Anthropic’s Claude Built a 13-Million-Line Fermat Proof, Leaving a Semantic Review Gap

Anthropic’s Claude reportedly generated an end-to-end Lean 4 formalization of Fermat’s Last Theorem in 11 days, creating a large formal proof that software can mechanically check. That is a meaningful new route to verification, not a new solution to the theorem.

Formalization converts mathematical reasoning into explicit steps a computer can check, including steps that conventional papers leave unstated. This artifact follows an established version of Wiles’s argument through Frey curves, Ribet’s theorem and Taylor-Wiles patching. Kevin Buzzard says it follows the Darmon–Diamond–Taylor exposition rather than the modern proof exposition he is developing.

The system divided a vast proof into smaller jobs

Dozens of Claude agents coordinated through Prove2Me to define concepts, prove intermediate results and assemble the final proof. The platform used a directed graph of theorem dependencies, separated theorem statements from proofs, and attached natural-language descriptions to help agents find relevant lemmas. The effort reportedly consumed about 6 billion output tokens from an internal research model described as roughly comparable to Claude Fable 5.1.

A checked artifact is not the same as understood mathematics

Lean’s kernel accepted the proof using only its three standard axioms, and nanoda, an independently implemented Lean kernel in Rust, also checked it. The artifact reportedly contains no sorry placeholders, added axioms or native_decide escape hatches. Those checks establish that the formal result follows under the specified rules.

They do not determine whether each intermediate lemma’s name matches its claimed mathematical meaning. Buzzard, who says he compiled the repository and ran Comparator successfully, argues that the work adds essentially no mathematical content—but demonstrates that AI could formalize extensive literature and expose incomplete or implicit arguments.

The cost of reproducible checking

• A from-scratch build reportedly takes about five and a half hours across 96 CPU cores, peaks at 153 GB of memory, and requires about 15 hours for a one-core nanoda replay.
• The repository is described as verbose and machine-flavored; about 7% of its non-boilerplate lines reportedly came from failed attempts that remained in the code.

A smaller Prove2Me experiment reportedly used three Claude Max plans to formalize Vinogradov’s Three Primes Theorem in three days. Buzzard’s own project aims to create a human-explorable document about the modern proof, underscoring that readable explanation remains a separate deliverable from checked code.