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Claude AI produces 13-million-line Lean 4 proof of Fermat's Last Theorem in 11 days

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Anthropic announced on September 4, 2026, that its Claude AI agents had generated a complete formal Lean 4 proof of Fermat's Last Theorem, spanning 13 million lines of code and roughly 29,500 intermediate theorems produced in just 11 days. The proof was verified mechanically by Lean's type checker and confirmed as valid by mathematician Kevin Buzzard of Imperial College London, who has been leading a human formalization effort toward the same goal since 2024. Buzzard acknowledged the proof checks out but described it as mathematically uninformative, characterizing it as a significant step for automated formalization rather than a contribution to mathematical understanding. The output, which exceeds five times the size of Lean's entire existing mathematics library, was designed to be machine-checked rather than human-readable, with all theorem names auto-generated. The computational cost of generating the proof has been estimated at around $300,000 in token fees, and a full build required over five hours on 96 parallel jobs, peaking at 153 GB of RAM.

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