MIT mathematician John Urschel: math is not solved by AI — the field is expanding faster than ever

Speaker 3: He's an assistant professor of mathematics at MIT. You know him because we discussed the Wall Street Journal article about them, and we're very excited... Professor. Welcome How to the are you guys? How are

Speaker 4: I'm you doing well. I'm looking forward to hanging out with you guys.

Speaker 3: You so much for I taking the wanted to start in a very maybe basic place. Like, what is the day to day life as an assistant professor at MIT? I think a lot of people are grappling with the fact that AI can do some mathematic research, prove theorems or disprove them. But how much of how much of your time is spent like working on hard math problems versus teaching versus doing something else? Like, what is a day in the life of a MIT mathematician?

Speaker 4: Yeah. So this is something that I feel like if you don't, you know, if you don't study mathematics at a high level, it can be hard to sort of know. You know, we spend so much time teaching, so much time talking with each other, trying to, you know, think about good math ideas

Speaker 3: Yeah.

Speaker 4: Trying to teach our students. These days with AI, it certainly looks different. I would say the thing that really is universal is that there's still an emphasis on understanding, whether it's ideas that a human came up with or ideas that, let's say, chat, GBT, or Anthropic came up with. The idea is trying to look at a proof, look at a solution, and understand something about what that means for the broader ecosystem.

Speaker 3: Yeah. How much of mathematical inquiry is, I I don't know, discovery versus understanding the process and then actually diffusing that information? I I feel like maybe I went through a small version of this like five years ago. I was interested in in business history and journalism and I'd go and and compile these these essays about a certain technology's evolution. Certainly not at the level of a non fiction writer, but it was very edifying work. Chatuchipiti can do that and has been able to assemble an essay about a technology and how it evolved and do some historical research. It's still fun for me. It's still edifying. And then I still have, I think, a purpose explaining that to other people and sharing that in different formats. And I feel like I've grappled with it, but how different is your experience is the experiences of the mathematics world to, like, the experience that I just described, which was I got steamrolled by AI, like, five years ago, maybe. I I don't know.

Speaker 4: No. I mean, it's true. I mean, the latest frontier models can do what a lot of good mathematicians have been doing for a lot of years. And the question now becomes, where do we focus our effort? Yeah. Understanding was always a crucial part of the process. Yeah. It's even more important now. Yeah. I still think there's room and I still think there's importance for problem solving even when AI systems can do this well. I think this is a fundamental joy of doing mathematics. You know, just because, you know, a computer can solve the crossword puzzle for you doesn't mean you don't want to do it yourself. I think there's personal joy and enjoyment in honing your skills to work on these things, but definitely there's a completely new aspect to doing mathematics, which is having this tool that can really crank in a way that, you know, humans just haven't been able to do.

Speaker 3: How do you think about mathematics progress in the very long term? It feels like AI can duke it out with the top mathematicians and solve really, really hard problems, but people are joking about mathematics is solved, but that doesn't seem like it's the case. It seems like this is sort of a rabbit hole that might just go deeper and deeper and deeper. But do you have an intuitive sense, or is the mathematics community coming to a consensus around how far we are away from actually the last mathematics question being solved?

Speaker 4: So definitely we don't have any consensus, I'd say, about how we should be using AI, what things are going to look like in a couple years. But I think we have pretty good consensus that, you know, math is not going to be solved.

Speaker 3: Yeah. I

Speaker 4: mean, the amazing thing we're seeing is that we're pushing the frontier of what we understand and know mathematically faster than we ever have in history. And so we're understanding more, we're pushing boundaries further. But there's so much farther to go and there are so many things we don't understand, so many tools that can be helpful, not just in mathematics, but in other areas. So, you know, these modern developments, this is just like, you know, people used to climb a mountain, you know, using their own little ropes and things. Now we have a helicopter, but still, you know, there are further places we need to explore and things that we need to understand.

Speaker 2: How, how is AI being used to come up with new problems? Like, is that is that... Is there any

Speaker 3: Progress there?

