Fermat's Last Theorem
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Search complete. 41 mentions across 23 episodes found for "Fermat's Last Theorem".
Oct 29, 2026
Rachel RileyGUEST
So there was this really well-known problem, Fermat.
Rachel RileyGUEST
Fermat's last theorem was...
Rachel RileyGUEST
There was a mayor, I think, a few hundred years ago in Italy that said he'd solved this problem.
Rachel RileyGUEST
So Pythagoras says a squared plus b squared equals c squared.
Hassaan SaleemHOST
So is there anything that we learned about any of these ingredients using this correspondence that was hard to learn without using this correspondence?
Kristaps BalodisGUEST
Uh, yeah, well, I mean, uh, well, I mean, for one, uh, Fermat's last theorem, right.
Kristaps BalodisGUEST
Uh, that's, uh, yeah, but like I said, it's a, that's basically a special case of, of the Langlands correspondence.
Kristaps BalodisGUEST
Right.
1 HR 3 MINS LATER
Kristaps BalodisGUEST
And I don't know.
Kristaps BalodisGUEST
I think that's fine to have...
Kristaps BalodisGUEST
I mean, you know, I don't know the proof of Fermat's last theorem.
Kristaps BalodisGUEST
I accept this on blind faith because the elders said it was true.
speaker_0NARRATOR
In the past few months, unreleased frontier AI systems have significantly disrupted a classic conception of mathematics.
speaker_0NARRATOR
They successfully established a complete formalization of Andrew Wiles' proof of Fermat's Last Theorem, found a solution to the Navier-Stokes problem, and, just a few days ago, generated hundreds of manuscripts that each purport to prove an important mathematical problem.
speaker_0NARRATOR
Most recently, on October 26, another of the Clay Millennium Prize problems was felled by an AI system.
speaker_0NARRATOR
Mathematicians reacted with a volatile mixture of optimism, anxiety, and deep disorientation.
speaker_0NARRATOR
The checklist model.
speaker_0NARRATOR
Under the checklist model, mathematical progress consists of resolving well-defined, complex problems that are specified in advance.
speaker_0NARRATOR
These include competition problems designed to measure the frontier of human mathematical capabilities, such as those of the International Mathematical Olympiad, famous conjectures, such as Fermat's Last Theorem or Last Conjecture, formalization benchmarks, such as Friedrich Wiedeich's list of 100 formalization challenges, and prize problems, such as Clay's Millennium Problems.
speaker_0NARRATOR
Each of these can be considered an item on a checklist.
Jason SorokoHOST
We started to use elliptic curve cryptography after we got a formal proof that It's actually very difficult.
Jason SorokoHOST
In fact, there is a formal proof that actually came out of Fermat's Last Theorem, believe it or not.
Jason SorokoHOST
One of the things to prove Fermat's Last Theorem was actually the proof for elliptic curve cryptography.
Jason SorokoHOST
Given certain kinds of curves, solving for two points on the curve, is actually, has a level of difficulty that forces a non-quantic computer to have to go through all the possibilities.
Jason SorokoHOST
And so therefore, it is a, let's call it a hard problem.
ParzivalHOST
In the summer of 2025, Axiom says, the biggest proof an AI had formalized on its own was about 3,000 lines.
ParzivalHOST
In September, Anthropics' Claude formalized Fermat's Last Theorem, about 13 million lines in 11 days.
ParzivalHOST
And now, 43 million lines in 24 days, about 14,000 times more in a little over a year.
ParzivalHOST
And their prologue, set in this very year, has two sentences I can't stop thinking about.
Ankur MoitraGUEST
What does a mathematician do? You know, the simplest and most visible part of the job is we proof theorems.
Ankur MoitraGUEST
And theorems about conjectures that were open for hundreds of years, like Fermat's Last Theorem, these are very visible things that we've spent a lot of time popularizing, but I don't think that that's all that a mathematician does.
Ankur MoitraGUEST
I like to think about it as a mathematician is someone who thinks deeply, and a byproduct of thinking deeply is proving old conjectures, but it's also building new theories, building new ways of looking at old things, making new conceptual connections.
Ankur MoitraGUEST
And these are parts that, you know, maybe AI will swallow up too, but we're not there yet at this moment.
50 MINS LATER
Alex KontorovichGUEST
Yeah.
Alex KontorovichGUEST
It's just, it was so far outside of, my model of what was possible.
Alex KontorovichGUEST
And this is, it's been a month of things happening way outside of my model of what was possible with the Fermat's last theorem formalization.
Alex KontorovichGUEST
I was sure we were three years away, at least from being able to do something like that.
speaker_1UNKNOWN
What's remarkable is that AI systems can now produce proofs that Lean verifies, even when the resulting code is enormous and nearly impossible for humans to interpret.
speaker_1UNKNOWN
The formalization of Fermat's last theorem stunned people.
speaker_1UNKNOWN
Roughly 13 million lines of valid code, reportedly produced with limited human guidance.
Lex FridmanHOST
But valid and elegant are not the same thing.
Tobias CarlisleHOST
I have a sort of like an amateur interest in that stuff.
Tobias CarlisleHOST
I read this book called Fermat's Last Theorem like 20 years ago where they'd solved it.
Tobias CarlisleHOST
And math is like a very, very funny place.
Tobias CarlisleHOST
Like they take these different...
Tobias CarlisleHOST
it.
Tobias CarlisleHOST
Did you read Fermat's Last Theorem?
Jake TaylorHOST
I did.
Tobias CarlisleHOST
I read that, I don't know how long ago, 20 years ago or something like that.
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