Anthropic's Claude AI formalizes Fermat's Last Theorem proof in 11 days

Anthropic’s large‑language model Claude has completed a formal verification of the proof of Fermat’s Last Theorem in under two weeks, a task that experts had projected would require several years of collaborative effort. The theorem, first conjectured in 1637, was finally proven by Andrew Wiles and his colleague Richard Taylor in 1994, but the original mathematical argument remained informal and difficult to translate into a machine‑readable format. Formal verification projects, which encode mathematical proofs in proof assistants such as Coq or Lean, aim to eliminate any possibility of hidden errors, yet the complexity of Wiles’s proof—spanning modular forms, elliptic curves, and Galois representations—has long posed a formidable challenge for automation.

Claude achieved the conversion by parsing the published proof, generating intermediate lemmas, and iteratively refining the code to satisfy the strict logical constraints of the verification environment. The process involved collaboration between Anthropic engineers and mathematicians familiar with the theorem’s structure, and the final codebase passed all automated checks without requiring manual intervention. The rapid completion demonstrates the growing capability of AI systems to assist in high‑level mathematical formalization, potentially accelerating the verification of other complex results and expanding the role of automated reasoning in research.