Claude wrote a 13.4-million-line, machine-checked proof of Fermat's Last Theorem in 11 days -- beating a five-year, £1 million human project built to do exactly that

Anthropic announced on September 4 that an internal research model -- roughly comparable in capability to Claude Fable 5.1 -- spent 11 days writing a complete, machine-checked proof of Fermat's Last Theorem in the Lean 4 programming language, working largely unsupervised through a multi-agent framework called Prove2Me. The headline framing across most of the coverage that followed was some version of "AI solves 350-year-old math problem." That framing is wrong in the way that matters most to a mathematician, and Kevin Buzzard -- the Imperial College London professor whose own funded project exists to do this exact work -- said so himself, in his own words, on his own blog, within a day of the announcement.

Fermat's Last Theorem was proven in 1995, by Andrew Wiles, in a 129-page argument that took mathematicians years to fully digest and confirm. What Claude produced this month is not a new proof of the theorem. It is a formalization -- a translation of an already-accepted argument into a language a computer can mechanically check line by line, against nothing but the axioms of mathematics itself, with no step left implicit and no gap papered over by human intuition. That distinction is the whole story, and most of the coverage of this achievement skipped it.

Buzzard is not a neutral bystander to this story. Since 2019 he has led a Lean formalization effort at Imperial College London, and in 2024 that project secured £1 million in EPSRC funding over five years specifically to formalize a modern, 21st-century reformulation of the Wiles argument -- incorporating later refinements by Khare-Wintenberger and Kisin -- into Lean's shared mathematics library, Mathlib. He learned that Anthropic had beaten him to a working Lean proof of the theorem while at a music festival in Wales, buried under nearly a thousand unread emails. His blog post announcing it is titled, plainly, "FLT: Anthropic has beaten me to it."

Buzzard's technical verdict, after compiling the code himself and running the comparator tool that checks the formalized theorem statement against Mathlib's own canonical version: it checks out. "I've compiled the code base and run comparator on it -- it checks out," he wrote, adding that he'd already been "99.9% sure that the proof of FLT is OK" going in, because the underlying mathematics was never actually in doubt -- only whether a machine could be made to verify every step of it without a human filling gaps by hand. What he does dispute is the idea that this represents new mathematical knowledge.

The formalization just faithfully follows the early literature on the proof and adds nothing to mathematical knowledge.

None of that makes the achievement small. Prove2Me -- built by Tianyi Peng at Columbia University -- coordinated multiple Claude agents against a shared, directed graph of theorem statements, letting different agents work on separate branches of the proof without duplicating effort or losing track of what had already been established elsewhere in a 13.4-million-line codebase. That coordination problem, not the mathematics itself, is what an earlier attempt failed at: Anthropic says a prior effort without Prove2Me's shared dependency graph produced only about 7% of the useful, non-boilerplate code before the team adopted the new framework -- which eventually proved 30,300 theorems in total, of which roughly 800 turned out unused in the final, 29,500-theorem proof. (The proof also builds on, rather than replaces, years of prior human work -- it adapts pieces from Buzzard's own Imperial College project and from the separate 2024 regular-primes formalization, following a simplified exposition of Wiles's argument by mathematicians Darmon, Diamond and Taylor rather than reproducing Wiles's original 1995 text directly.)

That coordination achievement is also exactly what should inform how much weight a reader puts on the general skepticism this kind of story usually invites. Fields Medalist Terence Tao has warned, in broader remarks about AI and mathematics, that AI-generated proofs can "look superficially flawless" while hiding a "subtle, plausible-looking error" -- reinforcement learning trains models to produce text that resembles correct reasoning, not text that is guaranteed correct. His example: a model confidently asserting that all odd numbers are prime. Tao's own remarks, notably, weren't made about this specific proof -- but his broader argument for why formal verification tools matter applies directly to it.

Buzzard's own conclusion is not that his project is finished, or that his job is now obsolete. "A naive reaction to the news above is that I no longer have any work to do," he wrote. "This is not the case." His EPSRC funding was committed to formalizing the *modern* reformulation of the proof -- the one built on Khare-Wintenberger and Kisin's later refinements -- and to building the reference documentation that lets other mathematicians navigate it. Claude's proof, by contrast, followed an older, simpler exposition. The two efforts sit closer to parallel tracks toward the same destination than one making the other redundant.

What genuinely changed this week, in Buzzard's own assessment, is a claim about capability rather than about this one theorem: "AI autoformalization artefacts are now robust enough to be built upon." If an AI system can be pointed at a well-documented, already-proven 30-year-old result and produce a working, mechanically verified Lean proof of it in 11 days, the more interesting question -- one this result does not answer -- is what happens when the same approach is pointed at something nobody has finished checking by hand yet. That test hasn't been run. This one wasn't it.