Claude Agents Formalize Fermat's Last Theorem in Lean
Anthropic says Claude agents machine-checked Wiles' proof in 11 days, producing roughly 29,500 intermediate theorems along the way.
Symbolic image: in a data center, a person slides a server module into a rack while status lights signal a verification run in progress.
No AI proved Fermat's Last Theorem here — Claude agents translated Andrew Wiles' 1995 proof into 13 million lines of Lean code that a computer can check step by step.
At a glance
- 13 million lines of Lean code and roughly 29,500 intermediate theorems, produced in 11 days by dozens of Claude agents.
- Compute cost: about 6 billion output tokens, which Anthropic estimates at $100,000 to $300,000.
- The template was not Wiles' 129-page original but the simplified account by Darmon, Diamond and Taylor.
- Kevin Buzzard of Imperial College London compiled the code himself; it uses only Lean's three standard axioms.
- Buzzard's own FLT project has run since 2024, is funded through 2029 and has an 86-page blueprint.
Anthropic says Claude agents have produced the first fully machine-checked version of Fermat's Last Theorem. The output is 13 million lines of code for the Lean proof assistant, covering roughly 29,500 intermediate theorems. What came out is a verification artifact, not a new theorem.
What a proof assistant actually demands
Andrew Wiles settled the theorem in 1995, some 358 years after Fermat left his claim in a margin. Human-written proofs lean on steps that specialists treat as obvious and skip. Lean refuses that shortcut and wants every inference spelled out. Filling those gaps at scale was the job the agents were given.
How the run was set up
The agents did not work from Wiles' 129-page original but from the streamlined account by Darmon, Diamond and Taylor. They ran on Prove2Me, a platform built by Columbia University researchers, and drew on Mathlib, the community library of formalized mathematics. Tianyi Peng coordinated the effort, and Anthropic describes the human contribution as occasional high-level direction. The code was finished after 11 days.
Verified, and not verified
The code compiles in Lean and relies only on the system's three standard axioms. Kevin Buzzard of Imperial College London compiled it himself and used a comparator to check it against Mathlib's statement of the theorem. He calls the work a large step toward automating the formalization of mathematical literature, while stressing that it adds nothing mathematically new. A wider judgment from the research community is still largely missing.
The bill
Anthropic puts the run at about 6 billion output tokens and estimates compute costs at $100,000 to $300,000. It does not publish an exact figure. The Claude version behind the agents is not named in the reporting either. The proof itself sits in a public GitHub repository.
How it compares with Buzzard's own project
Buzzard has led a separate formalization of Fermat's Last Theorem since 2024, funded through 2029. Its blueprint runs to 86 pages and targets the modern, far broader route through the proof. Anthropic's run covers the older and narrower path, so it does not replace that project. It does show how fast formalization work can now move.
What is confirmed so far is the engineering: the code builds and it checks out. Whether mathematicians accept the formalization as complete is still open. This report rests on a single independent newsroom.
FAQ
Did an AI prove Fermat's Last Theorem?
No. Andrew Wiles proved it in 1995. The Claude agents rewrote that proof so a computer could check every single step of it.
What is the Lean proof assistant?
Lean is a programming language paired with a checking system for mathematics. A statement written in Lean is verified line by line, with no step left implicit.
How much did the formalization cost?
Anthropic estimates compute costs of $100,000 to $300,000 for roughly 6 billion output tokens, and has not published an exact figure.
