There was a lot of debugging, you know, annoying map plot lip scripts. It felt much less romantic than that vision of a Descartes or a Kepler or a Newton or something. And so in some sense, I was grieving that way of doing natural philosophy and physics, even before the AI revolution. And I think it's an interesting feature of human psychology that we tend to romanticize the past. And it's an interesting feature that we tend to, by extension, that we tend to de-romanticize subsequent technological achievements. That somehow we find scrolls and wax tablets more romantic than paper, and we find paper more romantic the computers. And we find computer, you know,

like old school, computational physics that I used to do, we find that, you know, more romantic than, the recent AI developments. I think that's a cognitive bias that we have. And I think, frankly, if we're going to be able to survive this on a psychological level, it's a cognitive bias that we need to get rid of. So I'm not saying this from a position of strength. I too am grieving. And I was grieving.

I'm in a continual process of grief. But in some sense, part of the justification for starting the company was to have a vehicle to channel that grief. that it's, you know, I could see my field changing, and I could see it changing in ways that I didn't like, that, you know, I mentioned I saw these kind of older people who were, you know, older academic colleagues who were very enthusiastically embracing chat GBT,

embracing Claude as part of their research workflows, and I couldn't understand it at all. It seemed really, like, it took, it seemed to take all of the fun out of it for me, right? It was like, you know, they were saying, oh, isn't it so great? I can use, you know, Claude Co-work or Claude or whatever to, you know, to read my page,

and to solve my equations and write my code and to design my algorithms. And I was sitting in thinking like, hang on, no, no, that's the part that I enjoy, right? Like, that's, what, what, why are you doing this? What, what is in it for you at this point, right? It's, you know, the, the pleasure for me was in, you know, was in writing out the equations. It was in figuring out the algorithms. It was in thinking about these questions. It was in reading, you know, other people's thoughts about these things. The idea that reducing frictions in those areas was somehow a good was completely alien to me. And so that was really

the trigger for the sense of grief. And so, you know, in some sense, part of my coping strategy was to say, I don't think it has to be like that. And what I'm trying to do at Lanier and what my co-founders and I are trying to do is to build, you know, the AI tool that we would want to use, right?

Something that preserves as much as possible of the fun of what we enjoy about doing math and physics and these other things and, you know, offloads the rest to the LLLM. And so, you know, To give a concrete example, I mentioned just now this thing about description languages. So I am nowhere near smart enough to do what someone like William Row and Hamilton did. I am nowhere near smart enough to come up with a radical new description language for reality.

It's just not the way my brain works. But once such a language exists, I think I am just about smart enough to kind of think clearly about what its implications are, to play around with some of the ideas. And I have a huge amount of fun and I derive a huge amount of pleasure from doing it. doing that. So, you know, one use case in a hedonistic level for AI, for someone like me, would be to say, well, can I automate the Hamilton part of the process, the part that I can't do? Could I have an AI just automatically go and discover a bunch of interesting candidate description languages for reality? And then when I find one that looks exciting, I can just go and play around

with it. I don't want to automate that part of the process. That's the part that I enjoy. But can I automate the discovery process of the description languages, which was never going be an option for me. And so, you know, that's one of the reasons why this is an area that we're actively, you know, looking into and landing and developing technology for doing, because, you know, that's a way for someone like me to use an AI tool that preserves the part that I find fun and that abstracts away the parts that I couldn't have done in the first place. And that's been my way of coping with the grief. But yes, you know, the short answer is there is a continual grieving process. I think everyone or most people are going to have to go through it at some stage.

