Anthropic Publishes Mechanically Verified Proof of Fermat's Last Theorem Using Claude

Anthropic has published the first fully mechanically verified proof of Fermat's Last Theorem (FLT) using the AI model Claude. This formalizes Andrew Wiles's 1995 proof via the Lean proof assistant, representing computer verification of an existing proof rather than a new mathematical discovery.

Project Scale and Achievements

The project was conducted through 11 days of autonomous work, generating approximately 13 million lines of Lean code and 29,500 intermediate lemmas. This is more than five times the size of the existing Mathlib library. Led by Tianyi Peng and verified by Professor Kevin Buzzard, this proof contains no assumptions other than mathematical axioms and formalizes a wide range of fields including algebra, harmonic analysis, geometry, and number theory.

Verification Process and Technical Features

The proof was completed via a multi-agent harness called Prove2Me, with output tokens reaching approximately 6 billion. It relies solely on three standard Lean axioms, and incomplete code such as axiom or sorry was prohibited. Statement consistency and typing rules were re-verified through external tools (comparator, nanoda), and the process included Claude discovering and fixing its own errors.

Limitations and Future Challenges

The proof is currently awaiting independent re-verification, and integration with Mathlib faces technical barriers such as lack of comments, inefficient file structure, and duplicate declarations. While Anthropic hopes that formalization will become a tool to enhance the reliability of mathematical knowledge, it also mentioned academic concerns regarding the difficulty of evaluating AI-generated arguments and the potential for overstated promotion. The repository is released under the Apache License 2.0, allowing for research and commercial use.