On 4 September Anthropic published a proof of Fermat's Last Theorem checked end to end in Lean. Claude worked largely on its own for 11 days, wrote 13 million lines and proved 29,500 intermediate theorems used in the final result. The community expected the formalisation to take years.
- The proof follows a simplified version of Wiles's route; mathematical input from humans was limited to occasional high-level guidance from researcher Tianyi Peng.
- It is checked by Lean using only its three standard axioms; Kevin Buzzard, who has led the community project since 2024, reviewed it.
- About six billion output tokens from an internal model comparable to Claude Fable 5.1.
One hundred and twenty-nine pages. That is the length of Wiles's first proof from 1995, and checking it took several mathematicians months.
The new proof is 13 million lines of code, and a machine checks it, step by step, without skipping the obvious.
It matters what exactly is new. Claude did not discover a new proof - the theorem was proved more than thirty years ago. What is new is the verification: turning a human proof into chains that a machine walks from start to finish.
And one detail won me over more than the numbers. Anthropic itself writes that the proof is probably much longer than it needs to be. Mathlib is tight and reviewed; this is clumsy but correct. As a first version of something people expected to take years, clumsy and correct is enough.
For anyone who teaches or writes mathematics, the most telling is their last example: formalising Vinogradov's three primes theorem in three days, with three personal Claude Max plans. That is no longer a project only for a lab with a budget.