Anthropic: Claude Formalizes Fermat's Last Theorem in 11 Autonomous Days
Anthropic says Claude produced the first end-to-end, computer-checked proof of Fermat's Last Theorem, writing 13 million lines of Lean and 29,500 intermediate theorems in 11 largely autonomous days.
What happened
Anthropic has published the first complete, computer-checked proof of Fermat's Last Theorem. The company says Claude worked largely autonomously for 11 days to write the proof in Lean, a programming language built for formal verification, producing 13 million lines of code and proving 29,500 intermediate theorems along the way.
The work was led by Anthropic researcher Tianyi Peng, whose group at Columbia University builds tools for AI formalization. The finished proof is published openly on GitHub.
Why it matters
Fermat's claim — that no positive integers a, b and c satisfy aⁿ + bⁿ = cⁿ for n > 2 — dates to around 1637, and Andrew Wiles proved it only in 1995: a 129-page argument that took months to verify. Unlike recent AI work on the Riemann hypothesis, which produced new mathematics, the novelty here is verification: a formalized proof is checked by a machine.
What experts say
Kevin Buzzard of Imperial College London, who leads a multi-year community effort to formalize the theorem, called it "an extraordinary autoformalization achievement" that proves it with no assumptions beyond the axioms of mathematics. Anthropic says the result points to a future in which mathematical knowledge is easier to check — and easier to trust.