Anthropic's Claude formalizes Fermat's Last Theorem proof in 11 days

September 13, 2026 at 08:15 PM2 min

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Anthropic's Claude AI system converted Andrew Wiles' 129-page proof of Fermat's Last Theorem into 13 million lines of Lean code in 11 days. The formalized proof is fully computer-checkable and over five times larger than the Mathlib library. The project was expected to take several years, but Claude completed it with minimal human guidance.

Key Facts

Anthropic's Claude converted Andrew Wiles' 129-page proof of Fermat's Last Theorem into 13 million lines of Lean code.
The formalization was completed in 11 days, while the project was expected to take several years.
Claude's agents proved roughly 30,300 theorems, using 29,500 in the final proof.
The resulting proof is over five times larger than Mathlib, the community's main proof library.
Kevin Buzzard, a mathematician at Imperial College London, called the achievement 'extraordinary'.

The Formalization Process

Anthropic expected the formalization of Fermat's Last Theorem to take several years based on mathematicians' initial descriptions. Claude's internal research model completed the proof in 11 days of continuous, largely unsupervised work. The finished proof runs to 13 million lines of Lean code, a language used by mathematicians for formal verification. Human input was limited to occasional high-level guidance, with no direct hands-on coding during the process.

Mathematical Significance

The proof addresses Fermat's Last Theorem, first proposed by Pierre de Fermat in 1637 and proved by Andrew Wiles in 1995. Kevin Buzzard of Imperial College London stated the proof uses no assumptions other than the axioms of mathematics. The formalization includes autoformalization of algebra, harmonic analysis, geometry, and number theory. Anthropic's earlier attempts contributed roughly 7% of the final proof's non-boilerplate lines.

AI Math Race

The formalization comes one month after Anthropic detailed a breakthrough involving the Riemann zeta function. OpenAI is pursuing similar work with its Astra model, solving several classic Erdős problems. OpenAI's effort also narrowed long-standing open questions in theoretical computer science.