Claude Writes the First Computer-Checked Proof of Fermat's Last Theorem
Anthropic's Claude has produced the first complete computer-checked proof of Fermat's Last Theorem, working largely on its own over 11 days to write a proof in the Lean programming language.
The result, announced by Anthropic, converts Andrew Wiles's landmark 1995 proof into a form a computer can verify step by step. That matters because checking a complex mathematical proof is normally a slow, human process: Wiles's original proof ran to 129 pages and took months of painstaking review, and a critical gap was only caught two months into that effort. A computer-checked proof removes that uncertainty.
Claude wrote 13 million lines of Lean code and proved 29,500 intermediate theorems along the way. The proof is more than five times the size of Mathlib, the main community library of mathematical proofs it builds on. Dozens of Claude agents collaborated on the project, and the finished proof was checked by Lean using only its three standard axioms. Kevin Buzzard, the Imperial College London mathematician leading a multi-year community effort to formalize the theorem, called it an "extraordinary autoformalization achievement."
The most striking detail is the speed. The mathematical community had expected formalizing Fermat's Last Theorem to take years; the blueprint for just the initial phase runs to 86 pages. Claude did it in under two weeks, consuming about six billion output tokens from an internal research model. A smaller experiment using three personal Claude Max plans formalized Vinogradov's Three Primes Theorem in three days, suggesting collaborative formalization of major results may be achievable with consumer AI subscriptions.
For mathematicians, the practical consequence is a lighter refereeing burden. As AI systems produce more purported proofs, human review becomes a bottleneck. Anthropic expects it will become common to produce a computer-checked proof alongside any write-up intended for human readers, and Buzzard said the techniques could help "root out errors in the current mathematical corpus." The full proof is available on GitHub.