Claude Formalizes Fermat's Last Theorem: the 13-Million-Line Proof

Anthropic revealed that Claude produced — working mostly autonomously over 11 days — the first end-to-end, computer-verified proof of Fermat's Last Theorem in the formal language Lean. It's a mathematical milestone, but it's also a concrete case study in how much sustained intellectual work can now be delegated to an agent without constant supervision.

One theorem, 30,300 verified steps

Fermat's Last Theorem — which states that no three positive integers can satisfy a^n + b^n = c^n for n greater than 2 — was proven by Andrew Wiles in 1994, but it had never been fully formalized in a proof assistant like Lean, where every logical step is mechanically verified without anything taken for granted. According to Anthropic, Claude generated 13 million lines of Lean code and produced 30,300 intermediate theorems, of which 29,500 ended up being part of the final proof. Mathematician Kevin Buzzard, an authority on formalization, confirmed that the result "proves Fermat's Last Theorem with no assumptions beyond the axioms of mathematics."

The key piece: coordination, not just capability

The achievement didn't come from a single monolithic attempt. Anthropic notes that the real breakthrough came from adopting Prove2Me, an open collaborative platform built by researcher Tianyi Peng together with collaborators from Columbia University, which maintains a dependency graph between theorem statements so that multiple Claude agents can work in parallel without stepping on each other's work, reusing results already proven by other agents through natural-language descriptions.

Not everything worked on the first try

What this means for businesses already using Claude or other LLMs