Anthropic AI has successfully translated the proof of Fermat’s Last Theorem into computer-verified code, a feat mathematicians estimate would have taken humans a decade. The project, completed in 11 days, demonstrates the growing role of artificial intelligence in mathematical verification and potential discovery.
Alex Kontorovich, a number theorist at Rutgers University in Piscataway, New Jersey, stated the accomplishment “just completely blew my mind.” Anthropic AI, based in San Francisco, California, announced the breakthrough on September 4th. The 13-million-line proof formalizes the work of Andrew Wiles and Richard Taylor, who originally completed the proof in 1994. Fermat’s Last Theorem posits that there are no whole numbers x, y, and z that can satisfy the equation xn + yn = zn when n is greater than 2. The theorem was originally conjectured by Pierre de Fermat in 1637, but remained unproven for over 350 years.
Kevin Buzzard, a mathematician at Imperial College London, noted the complexity of this achievement, stating it was “maybe an order of magnitude more difficult” than previous AI-assisted formalizations, such as the certification of Maryna Viazovska’s work on sphere packing in February. Daniel Litt, a number theorist at the University of Toronto, Canada, believes this success indicates the AI’s capacity to formalize any mathematical proof: “If they can formalize Fermat's last theorem, they can probably formalize anything.”
The ability of AI to ‘formalize’ proofs—translating mathematical arguments into computer-certifiable code, typically using the Lean programming language—is increasingly seen as a powerful tool for mathematicians. Buzzard suggests that at the current rate of progress, AI could eventually scrutinize the entire body of mathematical knowledge, potentially identifying errors in established results. “Two years ago, that was a fantasy,” he said.
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