Anthropic

AI Research · Mathematics · Formal Verification

Milestone

Claude agents produce first computer-checked proof of Fermat's Last Theorem

A mathematician funded for five years to do this exact task says the math is unchanged, but the verification speed is the real story.

• Anthropic says Claude agents worked largely autonomously for 11 days to produce the first complete, computer-checked Lean proof of Fermat's Last Theorem, writing 13 million lines of code and proving 29,500 intermediate theorems.
• Formalizing a proof means translating human mathematical reasoning into a language a computer can check step by step; it doesn't create new math but eliminates reliance on human referees to catch errors.
• Dozens of Claude agents coordinated through Prove2Me, an open platform built by Anthropic researcher Tianyi Peng and Columbia University collaborators, after early solo agents lost track of the sprawling proof.
• The proof follows a simplified Darmon-Diamond-Taylor exposition of the Wiles/Taylor-Wiles argument and builds on existing formalized math, reusing over 100 files from Imperial College London's FLT project.
• The run consumed roughly six billion output tokens from an internal research model, which at published per-token pricing would cost about $300,000.
• Kevin Buzzard, who holds a five-year, EPSRC-funded grant to formalize the same theorem by hand, independently compiled Anthropic's code and confirmed it checks out, calling it an 'extraordinary autoformalization achievement.'
• The milestone signals that AI could soon formalize modern research mathematics as it's produced, turning a task that took Wiles years to write and referees months to verify into something checkable on the fly.