Anthropic · Claude · Susie Wiles · anthropic.com
Formalizing Fermat's Last Theorem
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Claude worked largely autonomously over 11 days to write the proof in the Lean programming language.
Key facts
- Claude completed the proof in 11 days, producing computer-verifiable proofs of 30,300 theorems along the way (using 29,500 in the final proof)
- The first proof, from Sir Andrew Wiles in 1995, ran to 129 pages and required months of painstaking work to verify
- At 13 million lines of Lean code, Claude’s proof is over 5x the size of Mathlib, the principal community library of mathematical proofs this theorem builds on. 3
- Recently, Tianyi Peng, an Anthropic researcher whose group at Columbia University builds tools for AI formalization, set out to test whether Claude could make progress on formalizing FLT. 1
Summary
The team are sharing the first complete computer-checked proof of Fermat’s Last Theorem. The first proof, from Sir Andrew Wiles in 1995, ran to 129 pages and required months of painstaking work to verify. A decade later, Dutch computer scientist Jan Bergstra proposed “formalizing” Wiles’s proof: converting the mathematical reasoning into a form computers can check automatically. Recently, Tianyi Peng, an Anthropic researcher whose group at Columbia University builds tools for AI formalization, set out to test whether Claude could make progress on formalizing FLT. 1 The result went further than he expected. The team shared the resulting proof with Kevin Buzzard, who said:. Automatically formalizing a proof as complex as FLT is a significant step towards a future in which all of mathematics can be readily checked.