Claude Produces First Formalized Proof of Fermat's Last Theorem in 11 Days
Anthropic announced that Claude has produced the first complete formalized proof of Fermat's Last Theorem, converting Andrew Wiles's 1995 proof into a machine-checkable form in Lean. In an experiment led by researcher Tianyi Peng, Claude worked largely autonomously for 11 days, generating over 13 million lines of Lean code (some reposts cite about 13.4 million) — the largest Lean formalization ever — for a project experts thought would take years.
Confirmed
- Anthropic's official account announced the result and published the GitHub repo anthropics/fermats-last-theorem, a complete machine-checked proof in Lean 4 (Lean 4.33.1, Mathlib v4.3)
- Along the way, roughly 29,000–29,500 intermediate theorems and lemmas were formalized; Anthropic says Claude ran mostly autonomously, the experiment was led by Tianyi Peng's team, and some reposts mention the prove2.me platform
- Mathematician Kevin Buzzard (Xena project) confirmed this is a complete Lean formalization of FLT and the final item on Freek Wiedijk's list of 100 formalization challenges, closing a 20-year benchmark
- Wiles's original proof ran 129 pages; jdlichtman tweeted that within months all known mathematics could be formalized, noting he had proposed taking on full FLT formalization to Buzzard last fall
- Community statistics relayed by sebpaquet suggest this represents a five-order-of-magnitude jump in automated formalization output versus 18 months ago; he also noted Buzzard had originally received 5 years of funding to formalize FLT
- The news spread widely via Reddit users and scholars including Alex Kontorovich, marc lelarge, and Ethan Mollick, widely viewed as a landmark in recent AI mathematical capability
- Background: FLT was posed by Fermat in 1637, remained open for over 350 years, and was first proved by Andrew Wiles in 1995
Unconfirmed
- Reinforcement-learning pioneer Csaba Szepesvari publicly asked Anthropic how one knows the formalization is correct, calling for an honest discussion of the verification work and its limits; no detailed response from Anthropic has been seen
Why it matters
- A milestone for AI in formal mathematics, showing frontier AI can complete large-scale mathematical engineering experts estimated would take years
- The proof is computer-verified, so reliability does not depend on human review, setting a demonstration for the mechanization of mathematical foundations
- Completing the last Wiedijk challenge closes a long-standing community goal and may accelerate routine AI-assisted proving in research, while also prompting debate about verification methods and limitations
2026-09-05 ~ 2026-09-07 · 52 related posts
Primary sources
- [source] 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
- Anthropic uses AI to formalize Fermat's Last Theorem proof — Unique-Bake-5796 · 2026-09-05
- RL Pioneer Csaba Szepesvari Grills Anthropic on Claude's Fermat Proof — CsabaSzepesvari · 2026-09-05
- Claude formalizes Fermat's Last Theorem, says all known math next — basedjensen · 2026-09-05
- Daily digest: Claude proves Fermat's Last Theorem in Lean, Apple's biggest launch wave — APPSO · 2026-09-05
- Claude formalizes Fermat's Last Theorem in 11 days, a project granted 5 years to a human mathematician — Singularitarian · 2026-09-05
- Anthropic formalizes Fermat's Last Theorem in Lean: 12M+ lines, 29k theorems — doodlestein · 2026-09-06
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