Claude formalizes Fermat’s Last Theorem in 11 days

Anthropic says its Claude artificial intelligence system has produced a fully computer-checked version of Fermat’s Last Theorem. Pierre de Fermat first proposed the theorem in 1637, while Andrew Wiles published the first full mathematical proof in 1995. Wiles’s proof spanned 129 pages.

Formalization converts mathematical reasoning into code that computers can check automatically. Anthropic had expected the project to take several years. Instead, its internal research model completed it in 11 days of continuous, largely unsupervised work.

The resulting proof contains 13 million lines of specialized Lean code. Claude’s agents reportedly proved roughly 30,300 separate theorems and used 29,500 of them in the final version. Human involvement was limited to occasional high-level guidance rather than hands-on coding.

The proof is more than five times larger than Mathlib, the community’s main proof library. Anthropic says repeated attempts contributed roughly 7% of the final proof’s non-boilerplate lines.

The work followed Anthropic’s separate breakthrough involving the Riemann zeta function one month earlier. Anthropic says access to Prove2Me, an open-source tool built by outside collaborators, helped Claude choose useful next steps and reduce inference costs.