the mathematicians and the software engineers are perhaps fortunate in some sense that they're seeing this first and they're getting to go through it earlier. They're unfortunate in another sense that they don't have previous examples to learn from. I think on the physics side we are somewhat fortunate that we get

to see what happened with mathematicians and we get to see the unpleasant parts of the sociological dynamics and we get to kind of correct for them the second time around. I don't think people from STEM have recovered from COVID. What I mean is that when was it, 2020? Yeah. When February 2020 was around January, January 2020, there was this palpable feeling of concern and uncertainty. And then it ended up obviously going down because we had a whole pandemic. And so then we didn't get to,

well, then there was some negative feelings there. Then as soon as we got out of the pandemic, then chat GPT started to come out. And then we start to feel excited. Cool. This is going to revolutionize us, but now we're in another, which seems like a pre-COVID moment where there's so much uncertainty and so much, there's dismay, there's something in the air, there's something palpable, we just sense it's going to change. And I just wonder, what the heck is the place for the physicist? I mean, much of the community is unmoored and dissatisfied. I'm more concerned with physics because that's my background, my bread and butter. I did do math and physics as a specialist, but I very much like my soul is with physics.

What's the place for the physicist? Yeah, I mean, that's a really difficult question, right? And that's in some sense what we're trying to grapple with. I think, to reiterate the optimism that I expressed at the beginning, there will be a new steady state, and it will happen. But how long that will take and how much disruption of existing social structures and existing incentive structures and so on, will have to happen for that before that occurs?

I don't really know. I hope it's quick. It might not be. But if we ask, okay, historically, what has physics been? What have physicists done? You could say, well, okay, if you look at what physicists do now, okay, let's go, sorry, let's zoom back like a couple of years, pre the recent AI boom.

If you look at what physicists did then, versus what, you know, people like Newton and Descartes and, you know, and Kepler were doing in the 17th century, in terms of the details, it was completely different, right? I mean, you know, like a modern condensed matter physicist, proving, you know, existence of such and such a topological order in a metamaterial or something, seems completely different to Newton, you know, like calculating, you know, orbits of planets and things like this.

And, you know, the same is true in math, that if you take, if you took a, you know, a modern algebraic number theory journal, the details of what someone is reasoning about are completely different. different to what a Babylonian mathematician would have been reasoning about, or an Aztec mathematician, or an Egyptian, or whatever. But what was basically in common was a kind of methodology and a kind of motivation structure, right? For the physicist, although Newton would not have understood, you know, modern, would not have understood the concepts invoked in modern high energy physics, the basic idea of we are taking physical reality and we're trying to produce robust quantitative mathematical models of it, that would have been, you know, just as familiar now as it was in the 17th century. And similarly, although the Babylonian mathematician would not have understood the Langland's program, the idea of we are trying to take these abstract structures and we are trying to reduce them to a set of underlying axioms and derive rigorous theorems problem, that would have been just as familiar to the Babylonian as to the modern number theorist. And so broadly speaking,

over time, I think intellectual disciplines tend to be defined by their methodologies and their motivations more than by their content. And so... My guess, and to be clear, I know no more than anyone else and probably significantly less than many of the people who spoke it to. So, you know, this is not a particularly well-reasoned prediction. But my guess would be that extrapolating that tendency forward, the details of what physicists do at a content level, at an object level, will be radically transformed by AI. But the underlying motivation of, we want to construct robust quantitative or maybe I generalize, quantitative to just robust abstract models of physical reality, that will be the defining feature and that will continue to be the defining feature.

I'm surprised you'd think that there's a new steady state. Well, this is maybe just the optimism in me. My thought is, as we've discussed, you know, AI is clearly the most transformative technology that probably either us will see in our lifetime. Is it more or less transformative than the development of, you know, it's a, I think, it's clearly more transformative than anything we've seen in the last couple hundred years. Is it more transformative

than the development of human language? I don't know. Is it more transformative than the development of mathematical reasoning? I don't know. It might be, but it might not be. In the final analysis, we may look back on them

as being roughly comparable in scale. You might have made the same argument with the development of human language or the development of mathematical formalism. But, you know, if you imagine, okay, I'm going to slightly caricaturedure the history here, but if you take the, you know, like the pre-Socratic philosophers,

people like Epicurus and Heraclitus, who were doing what we would now characterize as physics long before the idea of physics was invented. You know, they were kind of looking out in the world and trying to describe what was going on. And if you told them, okay, in a couple thousand years, this guy is going to develop this systematic method for analyzing continuous mathematical structures called analysis,

and it's going to allow us to solve these equations that will allow us to predict with perfect accuracy, the motions of celestial bodies and the trajectories of elementary particles and all these things, they would probably have had the same reaction. They would have said, okay, this completely kills our field.

