Anthropic says its Claude AI just wrote the longest math proof ever made, and used it to formally prove Fermat's Last Theorem, a problem that stumped mathematicians for 358 years.
Claude did it in 11 days, mostly on its own, producing 13 million lines of code that a computer can check line by line, instead of just taking a mathematician's word for it.
Fermat’s last theorem says you can't take three positive whole numbers, raise each one to a power higher than 2, and have the first two add up to the third. He scribbled that claim into the margin of a math book in 1637, adding that he had a "truly marvelous proof" that the margin was just too small to fit.
Then he died. Mathematicians spent the next 358 years trying to reconstruct whatever he thought he had.
Proving something and checking it are two different jobs
A math proof is a chain of logical steps, and if one link is broken, the whole thing collapses. Finding that one broken link, buried somewhere in a hundred pages of dense argument, can take other mathematicians years of their lives.
Formalizing a proof means translating it into a language so painfully literal that a computer can verify every step on its own without entering into subjectivities.
Mathematicians have been bad at policing this for a while. A 1908 German prize worth roughly $1 million to $2 million in today's money, offered for the first valid proof of the theorem, drew 621 wrong submissions in its first year alone.
The real proof didn't show up until 1995, from British mathematician Andrew Wiles, and it came with a plot twist. Wiles announced his solution across three lectures in June 1993, only for a reviewer to find a hole in it later.
He spent almost a year fixing it with a former student, Richard Taylor, nearly gave up, and finally published a corrected, 129-page proof in May 1995. It leaned on math that didn't exist in Fermat's lifetime, which is a big reason mathematicians now doubt Fermat's own "marvelous proof" ever actually worked.
Imperial College London mathematician Kevin Buzzard kicked off a project in 2024 to do exactly what Claude just did: translate Wiles's proof into Lean, a language computers can check. It's the kind of job that needs an army of volunteer mathematicians—the project's own outline runs 86 pages, and its funding is locked in through 2029.
Claude finished the whole thing in 11 days.
How Claude actually pulled it off
Anthropic explains in a more in-depth post that Tianyi Peng, who builds AI formalization tools with a team at Columbia, decided to see how far Claude could get on its own. Dozens of Claude agents worked in parallel, writing definitions, proving small results, and stacking those into bigger ones, with almost no human input beyond the occasional nudge like "prioritize this theorem next."
It didn't go smoothly at first. Early on, the agents kept losing track of what they'd already proven and stopped collaborating, and those false starts still make up about 7% of the lines in the final proof.
What fixed it was a tool called Prove2Me, also built by Peng's team, which gave every agent the same live to-do list of which smaller proofs still needed doing, so nobody duplicated work or wandered off. It also organized files so Lean could check everything faster, and kept plain-English notes on each result so agents could reuse each other's work instead of reinventing it.
By the time it was done, Claude had proven more than 30,000 supporting theorems and burned through billions of tokens, running on a research model Anthropic says is roughly comparable to Claude Fable 5.1, the version it later released to the public. The finished proof runs 13 million lines—more than five times the size of Mathlib, the shared library mathematicians already use for this kind of work.
A typical novel runs 80,000 words. Claude's proof is equivalent to 160 novels of pure logical argument.
So does this actually matter?
Buzzard—whose own version of this project remains funded through 2029—reviewed Claude's proof and gave it his blessing, saying it proves the theorem "with no assumptions other than the axioms of mathematics."
This isn't the same as Claude discovering brand-new math, which Anthropic also claimed with its cryptography research earlier this year. Wiles already proved Fermat's theorem three decades ago—Claude just built a machine-checkable receipt for it. That matters because mathematicians are increasingly swamped with unverified proofs, including AI-written ones, faster than humans can check them by hand.
Also, these types of proofs are deterministic and not prone to human errors, which is very important in math.
That's not a new problem. A computer-assisted proof of the Kepler conjecture took four years before a review panel would only commit to "99% certain," and Grigori Perelman's proof of the Poincaré conjecture took about as long to fully sink in.
