Anthropic's Claude Completes First Computer-Verified Proof of Fermat's Last Theorem

AI company Anthropic announced on September 4 that its Claude AI model has completed the first end-to-end, computer-checked formalization of Fermat's Last Theorem (FLT). The process took 11 days of largely autonomous operation.

The work did not aim to discover a new mathematical proof for the theorem but to translate an existing proof into a format verifiable by the Lean proof assistant. Lean is software that allows for computer verification of logical steps in mathematical proofs.

During the process, Claude generated approximately 13 million lines of Lean code and proved over 30,000 lemmas, a significant portion of which contributed to the final proof of FLT. The entire proof was verified by Lean using only three standard axioms.

Fermat's Last Theorem, proven by Andrew Wiles in 1995, states there are no positive integers a, b, and c that satisfy the equation aⁿ + bⁿ = cⁿ for integer exponents n greater than 2. Wiles' original proof was 129 pages long and required months of human review.

Anthropic stated the focus was on AI's ability to automate large-scale formalization of proofs, which could reduce the cost and time for verifying new mathematical results. The complete Lean proof has been published on GitHub.