Grant Sanderson: evaluation

Transcript context

…Today, I’m chatting with Grant Sanderson, who runs 3Blue1Brown and is now working on a new project documenting the progress AI is making in math. I wanted to talk to you about this because AI has been making the fastest progress in mathematics out of any other field. Whatever is happening here, and whatever way we’re seeing AI progress happen or not happen, will tell us about what will happen to the rest of the world as AI gets better and better. I wanted to start with this question I asked you when I first interviewed you three years ago. I asked you, once we have AIs that can get gold in the International Math Olympiad, wouldn’t that just be AGI? Wouldn’t this just be able to do anything any human can do, given how hard these problems are? You had an answer, which in retrospect turned out to be very wise and correct. You said it’ll be another benchmark, like all these other benchmarks that AI are passing. Obviously, AI has gotten better in a general way since then, but there won’t be some “aha” moment when this happens. First, I’d be curious to get your heuristics on why that turned out to be true. Second, I’m curious how long you think this narrowness can continue to be true. By the point that AI has solved a Millennium Prize problem, do you think it’s still possible that there are lots of tasks humans are doing that AI still can’t automate in the economy? It’s an interesting question because it’s hard to answer without knowing what the solution looks like ahead of time. If we take the IMO, the spirit of your question three years ago was in looking at how some of the solutions to these problems really seem to require creativity. The designers of these problems try to come up with things that you can’t train for as easily. The dirty secret with the IMO is that you really can train for a lot of them. With the whole AI and math project underway, as you point out, one of the reasons it’s interesting at all is that there’s a spiky frontier to AI, and math is just right there in one of the spikes. But there’s a fractal nature to that spikiness, because when you zoom into the specific progress within math, you have some things that are a lot easier than others. If we just think about IMO, which is old news at this point. It’s been two years since they’re really doing quite well. They would have gotten a gold in 2024 if not for the following reason. They’re very good. They just cold-solved geometry basically. The IMO has these four categories of problems: geometry, number theory, algebra, and combinatorics. Geometry, it just solves it in nineteen seconds since 2024 because it’s a brute force solver. The dirty secret is that for students, there’s also a brute force way you can go at it. Combinatorics is the wild card: much more playful, puzzly-seeming problems. There were two combinatorics problems on that year’s test, and there’s not always. There are four categories and six different problems, so it’s a toss-up which one is going to have two questions. Had it been more geometry questions, they would have gotten a gold that year. But it struggles on those combinatorics ones. Someone who’s trying to keep that torch of the last holdout of math for humanity might say those are the ones that require more creativity. Even then, the spirit of your question—if they’re solving a Millennium Prize problem, does that also service a lot of white-collar work?—suggests that whatever the rate limiter is between where we are now and that is the same as the rate limiter for making things better at white-collar work. We could paint a couple of different ways. If we focus on the Riemann hypothesis, what would it look like to solve that? These things are extremely good at a specific domain of knowledge, knowing it very deeply, and then knowing another domain, and another. You’ve pointed this out. It’s bizarre to have something with this superhuman breadth that knows all the fields so well, and yet isn’t finding those lightning bolts that connect them. I think we’re starting to see sparks of it actually finding connections between the things it’s an expert at. I’m sure we’ll talk about it. If the nature of the solution to the Riemann hypothesis was something like that, that feels pretty distinct to me from what’s necessary to get good at white-collar work. I’m sure we’ll talk about it. If the nature of the solution to the Riemann hypothesis was something like that, that feels pretty distinct to me from what’s necessary to get good at white-collar work. And there’s a reason to believe that might be the nature of the solution. I don’t know if you know the story of Hugh Montgomery and Freeman Dyson at the IAS. This is a side tangent, but it’s a fun story. I don’t know if it was over lunch or something like that, but you have this number theorist who is just trying to understand the statistical correlation between pairs of zeros of the Riemann zeta function. The Riemann hypothesis is all about whether all these zeros sit on a straight line. He finds this quantitative question you could ask, and he writes down a formula. It looks like one over sine squared or something like that. Freeman Dyson, a physicist, is like, “I know that expression. That expression comes up in studying the eigenvalues for random Hermitian matrices,” which was something that comes up in studying the energy levels of a nucleus. The idea that the statistics of those two seemingly different things were the same prompted an exploration of whether there are aspects of random matrix theory that might be relevant to the Riemann zeta function. I think it’s a little bit of an open question whether there is fruit to be had there. But that bridging together of two different fields—if it turned out that the solution to the Riemann hypothesis was exploring an idea like that even further—has the character of how you expect LLMs to be good at math. They’re experts at quantum physics. They’re experts at analytic number theory. They should be able to see that similarity in a way that doesn’t require Montgomery and Dyson to be having lunch and happen to talk about it. That’s totally different from white-collar work. To the extent that you have a hard time using an AI as an editor, it’s not because they know everything and you just need them to find that lightning bolt in between. A different possibility would be… What’s the right analogy? Maybe if we think of Fermat’s Last Theorem, between the moment of Fermat phrasing the question and what the solution itself looks like, where the solution ultimately involves such heavy machinery in math. The beauty of that problem is you can phrase it so simply. You ask about xn + yn = zn. Do you have integer solutions for this when n is bigger than three? It’s something you might expect there to be an elementary number theory approach to, but as far as we can tell, there’s just not. Whereas the actual solution, maybe there is something simpler, but this might be what it has to be. There’s such a complicated set of ideas that build on centuries of work centered around elliptic curves. Then there’s this other mountain of ideas centered around these things called modular forms. Both of those mountains have to be built before you can ask the right question that connects them. If the solution to the Riemann hypothesis involved building a new mountain, that’s a kind of skill—the ability to come up with the right new ideas—that feels sufficiently different from the character of how they’re intelligent right now.…

Stored transcript either side of the excerpt. The highlighted words are the published quote; the surrounding text is unedited source, never generated.