# AI uses accumulated knowledge and persistence in hard math

Markdown copy of https://realalpha.app/s/ai-uses-accumulated-knowledge-and-persistence-in-hard-math/ on Real Alpha, the best minutes from long interviews with the people building AI. Cite and link the page, not this copy.

- Speaker: [Greg Burnham](https://realalpha.app/people/greg-burnham/) · Greg Burnham is a leads capabilities research at Epoch AI.
- Host: [Sam Charrington](https://realalpha.app/people/sam-charrington/) · Host, The TWIML AI Podcast
- Show: The TWIML AI Podcast
- Episode: [AI Progress Explained: From Math Olympiads to Navier-Stokes](https://realalpha.app/v/lz9J-Dbj2zw/), Sep 29, 2026
- Moment: 30:45 to 36:17 of the episode (6 min), playing on https://realalpha.app/s/ai-uses-accumulated-knowledge-and-persistence-in-hard-math/; the episode from there: https://realalpha.app/v/lz9J-Dbj2zw/?t=1845

## Quote

> “One is it knows everything. It **knows all the prior work**. It's got the literature memorized.”
> — [Greg Burnham](https://realalpha.app/people/greg-burnham/) at [31:03](https://realalpha.app/v/lz9J-Dbj2zw/?t=1863) · The TWIML AI Podcast

## Takeaways

1. Models can draw on prior mathematical literature.
2. Persistence helps with intricate chains of reasoning.
3. Current solutions often build on human-developed theory.

## About this segment

Greg Burnham describes AI’s advantages as broad knowledge and patience with intricate work, while noting its solutions build on human foundations. Creating genuinely new mathematical ideas remains rare.

From “AI Progress Explained: From Math Olympiads to Navier-Stokes”, Sep 29, 2026. [Watch the full episode](https://realalpha.app/v/lz9J-Dbj2zw/)

## Transcript

Transcribed by machine (Whisper) from the episode’s audio, so a word may be off here and there.

[30:50](https://realalpha.app/v/lz9J-Dbj2zw/?t=1850) or are we past that point as well here i'd give more nuance uh we we um there's an emerging sense of, at least for the moment, what an AI-shaped problem looks like. Maybe I could say AI has two big advantages right now. One is it knows everything. It knows all the prior work. It's got the literature memorized. I'm speaking loosely, but this is basically valid. The other is it's extremely patient and persistent. So if there is some intricate calculation you have to do, I don't mean numerically or algorithmically. When I say calculation, I just mean lots of equations and you have to make all the pieces work out just as very high-level conceptual, logical kind of computation, but still something very intricate.

[31:45](https://realalpha.app/v/lz9J-Dbj2zw/?t=1905) They just have the patience to go for that. And if you take the Navier-Stokes example, I think it's not a coincidence that OpenAI's reported system that solved it included a swarm of thousands of different instances of AI systems trying lots of different things and sharing ideas where clearly it was able to like there is an element of brute force there so there's degrees of brute force this is where the nuance is it wasn't like somehow uh you know you you asked it to like it wasn't solving this in by any means in the dumbest most low-level way like we're past that point as well they used to solve some problems and like kind of surprisingly low-level like grind it out kind of ways like that's not really what these look like anymore. But like the, the high level, a higher level version of that still is maybe what you might, what you might say here. So, and I like the frame

[32:44](https://realalpha.app/v/lz9J-Dbj2zw/?t=1964) of precise and intricate computations here. It's important. I'll say one more thing about the Navier-Stokes solution. It's important to recognize that humans sort of put in place a lot of the structure through previous work that AI then went and as far as we can tell, I mean, humans are still figuring out exactly what goes into the AI solution. But as far as we can tell, it builds on a lot of prior human work. The AI didn't like build it up from the ground. That kind of theory building, as mathematicians call it, we still don't see that very much from AI systems. Last point I'll make before pausing on this is just remember its point in time. Like remember that trajectory. We've seen very rapid uh so so mathematicians who are saying we have to adapt our profession to the fact that now you can push a button and get what used to have been a career making result like you know

[33:37](https://realalpha.app/v/lz9J-Dbj2zw/?t=2017) are also i think cautioning and we can't expect the capabilities will freeze right now we we see you know that that linear whether it's linear or exponential as a matter of perspective but it's going up uh and it's probably like we see no reason to expect it to stop there so this is a big thing EPOC is looking for? Can AI move from intricate computations plus lots of background knowledge to more of a developing new ideas more from whole cloth? And if so, and that's a big thing we're watching for in our own math benchmarking activities. Yeah, it's interesting to think that, at least the way I characterize this as brute force versus pulling in things from other domains, those are, you know, those are not mutually exclusive. Like for an AI that has access to, you know, all of the research from every domain, you know, an approach that could be

[34:38](https://realalpha.app/v/lz9J-Dbj2zw/?t=2078) very fruitful is to brute force the exploration of adjacent domains and pull that into the solution to a given problem. That's it, I think, a lot of what we see. And maybe just to say the other thing that would really supercharge them and bring them closer to full human parity or even human, you know, dominating human capabilities would be something like coming up with a new idea. And maybe like in calculus, the idea of the derivative or the integral of a function, like that was something.

[35:11](https://realalpha.app/v/lz9J-Dbj2zw/?t=2111) Maybe mathematicians in the 1500s had been grasping for this idea, and then Newton or Leibniz or whomever comes up with, like, hey, here's, like, I can describe a new thing, a new mathematical concept, and that unlocks a lot for us. That lets us solve problems we previously couldn't solve. And so that's the sort of thing we don't yet see AI doing. It's also the sort of thing that's rarer for humans to do.

[35:37](https://realalpha.app/v/lz9J-Dbj2zw/?t=2137) A lot of human math progress has been, well, I sat down and I put in the work and I did the computation and I worked out which was the dead end and which was the good path and here's the answer. Now XYZ is true. I've proven it. Or I studied one area and I noticed something and I thought it might be applicable to this nominally superficially different area. Like humans do that sort of stuff all the time.

[35:59](https://realalpha.app/v/lz9J-Dbj2zw/?t=2159) Maybe that's 90%, vaguely speaking, of human mathematical work from what I hear from mathematicians. The new idea stuff is rarer, so maybe we should expect it to be not the first thing AI gets good at. But so far, we don't see AI really doing that yet.