The AI system Claude, developed by Anthropic, prepared the first fully computer-verified version of the proof of Fermat's Last Theorem in just 11 days. This was announced on September 4, 2026. The proof consists of 13 million lines of code, making it the largest proof ever created on the Lean platform, which is capable of verifying mathematical proofs. Fermat's Last Theorem, posited back in 1637, states that there are no three positive integers a, b, and c that satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2.
The project formalizing the proof of Fermat's theorem was launched in 2024 by mathematician Kevin Buzzard at Imperial College London. Unlike Claude, his team's work has not yielded results thus far. Buzzard confirmed that Claude's proof adheres to the fundamental axioms of mathematics and added that such formalization helps verify scientific papers and identify flaws in mathematical reasoning. The system utilized the Mathlib library and a methodology with multiple agents working in parallel, which helped effectively organize the proof development process.
The significance of Claude's achievement lies in its offering a new approach to verifying mathematical proofs. This work is expected to significantly accelerate the verification process and enable mathematicians to tackle formalization tasks more efficiently, which currently require substantial time and resources. The complete code has already been published on GitHub, allowing other researchers to review the results and verify them independently. Buzzard will continue his formalization project, thus enriching the tools for verifying mathematical arguments in scientific research.