Grant Sanderson (@3blue1brown) — Past, present, & future of mathematics

**Grant Sanderson** (0:00)
Grant, the videos were really inspiring. You're the reason I'm going into grad school.
And there's this little bell in the back of my mind that's like, do I want that? Do I get more people going into math PhDs? Math Academy of Finance and Computer Science almost certainly have an over allocation of talent.
Actually, I'm quite determined at some point to be a high school math teacher for some number of years. Math lends itself to synthetic data, how AlphaGo is trained. You could have it produce a lot of proofs and just drain on a whole bunch of those. And the thing that takes at most 30 minutes of the teacher's time, maybe even 30 seconds, has these completely monumental rippling effects for the life of the student they were talking to that then sets them on this whole different trajectory.

**Dwarkesh Patel** (0:44)
Okay, today I have the pleasure of interviewing Grant Sanderson of the YouTube channel 3Blue1Brown. You all know who Grant is.
I'm really excited about this one. By the time that an AI model can get gold in the International Math Olympiad, is that just AGI, given the amount of creative problem solving and chain of thought required to do that?

**Grant Sanderson** (1:05)
I, to be honest, have no idea what people mean when they use the word AGI. I think if you ask 10 different people what they mean by it, you're going to get 10 slightly different answers. And it seems like what people want to get at is a discrete change that I don't think actually exists. Where you've got, okay, AI is up to a certain point. They're not AGI. They might be really smart, but it's not AGI. And then after some point, that's the benchmark when like now they're, now it's generally intelligent.
The reason that world model doesn't really fit is it feels a lot more continuous where, you know, GPT-4 feels general in the sense that you have one training algorithm that applies to a very, very large set of different kinds of tasks that someone might want to be able to do. And that's cool. That's like an invention that people in the 60s might not have expected to be true for the nature of how artificial intelligence can be programmed. So it's generally intelligent, but maybe what people mean by, oh, it's not AGI is you've got certain benchmarks where it's better than most people at some things, but it's not better at most people than others. You know, at this point, it's better than most people at math.
It's better than most people at solving AMC problems and like IMO problems. It's just not better than the best. And so maybe at the point when it's getting gold in the IMO, that's a sign that, okay, it's as good as the best.
And we've ticked off another domain, but I don't know, like is what you mean by AGI that you've enumerated all the possible domains that something could be good at, and now it's better than humans at all of them?

**Dwarkesh Patel** (2:34)
Or enough that it could take over substantial fractions of, you know, human jobs or something. Where right now it's impressive, but it's not gonna be even 1% of GDP.
But in my mind, if it's getting gold in IMO, I mean, having seen some of those problems from your channel, I'm thinking, wow, that's really coming after podcasters and video animators, I don't know.

**Grant Sanderson** (2:56)
I don't know, that feels orthogonal, because getting a gold in the IMO feels a lot more like being really, really good at Go or Chess. Like those feel analogous. Well, it's super creative. Like I think anyone who, I don't know Chess as well as the people who are into it, but everything that I hear from them, the sort of moves that are made and choices have all of the air of creativity.
I think as soon as they started generating artwork, then everyone else could appreciate, oh, there's something that deserves to be called creative here. And the creative side of the math, I don't know how it would look when people get them to be getting golds at the IMO, but I imagine it's something that looks a little bit like how AlphaGo is trained, where you have it like play with itself a whole bunch. Math lends itself to synthetic data in the ways that a lot of other domains don't. You could have it produce a lot of proofs in a proof checking language, like Lean, for example, and just train on a whole bunch of those. And like, is this a valid proof? Is this not a valid proof? And then counterbalance that with English written versions of something. And so I imagine what it looks like once you get something that is solving these IMO level things.