Claude Just Produced the First Computer-Checked Proof of Fermat's Last Theorem

On September 4, Anthropic disclosed that Claude, working largely autonomously over 11 days, produced the first end-to-end, computer-checked proof of Fermat’s Last Theorem in the Lean proof assistant. Along the way it wrote 13 million lines of Lean code and proved 29,500 intermediate theorems, more than five times the size of Mathlib, the community library those theorems build on.

This matters less because of the theorem itself, Andrew Wiles already proved Fermat’s Last Theorem in 1995, and more because of what got checked. Wiles’s proof ran 129 pages and took a team of expert reviewers over a year to verify; two months into that process, a reviewer’s question exposed a gap that took Wiles another year to close. Formalizing a proof in Lean removes that ambiguity entirely: either the proof assistant accepts every step down to Lean’s three basic axioms, or it does not. What used to take human referees years now took a fleet of agents eleven days, and that compression is the actual story for anyone tracking what AI does to the economics of verification.

What actually happened#

A team of Claude agents worked against a shared plan, not in isolation. Early attempts failed because agents lost track of the project’s state and stopped collaborating effectively; those failed attempts still contributed about 7% of the non-boilerplate lines in the final proof. The breakthrough came from switching to Prove2Me, an open collaborative platform built by Anthropic researcher Tianyi Peng and collaborators at Columbia University. Prove2Me maintains a directed acyclic graph of theorem statements so agents can see what depends on what, splits statements from proofs into separate files to keep Lean compilation fast, and keeps a natural-language description of each theorem so agents can find and reuse existing work instead of re-deriving it.

The numbers are large enough to matter for planning, not just bragging rights. Dozens of agents proved 30,300 theorems total, using 29,500 of them in the final proof, while consuming roughly six billion output tokens from an internal research model comparable to Claude Fable 5.1. Human input was limited to occasional high-level nudges from Peng, things like “push Mazur’s theorem to be done soon.” A separate comparator tool confirmed the formalized statement matches Mathlib’s own statement of Fermat’s Last Theorem, so the result is not just internally consistent, it is checkable against an independent, human-curated reference.

Kevin Buzzard, the Imperial College London mathematician who has led the community’s own multi-year FLT formalization effort since 2024, reviewed the proof and called it “an extraordinary autoformalization achievement.” He added that if automatic formalization of Fermat’s Last Theorem is possible now, the field has taken a real step toward automatic formalization of the modern mathematical literature, with the side effect of catching errors already sitting in the published record and lightening the load on referees who currently have to check new results by hand.

Try it: sizing a formalization run#

Move the slider to estimate time and token cost.

At 1,000 theorems, roughly the scale of a single graduate-level topic area rather than a landmark theorem, this puts a project at under half a day of throughput and a few thousand dollars in tokens, which is the real signal here: formalization is moving from a multi-year specialist undertaking to something closer to a line item.

What this means for you#

If you work anywhere near formal methods, theorem proving, or even just AI-generated proofs you cannot fully verify by hand, Prove2Me’s DAG-based coordination is worth studying regardless of whether you use Claude: the pattern of externalizing shared state so parallel agents do not step on each other’s context is the same one that shows up in large-scale agentic coding, not just mathematics. Anthropic is explicit that this is a verification story, not a discovery story, Claude did not find new mathematics here, it checked seventeen-year-old mathematics rigorously enough that a human expert signed off on it in days instead of years. My own next step is reading through the published proof walkthrough on GitHub to see how much of the DAG-orchestration pattern is reusable for verifying AI-generated code changes rather than AI-generated math.