Anthropic utilized a research model comparable to the public Claude Fable 5.1 to formalize Andrew Wiles' 1995 proof of Fermat's Last Theorem. The original proof, which spans 129 pages and typically takes months to verify, was converted into a computer-verifiable format.
The resulting formalized proof consists of 13 million lines of code written in the Lean programming language, marking the largest volume of such code in history. The process was challenging due to the lack of explicit explanations in mathematical proofs that computers require for verification.
The AI model completed the task in 11 days, significantly faster than the several years mathematicians had anticipated. To achieve this, the model deployed several dozen agents that generated 6 billion output tokens and proved 29,500 intermediate theorems.
The breakthrough occurred after the model was granted access to the Prove2Me platform. Additionally, Anthropic reported progress in proving the Riemann hypothesis one month prior to this achievement.