Speaker 2: Is... Are... And you or any of your peers, like, thinking, like, well, if if you can use this to solve problems, can you generate

Speaker 3: Can we create new millennium problems?

Speaker 2: Can we at least create new problems faster than we can

Speaker 3: them, maybe?

Speaker 4: No. So this is the question. We're trying to understand, you know, these tools are very, very good at solving a well posed problem that we've been thinking about for a

Speaker 3: while.

Speaker 2: Yeah.

Speaker 4: The thing that we're still trying to figure out is how generative can this be?

Speaker 3: Sure.

Speaker 4: How well can this technology actually recognize what are important directions that we need to study and understand to help push ourselves forward technologically and mathematically?

Speaker 3: Mhmm.

Speaker 4: And that's the part that it's still, you know, the consensus is not there yet. I'm not gonna make a prediction for fear Sure. Being horribly wrong, but we're gonna have to wait and see.

Speaker 3: How do you think about the progress of mathematics education at this moment? Like, there's, you know, algebra and basic geometry. Like, these things are taught to... Almost every American gets exposure and learns a little bit and then calculus a little bit less. And I'm just imagining a future, maybe like the good outcome would be, yeah, everyone can actually sort of explain Navier Stokes and has gotten to a place where even the really, really hard math has been so so digested by AI and top mathematicians and understood that it's been turned into YouTube videos and turned into curriculum. And and maybe it never gets down to high school level, but at least if you're in college, you could go much further than we are currently. And it feels like humanity has been progressing towards more and more mathematical understanding even among like average non mathematicians. And that feels like it would be a really good outcome. But how do you grapple with that that fact or or or that potential outcome? No. I mean, you've got

Speaker 4: it exactly right. This is this is definitely the hope that Yeah. You with these new technologies, it somehow, like, levels the playing field for education. It somehow, you know, opens up possibilities for people to learn more advanced concepts much quicker. I mean, I remember when I was a kid, the fact that the internet existed and that, you know, top professors at universities would post lecture notes and things like this online. This was huge for me as a kid in Buffalo, New York. I can... You know, I have a computer and an internet connection and all of a sudden it's like I'm learning from top professors. Yeah. And you know, when I compare this to the way people learned in the eighties or seventies, know, you have to go to a library, you rent out a book. Yeah. It was just a game changer

Speaker 5: for me.

Speaker 2: Yeah. It was funny as as like a as a teenager realizing like, wait, this top university just publishes the entire course. Was like, why would I go to this school? Obviously, there's other, you know...

Speaker 3: Well, I I I wanna talk more about like the the the competitive dynamics between universities. We've seen some prize money up there, million dollars for a millennial millennium prize. I've seen $25,000 prize pools. This is not the funding mechanism for mathematics, correct? Is tuition, there's scholarships, there's government funding. But I don't know how deeply you're embedded in that side of it, it feels like there's a potential that much like chess has been solved by computers, I don't know that I'd want to go to a university where it had a really, really bad math program just because they're not winning the prizes anymore. Like, it feels like there's still a lot of value in having a fertile mathematics education program that's pushing the frontier both in terms of exploring new problems and working alongside AI, but also just being the best human mathematicians, that's going to have knock on effects around the entire organization. But how do you see it evolving?

Speaker 4: Yeah. I think you've got it exactly right. Okay. I think our roles are certainly going to change with the advent of AI. Yeah. But we're very much going to be needed. And I think understanding mathematics at a deep level, being able to help communicate that to young people, to help people gain the tools to be able to empower themselves Yeah. To solve problems in all areas of, you know, science, technology and engineering, I think it's important. And I think we really need to try to adjust to this world we're in and try to serve our students as best we can.

Speaker 2: So so do you think math ends up tracking exactly like chess has in that, like, chess was solved and then people just kept playing it and and kept watch... You know, kept following it and and and and the the sort of field continued to progress. Because the way that you're describing this just feels like, you know, one, the understanding is key, but then then the just enjoyment enjoyment of of understanding and like individual progression, I feel like is limitless regardless of the abilities of the models.

