Kontorovich had just told Princeton mathematicians that AI could only formalize proofs a step or two beyond the existing Lean library, and that Fermat's Last Theorem was years of work away. Two days later an AI-generated formal proof landed. On Lex Fridman's episode about AI and the crisis in mathematics.
…doing it for two different purposes, then they clash. You can't stitch these things back together. Like you really need the library, Mathlib, to grow in order to get to a place where you can do research manuscripts that are really using, synthesizing tons of different areas of mathematics. Which
is why you would expect Fermat's Last Theorem to take, because it's so far outside of the halo of Mathlib, it would take quite a bit of time.
Exactly right. So Kevin Buzzard had a million dollar grant to spend the next five years, or maybe he's already a year or two into that grant to reduce the formalization of Fermat's Last Theorem to things that were known in the 1980s. So he wanted to do that last step, those seven years of Wiles' work and Wiles Taylor to finally finish Fermat's Last Theorem, but built on top of things that we knew would be extraordinarily difficult. He wasn't going to do Langland's Tunnel. He wasn't going to do Maser. There are all kinds of things that were expected to be even much more difficult than what these five years would take. And everything I said in that colloquium was wrong. And I think my colloquium was on a Wednesday. On Friday, there was a drop of 13 million lines of code from the axioms. Fermat's last theorem is proved. The statement of Fermat's last theorem is completely elementary. There's no semantic alignment to check. You just glance at it. Yes, that's the statement. Lean says it's sorry-free.
Can you explain how it was done?
How it was done. So it was anthropic. And how it was done was AI systems just got really, really good. It's still not a nice proof. It's not the clean proof. There's still a ton of work that needs to be done to make that proof a Mathlib quality proof. And I think that's important work and work that…
By the way, it's beautiful to always, because of how rapid everything is, there's going to be a lot of statements that everybody makes, the world experts make that are wrong. That's the whole point of it. And that's the fun thing about human discussion: we have disagreements. And I would venture to…