Claude Just Formalized a Proof of Fermat's Last Theorem
On September 4, 2026, Anthropic said a research model it describes as roughly comparable to Claude Fable 5.1 had produced a complete machine-checked formalization of Fermat's Last Theorem in the Lean proof assistant, working largely autonomously over 11 days. This is not a new proof of the theorem. It is a translation of the existing proof into code that a computer can check line by line. Below we explain what was done, what the numbers mean, what critics point out, and how to read claims like this.
⚡ Quick facts
- Announced: September 4, 2026, by Anthropic, with the Lean code published on GitHub
- Model: an internal research model Anthropic calls roughly comparable to Claude Fable 5.1, run as dozens of agents
- Duration: 11 days of wall-clock time, largely autonomous, with occasional high-level steering from a human mathematician
- Scale: about 13 million lines of Lean and 30,300 theorems, of which 29,500 appear in the final proof
- Check: uses only Lean's three standard axioms; its statement was checked against Mathlib's statement of the theorem
What was actually done
Fermat's Last Theorem says no positive whole numbers a, b and c satisfy an + bn = cn for any n greater than 2. Andrew Wiles proved it in 1994, with a fix completed with Richard Taylor. That proof is accepted by mathematicians, but it runs to hundreds of pages and rests on decades of earlier work, so no single person can check every step.
According to Anthropic's announcement, its model rewrote the proof in Lean, a programming language in which every definition and logical step is checked by software. It followed a simplified version of the argument written up by Darmon, Diamond and Taylor. Anthropic says the final result depends only on Lean's three standard axioms, and that a separate comparison tool confirmed the statement proved is the same as the statement of Fermat's Last Theorem already in Mathlib, Lean's shared mathematics library.
How the 11-day run worked
Anthropic describes dozens of Claude agents working in parallel inside a harness built on Claude Code. They coordinated through Prove2Me, an open collaborative platform from Tianyi Peng and collaborators at Columbia. Prove2Me tracks the project as a graph of statements to prove and keeps those statements separate from their proofs, so many agents can work on different pieces without stepping on each other. Peng gave occasional high-level instructions; the agents did the line-by-line work.
It did not work first time. Anthropic says early attempts failed because the agents lost track of the state of the project, and work from those runs makes up only about 7% of the final non-boilerplate lines. The company reports roughly 6 billion output tokens over the run.
How big is it, really?
Anthropic reports about 13 million lines of Lean, which it says is more than five times the size of Mathlib, and about 30,300 theorems, 29,500 of which appear in the final proof. Those figures need context. Machine-written formal proofs are usually far longer than human-written ones, so line counts measure volume more than difficulty. The project also built on existing work: Mathlib itself, Kevin Buzzard's Imperial College project to formalize the theorem (started in 2024), and the earlier flt-regular project. Commentators reviewing the public repository noted that over a hundred upstream files are credited to the Imperial project and Mathlib.
Buzzard, who leads the Imperial effort, reviewed the work and, per Anthropic, called it a big step toward automatic formalization of the modern mathematical literature. Coverage from AI Weekly and Let's Data Science framed it the same way: a milestone for verification, not new mathematics.
Our take: how to read a claim like this
The useful questions to ask about any "AI proved X" headline, applied here:
- New proof or checked proof? Checked. The mathematics is Wiles's; the achievement is a complete computer-verifiable version of it.
- Can anyone verify it? Yes, and this is the strong part. The Lean code is public, and anyone can run the checker. You do not have to trust Anthropic's word for the result.
- Does it prove the right statement? Anthropic says its statement matches Mathlib's. That comparison is what stops a proof of a subtly different, easier statement.
- How much was human work? Some: Peng's steering, the Prove2Me platform, and years of community libraries. "Largely autonomous" is fair; "unaided" is not.
- What does it change? If formalization at this speed holds up, checking long proofs becomes much cheaper. That matters for mathematics and, later, for verifying software and AI systems themselves.
For other Anthropic model news, see our explainer on Claude Haiku 5.5.
Sources
- Anthropic: Formalizing Fermat's Last Theorem
- GitHub: anthropics/fermats-last-theorem
- AI Weekly coverage
- Let's Data Science coverage
Frequently asked questions
Did Claude prove Fermat's Last Theorem?
No new proof was found. Anthropic's model translated the existing Wiles proof, in the simplified Darmon–Diamond–Taylor version, into Lean code that a computer can check step by step.
What is Lean?
Lean is a programming language and proof assistant. Mathematical definitions and proofs written in it are checked by software, so a finished Lean proof does not depend on a human reviewer catching every error.
How long did it take?
Anthropic says about 11 days of wall-clock time, with dozens of agents working in parallel and a human mathematician giving occasional high-level direction.
Which model did it?
An internal research model that Anthropic describes as roughly comparable to Claude Fable 5.1, running in a multi-agent harness built on Claude Code.
What is Prove2Me?
An open collaborative platform from Tianyi Peng and collaborators at Columbia. It tracks a proof project as a graph of statements and keeps statements separate from proofs, so many agents can work at once.
Can I check the proof myself?
Yes. The Lean code is published on GitHub under anthropics/fermats-last-theorem, and anyone with Lean installed can run the checker on it.