Anthropic uses Claude to formalize proof of Fermat’s Last Theorem

Anthropic says it has turned one of mathematics’ most famous proofs into something a computer can verify. The target was Andrew Wiles’ 1995 proof of Fermat’s Last Theorem, the result that settled a problem first raised in 1637 and took months for humans to verify in its original form.

The company’s move wasn’t about finding a new theorem. It was about formalizing an old one: translating the proof into Lean, the programming language mathematicians use to make every step machine-checkable. That matters because the process strips out hidden assumptions and makes the logic easier to share, but it also exposes every weak link. One bad line can break everything that comes after it.

Anthropic says the final result was huge even by computer standards: 13 million lines of Lean code, which it calls the largest file of its kind. It also says the work finished in 11 days using an internal research model, rather than the several years mathematicians expected. The model worked with only limited high-level human guidance, spun up several dozen agents, produced 6 billion tokens, and proved 29,500 intermediate theorems along the way.

The path there wasn’t smooth. Anthropic’s first attempt failed, and the company says the breakthrough came after Claude was given access to Prove2Me, an open-source tool that helps agents choose the next step in a long workflow and lowers inference costs. Kevin Buzzard, a mathematician whose work Claude used, described the result as evidence that AI autoformalization is now robust enough to build on. Anthropic has also used Claude on the Riemann zeta function, while OpenAI Group PBC says its latest Astra model has been used on Erdos problems and open questions in theoretical computer science.