Anthropic Successfully Completes Full Formal Verification of Fermat's Last Theorem Using Claude in 11 Days

Anthropic's research team successfully formalized Fermat's Last Theorem, one of the most famous problems in the history of mathematics, into a fully computer-verifiable format in 11 days using the AI model Claude. This case demonstrates that AI can autonomously perform complex logical verification processes that would take humans months or even years.

Formalization Process and Technical Achievements

This project was conducted based on Prove2Me, an open collaborative platform developed in cooperation with Tianyi Peng from Columbia University. Dozens of Claude agents worked in parallel to perform concept definitions, intermediate theorem proofs, and final proposition proofs.

• Code Scale: The final proof consists of 13 million lines of Lean code, which is more than five times the size of Mathlib, a major mathematics library.
• Proof Structure: Generated verifiable proofs for a total of 30,300 theorems, of which 29,500 were used in the final proof.
• Core Mechanism: Maintained a Directed Acyclic Graph (DAG) of theorem propositions for inter-agent collaboration, and optimized compilation speed by separating proof files and proposition files.

Reliability and Significance of Verification

Kevin Buzzard (Imperial College London) evaluated this achievement as proving FLT without any assumptions other than the axioms of mathematics. The generated proof has been published on GitHub, confirming the absence of logical flaws by using only the three standard axioms of Lean.

Previously, verifying complex logical chains like Wiles's proof (1995) took humans months, but this formalization is expected to significantly reduce the burden of ensuring the reliability of mathematical results generated by AI. In particular, Anthropic successfully experimented with formalizing Vinogradov's Three Primes Theorem in 3 days using just three Claude Max plan subscriptions at the consumer level, suggesting that large-scale formalization is possible with the appropriate scaffold.