Claude formalizes Fermat's Last Theorem in Lean 4

It is worth being precise about what happened here. Claude's agents did not discover a new proof of Fermat's Last Theorem - they translated Andrew Wiles' original 1993/1995 proof (completed with Richard Taylor) into a form that a computer can mechanically verify, checked against only Lean's three standard axioms. ^[1]That distinction matters because the hard mathematical insight was already accepted by the field three decades ago; what Claude's agents contributed was the enormous, tedious labor of encoding every logical step so a proof assistant can check it line by line. Even Tianyi Peng, who designed the coordination platform that made the run possible, hedged his confidence accordingly: "I'm 99% sure, but it's hard to be 100% certain about a proof this long." ^[1]

That hedge lines up with how the broader mathematics community appears to be reading the result: reaction ranged from astonishment at the sheer speed of the run to pointed scrutiny of how much of the achievement rests on human-authored Lean library structure Claude was able to reuse, with the dominant framing being formalization throughput rather than mathematical discovery. ^[2]That framing is reinforced by a 2025 arXiv paper that had only managed to formalize Fermat's Last Theorem in Lean for the narrower special case of regular primes - a reminder of how much scaffolding already existed for Claude's agents to build on rather than invent from scratch. ^[3]

A proof this size cannot be trusted just because Claude's agents say it compiles. Anthropic's team ran a from-scratch Lean 4.33.1 kernel compile across all 60,475 modules of the final build, and then had a second, structurally independent kernel - nanoda, written in Rust - re-check more than 1 million declarations from the ground up; both passes returned zero errors. ^[4]Running two differently-implemented kernels against the same claim is the standard defense against a bug in any single kernel silently rubber-stamping a false statement, and it is notable that roughly 7% of the non-boilerplate lines in the final build are not part of the proof at all but failed multi-agent attempts still retained in the build. ^[4]

That double-kernel design is exactly what came up when the result hit X and Reddit. Commenters drew a direct line to a well-known prior incident in which a bug in Lean's trusted kernel had been exploited to construct a fake formal "proof" of the Collatz conjecture, and the consensus in the discussion was that this FLT result is not vulnerable to the same class of exploit, precisely because it does not rely on a single kernel's say-so - the from-scratch recompile plus the independent nanoda cross-check would have to both fail identically for a bad theorem to slip through. The Lean project's own official account added a striking framing of its own, calling the result "the largest Lean proof ever constructed" - a claim that lines up with the roughly 13 million lines and 30,300 intermediate theorems Anthropic reported, more than five times the size of Mathlib itself.

The most human part of this story belongs to Kevin Buzzard. The Imperial College mathematician has spent years running an EPSRC-funded, community-staffed effort to formalize Wiles' proof in Lean by hand, a project funded through 2029 and built around a route through Khare-Wintenberger and Kisin that Richard Taylor himself helped plan. ^[5]Reddit discussion pointed to Buzzard's own blog post on the news, reportedly carrying a title to the effect of him having been "scooped" - a mathematician who had committed years to painstakingly formalizing this exact theorem watching an AI system finish the job in eleven days, in the middle of his own still-running effort. It is a genuinely awkward moment for a field that has organized long-term human labor around exactly the kind of task Claude's agents just compressed.

The irony runs deeper than timing. Fermat's Last Theorem was, until this week, the last unformalized entry on Freek Wiedijk's well-known list of 100 landmark theorems that the formalization community uses as its benchmark of progress - the very list Buzzard's project was working toward closing out by hand. ^[6]Its closure by an AI system rather than the human project built to close it now forces an uncomfortable question for Lean's maintainers: whether to merge the roughly 29,500 new theorems Claude's agents produced, a body of work five times larger than Mathlib itself, into the shared library that the rest of the ecosystem builds on, and if so, how to review code nobody wrote by hand at a scale no human review process was designed for. ^[2]

What made eleven days possible was not a smarter model so much as a better way to split the work. Prove2Me, the coordination platform Tianyi Peng and collaborators built at Columbia, represents the proof as a directed acyclic graph of theorem statements and their dependencies, letting dozens of Claude agents parallelize across the graph without duplicating work or losing track of shared state. ^[2][4]Anthropic's internal research model generated roughly 6 billion output tokens against that structure with only limited high-level human guidance. ^[7]The same approach also formalized Vinogradov's Three Primes Theorem in about three days using nothing more than consumer-tier Claude Max plans - no special internal model required, just the same coordination trick applied to a smaller graph. ^[1]

That scaling story has a cost dimension worth being honest about. Commenters estimated the FLT run would cost roughly $300,000 at Anthropic's public list API pricing, though the real internal cost to Anthropic was likely far lower, in the rough range of $30,000 to $60,000. Either number is small next to a multi-year human formalization effort. Anthropic's push here follows its own earlier work applying Claude to Riemann zeta function research, and OpenAI has separately been running its own effort on Erdos problems - rival labs converging on formal mathematics as a proving ground for what frontier models can do unsupervised. ^[7][8]