Daniel Litt: The Mathematician's Guide to AI

**Daniel Litt** (0:00)
The goal of mathematics is not to produce mathematics papers, it's to produce some kind of understanding. Maybe some of that understanding resides in model weights. To me, that's like pretty unsatisfying.

**Lisha Li** (0:09)
Comparing Anthropic with OpenAI, do you detect any differences in how that is similar to human reasoning?

**Daniel Litt** (0:16)
They definitely are not good at it autonomously, but with some hints, you can kind of get them to do something interesting. A lot of progress in mathematics comes from like letting a thousand different flowers bloom and people pursue their own curiosity, and then the boundaries of knowledge expand in some kind of fairly uniform way.

**Lisha Li** (0:32)
What has been the most impressive result so far?

**Daniel Litt** (0:36)
My favorite fully autonomous result by an AI so far is the solution to the Erdos unit distance problem. There was some lemma I wanted to prove, none of the frontier models could do it. So I worked out a ton of examples on my own, and I realized, oh, well, maybe here's some reason why it could be true. Once I had that statement, the models were able to very quickly prove that sort of better statement.

**Lisha Li** (0:57)
How should the mathematics community best adapt and benefit from this?

**SPEAKER_3** (1:04)
AI can increasingly solve math problems that would challenge professional mathematicians. But solving a problem isn't necessarily the same thing as understanding it. In this episode, a16z infra partner, Lisha Li, sits down with University of Toronto mathematician, Daniel Litt, to separate the headlines about AI and mathematics from what the models can actually do today.
Daniel explains why recent results have changed his views of AI, where frontier models already resemble human mathematicians, and where they still fall short, particularly when it comes to intuition, developing new theories, and even figuring out which questions are worth asking. They also explore what happens to mathematics when generating a proof becomes cheap, why academic incentives may need to change, and how mathematicians can use AI without outsourcing the understanding that makes the work valuable in the first place. And more broadly, they ask what mathematics can teach us about working with AI, as increasingly capable models move into every knowledge profession.

**Lisha Li** (2:06)
I am so excited to have you on Daniel. And so Daniel Litt is a professor of mathematics at the University of Toronto. Toronto is my hometown, so also very exciting. But the thing that is most special here is Daniel is an actual practicing mathematician, and in addition, he's been incredibly vocal about his evolving views of AI in math. And so I feel like if I just don't check in with you, like in two weeks, something different has been revealed, and then you're very kind of like, what do you call it?

**Daniel Litt** (2:35)
You have a lot of opinions.

**Lisha Li** (2:36)
You have a lot of opinions, exactly. So I want to get into that. So I mean, one of the things that I'm most interested in is not just like a discussion of how the capabilities of advance, I feel like in math, that's definitely the headline, etc. But also, you've been very thoughtful about how practicing mathematicians should respond. And so that kind of gives us a chance and opportunity to talk about actually, what is special about math? It's not just like, hey, AI has been really making progress here, but delve into what actually mathematicians do. And so maybe like with that arc in line, we can start with what has been the most impressive results so far, given all the recent progress for you. And then maybe, yeah, we'll kind of take it from there.

**Daniel Litt** (3:14)
Yeah. So, okay. So there have now been a lot of results. Some of them produced autonomously, some produced semi-autonomously, some where the AI contribution is just not at all clear. There are a lot of different areas. So anything I say is kind of, I can only really comment on things that I have some expertise on. So it's quite possible that if you talk to a different mathematician, you'll get different answers here. So my favorite fully autonomous result by an AI so far is the solution to the Earth's unit distance problem, which I think was announced in mid-May.
So at least what I liked about that is it seemed to me that it was in some ways a little bit creative. So I think some of the results we've seen have had the flavor. If you take some known techniques and apply them in maybe a clever way, or you know, they have some results I would characterize as last mile, like where some recent work was done, quite deep work done by a group of human mathematicians, and then the AI took the final step.