What Claude Actually Did
Anthropic said on September 4 that Claude produced the first complete, computer-checked proof of Fermat's Last Theorem, working through the Lean 4 proof assistant for 11 days with only high-level guidance from a human researcher. The system generated 13 million lines of Lean code and proved more than 30,000 supporting theorems, of which 29,500 made it into the final, verified proof, using an internal research model that consumed roughly six billion output tokens across dozens of agents running in parallel on the Prove2Me platform.
The underlying mathematics is not new. Andrew Wiles proved Fermat's Last Theorem in 1995, and Claude formalized a later simplification of that proof by Darmon, Diamond, and Taylor, turning a 129-page argument that took the mathematical community months to check by hand into a form a computer can verify line by line. Mathematician Kevin Buzzard, who reviewed the output, told Anthropic the result was a big step towards automatic formalization of the modern mathematical literature, achieved in far less time than he had expected.
Why This Is a Cost Story, Not a Math Story
The number that matters here is not 13 million lines, it is 11 days. Formal verification, the practice of proving a piece of mathematics or software correct instead of testing it and hoping, has always been slow and expensive to do by hand, and formalizing a result of this size has previously taken specialist teams years of labor. That cost is exactly why so little of the world's safety-critical software carries a formal proof of correctness at all, and an automated system that can do comparable work in under two weeks changes the arithmetic for any European engineering organization that certifies systems under standards such as ISO 26262 for cars or DO-178C for aircraft, where formal methods are already used but rationed because of their price.
Anthropic's own account is candid about the failure rate behind that headline number: about 7 percent of the non-boilerplate code came from attempts that did not work, discarded along the way to the final proof. That is a normal part of how formal verification has always progressed, machine or human, but it deserves stating plainly, because a 13-million-line success invites the opposite impression.
The Boundary Nobody Should Skip
Claude formalized an existing proof, it did not discover a new one, and that difference matters more than the achievement itself once anyone tries to put engineering weight on it. Fermat's Last Theorem worked as a demonstration precisely because mathematicians had already agreed, for three decades, on what the correct proof looked like, which meant Claude's job was to translate a known argument into a language a machine could check, not to decide whether the argument was right in the first place.
A safety case for a braking system or a cryptographic protocol starts from a harder question: what does correct even mean here, and has anyone specified it accurately enough for a formal method to check it against. Automated formalization can now shrink the second half of that problem dramatically. It does nothing for the first half, and any organization that reads this result as a license to skip specification work rather than verification work has misread it.
Read next: 87 Years Fell to an Answer Anyone Can Check | Anthropic Moves Your Safety Logs Into Your Own Cloud