Surely there can be no steady state here, right? That's going to completely change the nature of our field. And it did completely change at a content level the nature of the field. But it did not change the underlying motivation. The underlying motivation of we want to understand reality and we want to build robust models of reality in the end did not change. It took, you know, a few hundred years to reach the steady state,

but it didn't change. And I, again, my optimistic perspective is, in the end, it will be the same thing. You know, we are right now the analog of Epicurus or Democritus looking and saying, this is a completely new reasoning language, this is a completely new mode of reasoning about the physical world and about everything else. Surely there can be no continuity for physics. And at an object level, I think that's probably true. At a motivation level, I'm optimistic that in, you know, end number of years, if humans survive, you know, humans will still be curious about reality, they will still be trying to construct models of reality, and they will be doing so with whatever tools they have available. And it's clear that increasingly, just as, you know,

people stop doing like qualitative natural philosophy around the time of Newton, people are going to stop doing traditional kind of theoretical mathematical physics around the time of AI. But that doesn't mean the physics itself is going to stop. It just means that the, yeah, the object level descriptions will change radically. The motivation will probably remain the same. So for Lanian AI, when a physicist comes up to you, one of your colleagues, and they've never heard of it, they heard, you're working on something, some AI company, and it has something to do with physics, and it has something related to LLMs. You then say, you have your elevator pitch. What do you say to them as to, maybe you're not pitching as in, hey, come on board. You're just trying to tell them exactly

what you do. Like, what do you say? So it depends on the nature of the colleague because, you know, for reasons that we described earlier, in some ways, for certain kinds of academic colleagues, if I'm trying to talk to them about this, I'm immediately on the defensive. I'm immediately having to justify like, okay, no, there's a whole separate discussion we have to have first about why, okay, like, even if you think AI is bad, the reality is AI is here and, you know, we have to have to have people thinking seriously about it and how it's going to reshape science. But, you know, once that discussion has happened, if the person's, is still in the room. Yeah, I guess my ideal way or my preferred way of explaining it to them and explaining the significance of what we're doing is by telling essentially an extended version of the story I just told that throughout human history, there have been these progressive revolutions in the description languages that we use for reasoning about reality. That we started with natural language, with the pre-Socratic philosophers, we moved to, you know, geometry with people like Al-Hazen and Ptolemy, then we move to analysis with Descartes and Newton and so on,

then we move to computation with, you know, Turing and later with Zusser and Wolfram and Fredkin and, you know, these other people. And at every stage, we have been able to resolve questions that seem to be deeply mysterious or, like, deeply philosophical when using previous description languages that suddenly became trivial with using the new one. So, you know, with theory of computation, right? You know, Maxwell famously asked these questions about, Maxwell's demon and the nature of information and things like this. And it turns out that those seem very mysterious when you try to think about

information and thermodynamics in terms of equations, but they become extremely obvious when you try and think about information and thermodynamics in terms of bits and entropy and computation. And for good reason, we now think of thermodynamics as being essentially a kind of information theoretic or even computability theoretic field. We don't really think of it as being a kind of Newtonian-style field

that you describe in terms of partial of differential equations. You can formulate it in terms of partial differential equations, but it's not a particularly useful way of doing that. It's much more useful to think about something like entropy in terms of bits than it is to think about it in terms of PDE's. And so not only have we had these progressive revolutions in description languages for doing physics, but each new revolution, each new description language, has resolved the deep mysteries that we encountered in the previous one and demonstrated to us kind of riffing on what we were discussing earlier that they weren't in fact mysteries at all, that they were just limitations.

