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Anthropic's Claude Formalizes Fermat's Last Theorem

Anthropic's Claude AI system autonomously produced the first complete computer-checked proof of Fermat’s Last Theorem in the Lean programming language over 11 days.

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Source · Sep 4, 2026, 6:21 PM · On Illumora · Sep 4, 2026, 6:27 PM

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Read the source →Anthropic Research — Formalizing Fermat's Last Theorem
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Anthropic Research announced that its Claude AI system has generated the first complete computer-checked proof of Fermat’s Last Theorem. The AI worked largely autonomously over 11 days to write the proof in the Lean programming language. This effort aimed to test Claude's ability to formalize complex mathematical proofs.

Key Points

  • Claude produced the first end-to-end, computer-checked proof of Fermat's Last Theorem.
  • The AI completed this task in 11 days, working largely autonomously.
  • The proof was written in the Lean programming language.
  • Claude generated 13 million lines of Lean code.
  • The process involved proving 29,500 intermediate theorems used in the final proof, out of 30,300 total theorems proved.
  • The proof follows a simplified version of Andrew Wiles's proof from Darmon, Diamond and Taylor.
  • Human input was limited to occasional high-level instructions from researcher Tianyi Peng.

Context

According to Anthropic, the formalization of Fermat's Last Theorem (FLT) was a significant challenge, with previous community efforts, such as one kicked off in 2024 by Kevin Buzzard at Imperial College London, expecting the process to take years. The goal of formalization is to convert mathematical reasoning into a format that computers can automatically check, ensuring correctness beyond doubt. Unlike recent AI work that produced novel mathematics, the novelty in this case is the verification process itself, checking a mathematical proof as one would a computation.

Why It Matters

This development demonstrates a capability for AI systems to significantly accelerate the verification of complex mathematical proofs, potentially reducing the time and effort required for human mathematicians to confirm new results. For builders and researchers, it highlights the potential for AI to assist in ensuring the rigor and reliability of mathematical knowledge bases.

What To Do

  • Note the 11-day duration for Claude's autonomous work on a complex mathematical proof.
  • Observe the scale of the output: 13 million lines of Lean code and 29,500 intermediate theorems.
  • Consider the implications of AI-driven formalization for the verification of mathematical research.
  • Watch for further research from Anthropic on AI's role in formalizing complex logical chains.