Speaker 4: So I feel that it's a bit different. So I'm not that good of a chess player. Mhmm. But okay, I play a bit of chess. I feel like chess has very much hit some sort of like plateau in equilibrium. Like, yeah, you had Kasparov and Deep Blue, but really after, like, you know, this AlphaZero stuff from DeepMod, you know, there were some great chess innovations that were really new things that affected actual top players and how they played. But really, things started to sort of like level off, and, you know, there there is only so much in

Speaker 9: chess.

Speaker 4: You know, there's so many moves. Yeah. There's so many optimal things that you can do. Whereas in math, I really do think it's generative. It's really not nearly as limited in the same way and the directions you can sort of move forward in. And the directions we're going to need sort of four applications of applied math, I think are much more limited. So I I really don't see it going that way. Instead, I see it sort of really exploding. Like, the field of mathematics and what falls under math is just going to get bigger and bigger.

Speaker 3: Yeah. Do you have... This is an odd question but you're like the person to ask this. Do you have any intuitive feeling for how AI might change football?

Speaker 4: Oh, that's a great question.

Speaker 3: I'm just thinking even like when you go for two points like these things, statistical models, money ball has been around but we're in a new territory now where you might see a team be like, what if we spent a million dollars of compute crunching all the numbers and we don't even know but we just call the plays this way. I'm just wondering if you have any feel for it.

Speaker 4: No. I think I think there's definitely potential because, you know, fundamentally, football is so much harder a problem than baseball. Yeah. Like, if you think about sabermetrics, like like, Moneyball worked in baseball because it's so... Such an easy problem if you think about it.

Speaker 3: Yeah. One player at a time.

Speaker 4: People are in set pieces. Yep. The rules are so straightforward.

Speaker 3: Yep.

Speaker 4: Like, you know, it... You know, someone's batting, someone's pitching, then something happens and it's really well understood.

Speaker 3: Yeah.

Speaker 4: Whereas football, you've got 22 guys on a field and it's just complete chaos from a data statistical point of view. And so bringing, like, better technology to bear on that, I think, can definitely be useful. Because I remember, like, even a couple years ago, it was not easy to take player tracking data and actually recognize what play just happened.

Speaker 3: Oh, sure.

Speaker 4: You know, was the defense in cover two? Were they in cover three? What was, you know, what run play did the offense do? What was the passing scheme? And so I think there's a huge potential for AI to help

Speaker 3: with that. Interesting. Yeah. Very cool.

Speaker 2: Jordy? Yeah. My big... Biggest takeaway from this is just this side... Like, this idea of, the the models are... Don't seem to be generative in the sense of like coming up with like what to solve. Right? And and we experience this when anytime you see a piece of AI content, the models are good at making content now. If you have like an amazing idea. Right? And it's always like one human out there came up with the idea of like combining like these two different IPs into something that is like entertaining or funny. Yeah. And and even with with marketing, you can have a brilliant marketing idea and then an AI can like one shot it really quickly. But the AI, again, is not generative when it comes to marketing. It's not on the fly coming up with great marketing ideas and that's still the domain of of humans.

Speaker 3: Yeah. It just feels like the intelligence moment. It's very spiky. Yeah. Very interesting.

Speaker 2: Pure execution.

Speaker 3: Thank you so much for taking the time to come chat with us.

Speaker 4: Yeah. Absolutely. I mean, okay. We'll we'll see how long that persists.

Speaker 3: Yeah. Yeah. Yeah. Yeah.

Speaker 4: Way right now.

Speaker 3: Yeah. I don't know if you're fan of like the the bubble with the spikes and then the doll just gets bigger until it just goes over everything. But yeah, we are in this odd transition moment. But but thanks so much for coming on here. We really

Speaker 2: appreciate it.

Speaker 4: Yeah. Absolutely. Thanks for having me.

Speaker 3: Yeah. Have a great rest of your day. Cheers, John. Talk to you soon.

Speaker 2: You're the man.

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