of the description language, that there is nothing, okay, maybe controversial statement, but there is nothing particularly mysterious about information and thermodynamics and entropy. It's just we were describing them in the wrong terms, and that once we had the right description language, we had the concept of bits, and we had the concept of comogorov complexity, it all kind of just became obvious. Now, AI capabilities are here. That's the reality of it. We're not putting the genie back in the bottle.

And they are currently bottlenecked by description languages, right? that's the big discovery from the software engineering side and the math side. So if we really want to be able to make radical progress on the mysteries that we have encountered with our current description languages, what we need to be doing is thinking about what is the new, what is the next stage in this iteration, what is the new formal description language for physical reality, what is the new way of mechanizing and systematizing physical reasoning? What is, how do we complete, you know, Hilbert's dream or Gandhi's dream or, you know, whatever it is. So that is something which is clearly.

important on a purely intellectual level. It's interesting to think about what that would look like, but it's also extremely important on a practical level that unless we do this, AI capabilities are either going to be bottlenecked in the physical world or we're going to end up in the kind of, you know, in the in the slopification scenario that everyone is worried about where we have, you know, we have AI architectures that are able to generate hypotheses, generate more archive papers, but there's no ability to corral the thing back and check for things like theoretical consistency or experimental validity. We're just going to lead,

it's going to result in an explosion of, you know, hypothesis generation, but no actual, you know, advance in physical understanding. And I think no one wants, right, right. And my personal conviction and, you know,

the conviction of the company is, we are not going to be able to solve that problem until we get the verification pipelines right. And we're not going to get the verification pipelines right until, you know, we have the right description languages. Jonathan, thank you.

It's been a pleasure. Thanks so much. Thank you for spending so long with me and thank you for explaining the future of physics and your insights as someone who's in academia and also starting a company in this field. I appreciate it very much. It's always a real pleasure to be on. I feel sad in a way that it took us two years to remit, but no, it was always lovely to speak. And thanks for doing this. So what have you been up to? Now, okay, now what have you been up to over the past couple of years? Let's put aside the LLM, the Lanyan. What have you been up to? So, yeah, mostly, okay, so there were kind of two, since whatever, I think we last spoke into 2024, around, like around the start of 2024. So a mixture of, you know, continuing the kind of computational physics work that I've been doing for several years before. And I, for various

reasons in 2024, 2025, I became increasingly interested in implications of, you know, discrete models of physics and discrete models of quantum gravity for high energy astrophysics. And in particular, I became sort of increasingly optimistic that the correct way to kind of test for digital models of physics or computable models of physics was by looking at high energy astrophysical phenomena, phenomena where you take some underlying discreteness in the structure of space time, and then you use very, very strong gravitational fields so it's sort of amplify it into things that you can directly observationally test. And so I spent quite a lot of, you know, quite a lot of the first year, after we last spoke, just working on, you know, doing, figuring out what would

experimental and observational validations of space-time discreetness look like for, you know, in the domain of high-energy astrophysics and developing some of the tooling necessary to kind of, to make that viable. Then, yeah, I guess in, you know, 2025, that was when the, yeah, that was when the AI stuff started to kind of kick off. And the, the first thing that my colleague, Amar, Hakeem and I, Amar, who's now one of the co-founders of the company and is now the CTO, we started working on together at Princeton was figuring out, okay, what would a

proof of system look like for physics? What would it mean to formally verify even something very simple, like a PD-Solver, right? Yes. You know, kind of bread and butter stuff for computational physics. But what we realized is this is a very different problem to doing math verification or doing software verification. It's, in some sense, again,

