Grant Sanderson – AI and the future of math

**Dwarkesh Patel** (0:00)
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. And I wanted to talk to you about this because AI is making the fastest progress in mathematics as of any other field. So whatever is happening here and whatever way we're seeing AI progress happen or not happen would tell us about what will happen to the rest of the world as AI gets better and better. So I wanted to start with this question I asked you when I first interviewed you three years ago.
And 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? And you had an answer which in retrospect turned out to be very wise and correct, which is like it'll be another benchmark like all these other benchmarks that are passing. Obviously, AI has gotten better in general ways since then, but there won't be some aha moment when this happens.
First, I think I'd be curious to get your heuristics on why that turned out to be true. And second, I'm curious how long you think this narrowness can continue to be true. So, by the point that AI has solved the Millennium Prize problem, do you think it's still possible that at that point, there's lots of tasks that humans are doing that AI still can automate in the economy?

**Grant Sanderson** (1:11)
It's an interesting question because it's hard to answer without knowing what the solution looks like ahead of time. I mean, if we take the IMO, that's something where I think 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, they'll try to have them come up with things that you can't train for as easily. I think the dirty secret with the IMO is that you really can train for a lot of them. And so, with the whole AI and Math project undergoing, I think as you point out, one of the reasons it's interesting at all is that there's a spiky frontier to AI, math is just right there in one of the spikes. But there's kind of 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. So, if we just think about IMO, which is old news at this point, it's kind of like two years ago that they're really doing quite well. They would have gotten a gold in 2024 if for not the following reason. They're very good, they're just like cold solved geometry basically. The IMO has these four categories of problems, this geometry, number theory, algebra, and combinatorics. So, geometry just solves in 19 seconds in 2024, because it's kind of a brute force solver. The dirty secret is for students, there's also sort of a brute force way that you kind of can go at it. Combinatorics is the one that's the wild card of much more like playful, puzzly seeming problems, and there were two combinatorics problems on that year's test. There's not always, there's four categories, six different problems. So, it's kind of 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 hold out of black math for humanity might say, well, those are the ones that require the more creativity. Even then though, I think the spirit of your question, like if they're solving a millennium prize problem, does that also service a lot of white collar work?
It 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 can maybe paint a couple of different ways that we focus on, I don't know, Riemann hypothesis. What would it look like to solve that?
One possibility would be these things are extremely good at a specific domain of knowledge and just knowing it very deeply, and then knowing another domain, and knowing another domain, and you've pointed this out. It's bizarre to have something with this superhuman breadth that knows all the fields so well, that's not just finding those lightning bolts that connect them.
I think we're starting to see sparks of that, of actually finding connection between the things that 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 than what's necessary to get good at white-collar work. There's a reason to believe actually that 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.