Anthropic's AI completes formal proof of fermat's last theorem in record time

Anthropic's AI model, Claude, has completed the first end-to-end, computer-checked formal proof of Fermat's Last Theorem using the Lean proof assistant. The achievement, which took 11 days, involved generating 13 million lines of Lean code and proving 30,300 theorems, with 29,500 intermediate theorems incorporated into the final proof. Kevin Buzzard, a mathematician, praised the result as significant progress in AI-assisted formalization of complex mathematical proofs. The project, led by Anthropic researcher Tianyi Peng, utilized the Prove2Me platform to enable multi-agent collaboration among Claude models. The final proof followed a simplified version of Andrew Wiles' original proof from 1995, which was 129 pages long. Anthropic emphasized that the goal was not to discover a new proof but to automate the formalization process, with the final result verified by Lean using only three standard axioms. The project consumed 6 billion output tokens, using a model equivalent to Claude Fable5.1. The generated proof is more than five times the size of Mathlib, the main mathematical proof library. Anthropic highlighted that this work demonstrates the potential of AI to reduce manual verification costs in mathematical research and make formalized proofs a common practice.