Claude Builds a Verified Proof of Fermat's Last Theorem

Anthropic said this week that its Claude models produced the first complete, machine-checked proof of Fermat's Last Theorem, rendering one of mathematics' most famous results into code that a computer can verify line by line. The company described the work in a research post published on September 4, and the claim has since spread well beyond the usual mathematics circles.

The theorem itself is old and short to state. In 1637 Pierre de Fermat scribbled that no three positive integers can satisfy the equation for any exponent greater than two, and famously added that he had a proof the margin was too small to hold. It took until 1994 for Andrew Wiles to actually prove it, in a dense argument that runs to more than a hundred pages and draws on much of modern number theory. Very few people on earth can follow it end to end.

What Claude did is different from proving the theorem afresh. It formalized a version of Wiles's argument in Lean, a language in which every logical step must be spelled out precisely enough for the computer to check it. That process, called formalization, is notoriously slow and unglamorous. Experts had estimated it would take a large team many years. Claude did the bulk of it in eleven days.

What the run actually involved

According to Anthropic, the effort was directed by researcher Tianyi Peng and ran on Prove2Me, an open platform that tracks theorem statements as a graph and lets many agents work on different branches at once. Dozens of Claude agents, coordinated through a Claude Code workflow, chipped away at the proof in parallel. The final artifact is large by any measure: roughly 13 million lines of Lean, some 30,300 theorems proved along the way, and about six billion output tokens consumed.

Kevin Buzzard, the Imperial College London mathematician who has spent years pushing to formalize hard results, reviewed the output and called it an extraordinary achievement, noting that it proves the theorem with no unproven assumptions left dangling. That last point matters. A formal proof that quietly leans on an unchecked lemma is not really finished, and reviewers look for exactly that kind of gap.

The caveats worth keeping in view

It is easy to read a headline like this and conclude that AI has started doing original mathematics. That is not what happened here, and Anthropic is fairly candid about it. Claude followed a simplified route through Wiles's existing proof rather than inventing new mathematics, and it built on Mathlib, the large community library of already-formalized results, along with earlier formalization work from Imperial and elsewhere. Human researchers stepped in with occasional high-level guidance when agents got stuck, and roughly 7 percent of the substantive code came from attempts that failed before something worked.

So the honest framing is narrower than the hype, and more interesting for it. The hard, tedious job of translating a human proof into fully verified code, the kind of work that has bottlenecked formal mathematics for a decade, turns out to be something these models can now do at speed. Buzzard suggested it opens the door to formalizing large stretches of the mathematical literature automatically, which would give mathematicians a searchable, machine-verified foundation to build on.

It also fits a pattern we have been tracking. Anthropic has been steering Claude toward long, autonomous technical runs, from the Fable 5.1 models tuned for multistep work to earlier experiments in reproducing published science. A proof that holds up under a computer's scrutiny is a cleaner test than most. Either the checker accepts it or it does not, and this time it did.