GoKawiilAnthropic's Claude produces first fully computer-verified proof of Fermat's Last Theorem
Anthropic researcher Tianyi Peng tested whether the Claude AI model could formalize Fermat's Last Theorem in the Lean proof assistant, and over 11 days of largely autonomous work, Claude generated an end-to-end, machine-checked proof. The system wrote roughly 13 million lines of Lean code and proved about 29,500 intermediate theorems, building on decades of prior work including Andrew Wiles's 1995 proof and a community formalization effort led by Kevin Buzzard since 2024.
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A proof of this scale, previously requiring years of collaborative human effort to formalize, being produced largely autonomously in under two weeks signals a major shift in what AI can contribute to advanced mathematical research. It suggests AI could soon serve as a serious partner in verifying and even extending complex mathematical arguments across fields like algebra, geometry, and harmonic analysis, not just as a coding assistant.
- Claude produced the first complete, computer-checked proof of Fermat's Last Theorem in Lean.
- The AI worked largely autonomously for 11 days, generating 13 million lines of code and 29,500 intermediate theorems.
- Mathematician Kevin Buzzard called it an extraordinary autoformalization achievement built on rigorous mathematical axioms.
Simon Singh "Fermat's Enigma — Before diving into Lean proofs and machine-checked mathematics, this classic tells the human story behind Fermat's Last Theorem and Andrew Wiles's decade-long quest to prove it. It's the perfect companion read for anyone fascinated that a computer just verified the whole thing in 11 days.
See Simon Singh "Fermat's Enigma on Amazon → Affiliate link — we may earn a commission on purchases, at no extra cost to you. Product picked by AI based on this article; it is not a tested recommendation.Source: anthropic.com, 2026-09-04
Published there as: “Formalizing Fermat's Last Theorem”
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