Formalizing Fermat's Last Theorem

This article reports on the first complete, computer-checked proof of Fermat's Last Theorem (FLT), produced by the Claude AI model in collaboration with researchers. In an experiment, Claude worked largely autonomously over 11 days, using the Lean proof assistant and the Prove2Me collaborative platform, to formalize a proof of the theorem. The resulting proof consists of 13 million lines of Lean code and verifies 29,500 intermediate theorems. The work follows a simplified version of Sir Andrew Wiles's 1995 proof. The authors, led by Anthropic researcher Tianyi Peng, highlight that while the theorem itself is not new, this achievement is significant for the field of formal mathematics. Automated formalization can help verify complex proofs, catch errors in mathematical literature, and reduce the burden on human referees. Kevin Buzzard of Imperial College London, who reviewed the proof, praised it as a major step toward automatic formalization of modern mathematical literature. The article concludes by noting that this project demonstrates the potential for AI to assist in rigorously checking mathematical results and maintaining trust in mathematical knowledge.

(Source：Anthropic)