Andrew Wiles

So, uh, Fermat's last theorem was like a really, really big thing in the nineties when it was proven.

Uh, I'm sure you know the story, but for, for your viewers, there was this mathematician, Andrew Wiles, who was at Princeton, and the story goes, he basically locked himself, you know, in his basement for seven years working out this proof, and then he went out and, and announced it.

He unveiled it at, at a conference or an event, and it took people months to even read it and understand it.

And then they found an error, right? So they're like, "Oh, well, it's...

Someone found an error.

It's not right." Um, and then it took another six or seven years for him to fix the error and ultimately for it to be accepted by a panel of mathematicians, and, and that made the proof correct.

So, you know, AI producing a thirteen million line proof, no human's gonna read that.

Uh, how do you know that it's, it's correct, right? And, uh, and I think it's an analogous problem to what we've been talking about.

And I read that mathematicians today are rather skeptical that he really did have a proof.

because the proof that was found after, well, almost 400 years of work by Andrew Wiles, to put the finishing touches on, or I don't want to mischaracterize, he built on a lot of work, and no doubt he did a lot of incredible work himself.

But it was the work of a bunch of people.

In fact, I've read it described that probably no one mathematician understands all the math that goes into the proof of Fermat's last theorem, because it draws on a lot of different areas of math.

... and they're like, "Oh, I have a model two generations ahead of it," so if this person is working on it, like should we not be able to talk about it? Because then the assumption is like, oh, now the labs know that actually the models which we don't have access to, if they can do it with the public models, they can race ahead faster.

Well, so there is something about the premise that I, I do find a little surprising, which is, for example, for, for Mao's last theorem, Andrew Wiles, I believe, solved it, famously spent 10 years secretly working on it-

Yeah

...

Anthropic announced a complete formal proof of Fermat's last theorem, a claim scribbled around 1637 in the margin of a book by a French lawyer doing maths in his spare time.

It took 350 years to settle, proved by Andrew Wiles in 1995, 129 pages and months of human checking.

Claude rewrote that proof.

In a language machines can verify.

Fermat claimed to, uh, to have proof that this was too large to fit in the margin in his copy of the ancient Greek text, Arithmetica.

Andrew Wiles, that's the mathematician.

Right.

Yes.

Uh, so the theorem was finally proved in 1994 by a British mathematician, Andrew Wiles, blah, blah, blah.

Right.

Can, can you look and see what, like, uh, what any kind of AI advancement of this theory?

Yeah.

But now with the advance of AI, AI's very good at doing Lean because it doesn't give up.

In fact, last week we had the biggest Lean proof of all, which is a Lean formalization of Fermat's last theorem, Andrew Wiles's proof.

Yes.

And so Anthropic announced that, and it's 13-