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

September 5, 2026 at 05:41 AM2 min

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Anthropic used its Claude model to create a computer-verifiable version of Andrew Wiles' proof of Fermat's Last Theorem, completing the task in 11 days. The formalized proof comprises 13 million lines of Lean code, the largest file of its kind. The project marks a significant advance in AI-assisted mathematical verification.

Key Facts

Anthropic's formalized proof of Fermat's Last Theorem comprises 13 million lines of Lean code, the largest-ever file of its kind.
The formalization was completed in 11 days using an internal research model roughly on par with Claude Fable 5.1.
The model generated 6 billion tokens of output and proved 29,500 intermediate theorems during the process.
Anthropic's breakthrough came after giving Claude access to an open-source tool called Prove2Me.
Mathematician Kevin Buzzard, whose work Claude used, commented on the multi-layered nature of the proof.

The Formalization Project

Anthropic PBC detailed the project in a blog post published today. The proof of Fermat's Last Theorem was originally developed in 1995 by mathematician Andrew Wiles and runs for 129 pages. Anthropic's research project formalized Wiles' proof, turning it into a form that can be automatically verified by computers. The formalized proof takes the form of a code snippet written in the programming language Lean. Anthropic's proof comprises 13 million lines of Lean code, making it the largest-ever file of its kind.

Technical Challenges and Breakthrough

Formalization is difficult because proofs tend to be terse and lack explanations that a computer needs. Lean developers must add missing explanations manually, and one erroneous line of code can invalidate subsequent code. Mathematicians expected the formalization process to take several years, but Anthropic completed it in 11 days. The model used only a limited amount of high-level human input and spun up several dozen agents. Anthropic's initial attempt was unsuccessful until Claude was given access to the open-source tool Prove2Me.

Mathematical Significance

Kevin Buzzard, a mathematician whose work Claude used, said the proof is multi-layered and robust enough to be built upon. The milestone comes a month after Anthropic used Claude to discover new information about the Riemann zeta function.