Anthropic says dozens of Claude agents worked almost autonomously for 11 days to produce the first complete, machine-verified proof of Fermat's Last Theorem in the Lean proof assistant. The project generated 13 million lines of code and proved over 30,000 theorems after early agents lost track of the proof and had to be coordinated through a shared dependency graph called Prove2Me.

Anthropic says dozens of Claude agents worked largely on their own for 11 days to produce a complete, machine-checked proof of Fermat's Last Theorem in the Lean proof assistant, generating 13 million lines of code and burning through 6 billion tokens along the way.

Fermat scribbled his famous claim in a margin in 1637 and said he had a proof too big to fit there. Andrew Wiles needed seven years and 129 pages to actually deliver one, in 1995. Anthropic says a swarm of Claude agents just did something almost as remarkable: they took Wiles's proof and translated it into a form a computer can check step by step, and they did it in 11 days.

According to Anthropic's research team, dozens of Claude agents wrote about 13 million lines of code in Lean, the proof assistant built originally at Microsoft Research. They ran on an internal model that Anthropic says performs roughly on par with Claude Fable 5.1. That is five times the size of Mathlib, Lean's core math library, which human contributors have built up over more than a decade. Along the way, they proved 30,300 theorems. About 29,500 of them made it into the final proof. The whole run burned 6 billion tokens.

That's an enormous amount of effort. All spent re-deriving a result mathematicians already trust.

How the swarm actually pulled it off

Formalizing a proof doesn't mean discovering new math. It means re-deriving every logical step of an already-accepted proof in a language a computer can verify clause by clause, with no room for the small gaps and hand-waves that occasionally slip into published mathematics. Wiles's proof is one of the most scrutinized results of the twentieth century, and formalizing it by hand was still expected to take mathematicians years. Kevin Buzzard is the Imperial College London mathematician who has led a volunteer project to formalize the theorem in Lean since 2022, with more than 60 contributors submitting verified code. He called Anthropic's result an "extraordinary autoformalization achievement" that "proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics."

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The first attempts didn't go well. Anthropic says its agents made real early progress, then lost track of what had already been proven and what still needed work. Each agent held its own mental model of the sprawling proof in its context window. Those models drifted apart, and the effort collapsed into noise: agents duplicating work, contradicting each other, or building on theorems nobody had actually finished.

The fix came from a tool called Prove2Me. It's open-source, built by Tianyi Peng and collaborators at Columbia University. Instead of asking each agent to hold the entire project in its head, Prove2Me keeps a directed acyclic graph of every theorem statement the proof still needs. It shows which ones are ready to attempt, and lets an agent grab an open node, prove it, and publish the result for the rest to build on. It's a shared to-do list. It stands in for the memory none of the agents could hold alone. Anthropic had already tested the idea at a smaller scale, using three Claude Max subscriptions to formalize Vinogradov's Three Primes Theorem in three days, before pointing the same setup at Fermat.

Coordination, not raw model horsepower, was the unlock.

What the proof does and doesn't show

Anthropic is careful about what the result does and doesn't show. The company's own writeup calls the 13-million-line proof likely much longer than it needs to be, and says formalization should complement human-readable mathematical exposition, not replace it. Nobody at Anthropic is claiming Claude discovered anything new about elliptic curves or modular forms. What it did is take math the field already trusts and remove any remaining doubt that every step actually holds together logically. That's a tedious, exacting job, and until recently it was assumed to need years of specialist labor.

Frankly, the harder question isn't whether an AI swarm can formalize a proof mathematicians already believe. It's whether the same shared-memory trick that got Claude through Fermat scales to problems nobody, human or machine, has solved yet. Anthropic isn't claiming that leap. For now the record stands: dozens of agents, 11 days, 13 million lines of Lean code, and one 389-year-old margin note finally checked by machine from top to bottom.

Also read: Seattle Times and Newsday Sue OpenAI and Microsoft Over News Scraping * Z.ai's New GLM-5.3-Flash Model Runs 3.3 Times Faster on a Single Workstation * Oxford Professor Warns AI Is Plausibly Close to Runaway Self-Improvement

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