Claude formalizes Fermat's Last Theorem in 11 days, undercutting human timeline by years

Anthropic’s AI model Claude has produced the first fully computer-verified proof of Fermat’s Last Theorem, generating 13 million lines of Lean code in 11 days. The feat cost roughly €276,000 ($300,000) — a fraction of Kevin Buzzard’s €1.17 million (£1 million) five-year project at Imperial College London, which aimed to do the same manually.

Bottom line — Anthropic's Claude verified Fermat's Last Theorem in 11 days for about €276k, less than a quarter of Buzzard's five-year grant.

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• The Claude agents generated 13 million lines of Lean code, proving 30,300 intermediate theorems, with 29,500 used in the final proof, per Nature and The Pioneer.
• The run consumed about 6 billion output tokens, costing roughly €276k ($300,000) at Anthropic's rates, according to Forbes.
• Kevin Buzzard, who leads the Imperial College project, called the result 'extraordinary' but said it 'tells us essentially nothing' new about the mathematics, per his blog (via Forbes).
• The verification separates proof from understanding: the 13-million-line file is not intended for human reading, and no human can comprehend it, per The Pioneer.
• The Lean kernel that checks the proof is a few thousand lines of code; a soundness bug last summer briefly allowed a false proof to pass, per The Pioneer.
• The achievement builds on a 2024 milestone where AI formalized Viazovska's sphere-packing proof, but this was 'an order of magnitude more difficult', per Kevin Buzzard (via Nature).
• Anthropic stressed the novelty is in verification, not discovery, as Wiles' proof from 1994 remains unchanged, per the company's statement (via Forbes).

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