Claude AI Formalizes Proof of Fermat's Last Theorem

Anthropic announced on September 4 that its Claude models formalized a complete, computer-verifiable proof of Fermat's Last Theorem, a task the mathematics community had expected to take several years of human effort.

The project, led by researcher Tianyi Peng, used dozens of Claude agents working in parallel on Prove2Me, a platform for translating mathematical arguments into the Lean proof language. Over 11 days, the agents produced roughly 13 million lines of Lean code, proving about 29,500 intermediate theorems, a formalization about five times larger than Lean's entire existing mathematics library, Mathlib. Anthropic said the work consumed roughly 6 billion output tokens from an internal general-purpose research model with capabilities comparable to Claude Fable 5.1.

Fermat's Last Theorem, first proposed in 1637, states that no three positive integers can satisfy the equation a^n + b^n = c^n for any integer n greater than 2. Andrew Wiles proved it in 1995 after years of work, but his proof, like most advanced mathematics, was written in natural language and relied on readers and reviewers to catch errors. Formalization converts that reasoning into a form a computer proof assistant like Lean can check line by line, using only Lean's three standard logical axioms, removing any dependence on human review to confirm correctness.

Why now: Anthropic published the formalization on GitHub and said an independent comparator tool confirmed the final theorem statement matches the standard mathematical formulation, addressing a common concern that an AI system could formalize an easier, subtly different statement than the one it claims to prove.

Why it matters: Kevin Buzzard, a mathematician at Imperial College London and a prominent voice in the formalization community, said the result shows autoformalization now succeeds across algebra, harmonic analysis, geometry and number theory, not just isolated toy problems. Checking a major mathematical proof by hand can take mathematicians years, as it did for Wiles' original work. If AI systems can reliably convert dense human proofs into machine-checked formalizations, it could give the field a faster, more reliable way to confirm that new results are correct, and let AI systems tackle unsolved problems with results other mathematicians can verify quickly rather than trust on reputation alone.

Disclosure: NewUJ's editorial process uses Anthropic's Claude models.