Claude completes first formal proof of Fermat's Last Theorem in Lean
Anthropic announced that Claude has completed the first full formalization of Fermat's Last Theorem (FLT)—transforming Andrew Wiles's classic 1995 proof into a machine-verifiable form in Lean. In an experiment initiated by researcher Tianyi Peng, Claude worked nearly autonomously for 11 days, producing over 13 million lines of Lean code (some reports say around 13.4 million), the largest Lean formalization proof ever. Experts had expected the project to take years.
Confirmed
- Anthropic's official account announced the result and published the GitHub repo anthropics/fermats-last-theorem, providing a complete machine-checked Lean 4 proof built on Mathlib (Lean 4.33.1, Mathlib v4.3)
- Along the way, roughly 29,000–29,500 intermediate theorems/lemmas were formalized, covering several areas never formalized before
- Mathematician Kevin Buzzard (Project Xena) independently confirmed in a post that an internal Anthropic model completed the full Lean formalization of FLT via the prove2.me platform—also crossing off an item on Freek Wiedijk's famous list of "100 formalization challenges"
- Background: FLT was proposed by Fermat in 1637, remained open for over 350 years, and was first proven by Andrew Wiles in 1995
Why it matters
- This is a milestone for AI in formal mathematical proof, showing that frontier AI can now undertake large-scale mathematical projects experts expected to take years
- Formal proofs are computer-verified, so reliability doesn't depend on human review—a demonstration of what mechanizing mathematical foundations can achieve
- Completing a long-standing goal of the formalization community (Wiedijk's list) may accelerate the normalization of AI-assisted proof in mathematical research
2026-09-05 ~ 2026-09-05 · 20 related posts
Primary sources
- Claude completes first formalized proof of Fermat's Last Theorem in 13M lines of Lean — AnthropicAI ·
- Claude writes first computer-checked proof of Fermat's Last Theorem in 11 days — sammcallister ·
- Anthropic model formalizes Fermat's Last Theorem in Lean, 13.4M lines closing 100-theorem benchmark — littmath ·
- Anthropic posts a complete Lean 4 machine-checked proof of Fermat's Last Theorem — scaling01 · 2026-09-05
- [source] Claude completes first formalized proof of Fermat's Last Theorem in 13M lines of Lean — AnthropicAI · 2026-09-05
- Anthropic's Machine-Verified Fermat Proof Spans 13M+ Lines and Formalizes 29,000+ Theorems — Dr_Singularity · 2026-09-05
- Anthropic announces it has formalised Fermat's Last Theorem — Wonderful_Buffalo_32 · 2026-09-05
- Anthropic uploads machine-verified Lean 4 proof of Fermat's Last Theorem — Chris_Armstrong · 2026-09-05
- Anthropic model formalizes Fermat's Last Theorem in Lean in 11 days, 13.4M lines of proof — sammcallister · 2026-09-05
14 near-duplicate retellings: sammcallister · Dr_Singularity · scaling01 · Dr_Singularity · Dr_Singularity · littmath · burny_tech · dioscuri · littmath · rohanpaul_ai · rohanpaul_ai · marc_lelarge · AlexKontorovich · AlexKontorovich