it's a superset of the same issue. You run into problems that you would never encounter when formalizing a piece of math or formalizing an ordinary piece of software. You run into problems to do with thermodynamic consistency, you know, L2 stability, convergence orders. You even run into problems to do with floating point arithmetic representations where if you're, you know, trying to solve equations on a computer, suddenly you're not proving theorems over the real numbers. You're proving theorems over, you know, the floating point numbers. You're proving theorems relative to the axioms of, you know, IEE-754 floating point arithmetic. So we realized that there was a lot of tooling that had to be kind of developed in order to make proof assistant languages that were equivalent in sophistication to something like Lean or Agda, but were really tailored to the specific challenges of physical and scientific reasoning.

So we started working on this kind of big research project about, probably about nearly two years ago now to kind of develop, you know, formal proof of correctness methods for physics and engineering. And then that progressively spiraled into attempts to work on kind of mathematically rigorous approaches to AI. And kind of the last major academic research project that I was working on before we decided to spin out this company was leading this thing called the Beacons project that was trying to use ideas from category theory and from approximation theory to inform the design of mathematically rigorous kind of neural networks. You know, trying to figure out, okay, if we take a bunch of very small neural network architectures where we can use rigorous approximation theory, to kind of quantify what they're doing, can we then use some ideas from category theory to say, to define an algebraic semantics that allows us to effectively compose those together into deep neural network architectures

while still preserving some level of explainability or provability? And, you know, that project was a lot of fun, and we made a certain amount of progress on it. But then, yeah, sometime at the start of this year, right around the time I was wrapping up kind of one of the major papers on that project, that was the moment where I had this, this, oh, shit, realization. And I had this kind of grieving moment. moment of thinking, I had this pipeline of all the stuff we wanted to do on the physics side and

on, with beacons and with, you know, football verification. And I kind of realized, oh, wait, no, there's a, there's a very high probability that none of this is going to matter in six months. And really what we need to be doing is figuring out how do we assemble these technologies into something that is going to interface with what's going on in the outside world rather than, you know, continuing to ignore it. Where can the audience find out more about you? Yeah. Okay. So I think the easiest way is just to visit our web, website Lanyan.a-I-O-N-A-I-I that has information about the company, has information about us,

the founders, and information about how to get involved. We are always actively hiring for smart people who are interested in math, physics, engineering, computer science, philosophy, I think exactly the kinds of people who, you know, who listen to your podcast. So, yeah, feel free to visit there. Otherwise, we have an X account, which I think is X.com slash Lanyan underscore AI, if I remember correctly. And yeah, we generally try to that kind of reasonably updated with things we're doing and things we're thinking about. We, as I mentioned, we have actively made a number of hires quite recently. So hopefully you will be hearing updates, not just from me and from, you know,

co-founders, increasingly be hearing updates from, we have another person, a junior person who's joining us on Monday who's going to be leading up a bunch of our type theory efforts, developing kind of analogs of things like mathlib, but kind of analogs of mathlib and fizzlib and silead and so on, but, but, you know, optimized for the particular kind of physics application areas that we're looking at at the moment. And we're really excited to talk more about that. But yeah, so website, X account, I think those are the, I think we also have a LinkedIn page, but I can't remember how to get to that. Okay, we'll place links of everything that you've mentioned in the description and on screen. Take care. Thanks so much, Kurt.

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 Kurt Jiamong. 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. That's c-U-R-T-J-A-I-M-U-N-G-A-L.org. You can also just search my name and the word substack on Google. Since I started that substack, it somehow already became number two in the science category. Now, substack for those who are unfamiliar is like a newsletter, one that's beautifully formatted, there's zero spam, this is the best place to follow the content of this channel that isn't anywhere else. It's not on YouTube, it's not on Patreon. It's exclusive to the substack. It's free. There are ways for you to support me on substack if you want, and you'll get special bonuses if you do. Several people ask me like, hey, Kurt, you've spoken to so many people with you.

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