OpenAI Researchers on the Future of Mathematical Reasoning

Mark Sellke (0:00)

Often as a practicing mathematician, you have an idea, and then you kind of think it might work. Then you try for a few hours, a few weeks, and at some point, you give up.

Lisha Li (0:09)

Whereas for GPT, like, okay, a human told me to do this, like, let's just do this. And so that's why we're sort of in this renaissance of like reachable results.

Mark Sellke (0:17)

This is the best part about this problem, which is really nobody had any idea. Is the model just guessing in some insane way?

Lisha Li (0:23)

Doesn't seem like there's a limit so far, but it doesn't have that context yet.

Mark Sellke (0:28)

It'd be nice for the world if we applied mathematics on it a lot faster. The ceiling for difficulty of a math problem is pretty high. Even if AI continues getting exponentially better at math, plausible will never solve something like P versus N.

Lisha Li (0:39)

What's the ideal way that this is being taken up by the math community? Probably most at this point are like, okay, AI is obviously doing some non-trivial stuff.

Mehtaab Sawhney (0:48)

So AI isn't just getting better at math benchmarks. It's beginning to make progress on mathematical problems that have resisted humans for decades.

In this episode, a16z Infra partner, Lisha Li, sits down with OpenAI mathematicians, Mehtaab Sawhney and Mark Sellke to understand what's actually changing. They walk through recent results in sphere packing, coding theory and group theory, and explain why these advances can't be reduced to brute force. The models try different approaches, abandon dead ends, connect ideas across fields, and in some cases, produce reasoning that reads surprisingly like the notes of a human mathematician.

They also tackled the bigger question. What happens to mathematics when proving a result becomes less of a bottleneck? From mathematical taste and human judgment to understanding an explosion of new results, Lisha, Mehtaab and Mark explore how AI could change not just what problems get solved, but what it means to practice mathematics.

Lisha Li (1:47)

Well, thank you guys for coming. This is really exciting because I think math has been moving so fast. AI would just love to get to both practicing mathematicians and who work at OpenAI to chat on some of these results. So we have with us Mark Sellke and Mehtaab Sawhney. We're connected actually because you, Fei, was actually your advisor. So both of you guys have worked much more deeply in math since I have quit. Many, many, like over a decade ago. So this is very exciting to kind of hear a download of your thoughts on how OpenAI has been sort of approaching this and also just like, where you think math is going with the incredibly rapid advance of how AI has been helping.

We can start off with some very basic questions. What do you do to the extent that you can of course share? And how did you come from being a practicing mathematician to working at OpenAI?

Mark Sellke (2:41)

Yeah. I mean, I guess we both broadly got excited last year when the models started to really take off in math.

So I joined a little bit before Mehtaab. I saw the IMO gold medal last summer basically. I thought, this is amazing. I want to see what the heck they did. Yeah. Let me go see. And then, yeah, I guess in the fall, Mark gave me a GPT-5 account and then I started playing with the models. I very quickly became convinced that, yeah, it was extremely exciting to play with them.

Lisha Li (3:09)

You two were collaborating before.

Mark Sellke (3:10)

Yeah. We've known each other for a while. Yeah. We have one paper we actually wrote jointly.

Lisha Li (3:15)

Yeah. So GPT-5 was your conversion?

Mehtaab Sawhney (3:19)

Yeah.

Lisha Li (3:19)

What was the magic that sort of, what question do you throw at it?

Mehtaab Sawhney (3:23)

What process? Yeah.

Mark Sellke (3:23)

So I think actually, yeah, so I think how this started was, at least for me, the starting moment was something like, there's a collection of problems called, so Paul Erdrich is a very famous mathematician, he posed a bunch of problems and so they've now all been collected on this site. And so I specifically worked in combinatorics and a lot of these questions are among the most important, so it's always fun to flick through this slide. But one thing that often happened to me that was extremely frustrating was, I would look at a question, see that it's marked as open, and then not actually know if it's correct, not actually know if it was still unsolved, because the literature is often quite hard to search.