Andrew Wiles proved Fermat's Last Theorem in 1994, and the proof is long enough that only a few dozen people have ever checked the whole thing. A machine has now checked all of it, from a formalisation a model wrote in 11 days.

The work was done in Lean, a language where every step of an argument is verified by the computer instead of being left to a reader. Claude produced 13 million lines and proved 29,500 intermediate theorems, out of 30,300 produced in total, which is more than five times the size of Mathlib, the standard library Lean users build on. Anthropic puts the cost at about six billion output tokens from an internal general purpose research model, running largely autonomously across eleven days. Kevin Buzzard of Imperial College called it an extraordinary autoformalization achievement.

Why this one is different

Machines have checked proofs before, and models have written proofs before. The size is the whole of the difference. A formal proof cannot skip a step: everything a mathematician leaves to the reader as obvious has to be written out and checked, and for this proof that came to thirteen million lines. Formalising Wiles was understood to be years of human work for exactly that reason, which is why it had not been done.

Wiles proved it. This is the first time a machine has checked that he was right.

How we got here

1. 1637Fermat writes in the margin of a book that he has a proof, and that the margin is too small to contain it.
2. 1994Andrew Wiles publishes a proof after seven years of work. A gap is found and closed the following year.
3. 3 Sep 2026An AI outscores every human at the International Olympiad in Informatics, on problems that come with an answer key.
4. 4 Sep 2026A model writes a proof with no answer key, in a form a computer can check line by line.

What it does and does not mean

Claude did not prove Fermat's Last Theorem. Wiles did, in 1994, and this is a translation of an existing argument into a language a machine can check, not a new result. It was also not unassisted: it ran on Prove2Me, a platform built by Tianyi Peng's group at Columbia, it took occasional high level human instruction, and it built on Mathlib and on a simplified exposition by Darmon, Diamond and Taylor. Anthropic adds two limits of its own, which is unusual enough to be worth noting: the proof is likely much longer than it needs to be, and about 7% of the non-boilerplate lines are the residue of attempts that failed. What it does show is that the translation step, the part that has kept most of modern mathematics out of reach of machine checking, is no longer the thing that makes it impossible.