Anthropic: Claude formalizes Fermat’s Last Theorem in Lean

Anthropic published that Claude produced a computer-checked proof of Fermat’s Last Theorem in Lean after working largely autonomously for about 11 days — a verification story, not a new human proof or a Clay prize.

Checking a famous proof at Lean scale is a verification filing with Anthropic’s own numbers. It is not a new human proof of Fermat’s Last Theorem, and it is not a Clay award.

Anthropic published “Formalizing Fermat’s Last Theorem.” The company says Claude produced the first complete computer-checked proof of Fermat’s Last Theorem in Lean. Lean is a programming language used to check that a math proof has no holes. That research post is the primary.

Anthropic says Claude worked largely autonomously for about 11 days and produced the first end-to-end, computer-checked FLT proof in Lean. FLT is Fermat’s Last Theorem. Those autonomy claims are the company’s — not an independent audit.

Anthropic’s figures on the same page: 13 million lines of Lean; 29,500 intermediate theorems in the final proof; 30,300 theorem proofs along the way; more than 5× the size of Mathlib, Lean’s main mathematics library. Those are company figures.

Anthropic says the proof follows a simplified version of Wiles’s path from Darmon, Diamond, and Taylor. Human math input, on the company’s account, was limited to occasional high-level instructions from Tianyi Peng, an Anthropic researcher whose Columbia group builds AI formalization tools.

The finished proof was checked by Lean, Anthropic says. It uses Lean’s three standard axioms. A comparator confirmed the statement matches Mathlib’s own statement of FLT. Treat the Lean check and the comparator as Anthropic’s verification claims.

The effort succeeded after switching to Prove2Me, an open collaborative platform designed by Tianyi Peng and Columbia collaborators. Anthropic says it kept a DAG — a directed acyclic graph, meaning a map of which claims depend on which — of theorem statements, split statement and proof files, and attached plain-language descriptions for search. How that graph is stored is in Sources. Earlier attempts failed. Anthropic says those failed efforts contributed about 7% of the non-boilerplate lines in the final proof.

Kevin Buzzard, quoted on the page: the autoformalization “proves Fermat’s Last Theorem with no assumptions other than the axioms of mathematics,” that the artefact is “multi-layered” and “robust enough to be built upon,” and that if FLT autoformalization is possible now, “we have taken a big step towards automatic formalization of the modern mathematical literature.” Those are Buzzard’s comments as published by Anthropic.

Anthropic frames the novelty as verification — checking a known proof the way a calculator checks a sum — not new mathematics like recent AI-driven Riemann hypothesis work. This is not a new human proof of FLT, and it does not replace Wiles. FLT is not a Clay Millennium Prize problem; no Clay prize was awarded.

Also on the same post: the run used about six billion output tokens from a general-purpose internal research model Anthropic says is roughly comparable to Claude Fable 5.1. The full proof is on GitHub (anthropics/fermats-last-theorem). Acknowledgments name the Imperial College London FLT project, flt-regular, Lean, and Mathlib.