# Anthropic's Claude formalizes Fermat's Last Theorem proof in 11 days

Digest AI · Research · published 2026-09-07T00:00:00Z

Canonical: https://digestai.news/story/anthropic-s-claude-formalizes-fermat-s-last-theorem-proof-in-11-days

## Summary

Anthropic announced that its AI model, Claude, has successfully formalized the proof of Fermat’s Last Theorem into computer-verified code. This achievement marks a significant milestone in mathematical AI, as the model translated the complex 1994 proof by Andrew Wiles and Richard Taylor into 13 million lines of Lean code. The process took only 11 days, a task estimated to require approximately 10 years of human effort.

Mathematicians, including Alex Kontorovich from Rutgers University and Kevin Buzzard from Imperial College London, described the result as a breakthrough that demonstrates the rapidly improving capability of AI to handle high-level mathematical reasoning. Buzzard noted that this task was an order of magnitude more difficult than previous AI formalization successes, such as the certification of Maryna Viazovska’s sphere-packing work earlier this year.

The development suggests that AI will play a crucial role in verifying existing mathematical knowledge and potentially discovering errors in established results. Experts believe that at the current pace of progress, AI systems may soon be able to scrutinize the entire library of mathematical proofs, fundamentally changing how mathematical validity is established and checked.

## Key points

- Claude formalized Fermat’s Last Theorem into 13 million lines of verified Lean code in 11 days.
- The task was estimated to take humans 10 years, highlighting a massive efficiency gain for AI.
- Experts view this as a major step toward AI verifying the entire library of mathematical knowledge.

## Why it matters

This demonstrates AI's capability to handle complex, high-level logical reasoning and formal verification, potentially automating the validation of mathematical proofs and accelerating research in mathematics and related fields.

## Sources

1. [Anthropic AI ‘formalizes’ proof of Fermat’s last theorem — a milestone for mathematics](https://nature.com/articles/d41586-026-02822-9) (Nature Machine Learning, 2026-09-07, primary source)

## Cite

Digest AI, "Anthropic's Claude formalizes Fermat's Last Theorem proof in 11 days", 7 September 2026, https://digestai.news/story/anthropic-s-claude-formalizes-fermat-s-last-theorem-proof-in-11-days

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