AI Agents Formalize Fermat's Last Theorem in 11 Days, Compressing a Multi-Year Mathematical Project

The ultimate arbiter of modern mathematical truth is no longer a peer-review committee, but a software kernel. A proof assistant like Lean evaluates logical dependencies without intuition or fatigue, deciding definitively whether a mathematical claim holds. On September 4, 2026, that kernel verified the first complete, end-to-end formalization of Fermat's Last Theorem. The 13-million-line proof certificate was not written by a team of human mathematicians over a decade, but by a coordinated swarm of artificial intelligence agents operating largely autonomously over 11 days.[2]

The milestone, announced by Anthropic, does not represent a new mathematical discovery. British mathematician Andrew Wiles, alongside Richard Taylor, proved Fermat's 1637 conjecture in 1995. Instead, the AI system translated that historic 129-page human proof into Lean, a specialized programming language that requires every hidden dependency, omitted algebraic step, and logical implication to be explicitly defined. Human mathematical prose routinely skips steps that experts consider obvious; Lean does not.[1][2]

To bridge that gap, an internal research model comparable to Anthropic's Claude Fable 5.1 generated approximately six billion output tokens. The resulting artifact is massive: it contains roughly 30,300 newly proved theorems, with about 29,500 intermediate theorems woven into the final dependency structure. By line count, the 13-million-line file is more than five times larger than Mathlib, the principal community-built mathematical proof library it builds upon.[1][2]

Early attempts at this scale failed because individual AI agents lost track of the project's state and stopped collaborating effectively. The breakthrough relied on Prove2Me, an open collaborative platform developed by Tianyi Peng and researchers at Columbia University. Prove2Me maintains a shared directed acyclic graph of theorem statements. This architecture allowed dozens of Claude agents to work in parallel, defining concepts, proving sub-results, and reusing completed work without trampling each other's progress.[1][2]

The proof relies on only three standard mathematical axioms and contains no omitted steps or unverified placeholders. To ensure the result was genuine, the theorem statement was computationally compared against Mathlib's existing statement of Fermat's Last Theorem, and the logic was verified by an independent Lean kernel implementation.[2][3]

Kevin Buzzard, a mathematician at Imperial College London who has led a human community effort to formalize the theorem since 2024, reviewed the AI-generated artifact. "This extraordinary autoformalization achievement, which Anthropic researchers say only took 11 days, proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics," Buzzard stated. He noted that the success signals a major shift: "If the automatic formalization of FLT is possible now, then we have taken a big step towards automatic formalization of the modern mathematical literature."[1][2]

While the achievement compresses a multi-year human timeline into less than two weeks, the resulting code is highly verbose. Anthropic researchers acknowledge that the 13-million-line proof is longer than strictly necessary, lacking the conciseness and elegance of human-curated Mathlib entries. Furthermore, formalizing a known proof path is fundamentally different from discovering a novel mathematical truth from scratch.[2]

The immediate consequence is a collapse in the barrier to entry for machine-checkable mathematics. In a separate experiment, three consumer-tier Claude models formalized Vinogradov's Three Primes Theorem in just three days using the same Prove2Me platform. As AI models begin generating novel conjectures and proofs at scale, the Lean kernel will serve as the necessary bottleneck, capable of instantly separating hallucination from absolute mathematical certainty.[1][2]