Claude Formalizes Fermat’s Last Theorem in 11-Day Lean Project
Claude formalizes Fermat’s Last Theorem in a new research release from Anthropic, which says its AI agents produced an end-to-end Lean proof over 11 days. Announced September 4, the result turns an established mathematical argument into code that a proof checker can verify.
The achievement concerns the scale and automation of verification. Andrew Wiles and Richard Taylor established the theorem decades ago. Anthropic’s release provides a machine-checkable formalization of that mathematical tradition, alongside public code and an outside mathematician’s report that he compiled and checked it.
Claude Formalizes Fermat’s Last Theorem in Lean
According to Anthropic’s research account, the run generated about 13 million lines of Lean and proved 30,300 intermediate theorems, with roughly 29,500 used in the final proof. Dozens of agents worked through the project using the Prove2Me collaboration platform.
The company says the work consumed approximately six billion output tokens from an internal research model roughly comparable to Claude Fable 5.1. Human mathematical input consisted of occasional high-level direction. Those details describe the company’s research setup, rather than a performance guarantee for a publicly available subscription.
Fermat’s Last Theorem states that positive integers cannot satisfy aⁿ + bⁿ = cⁿ when the integer exponent n is greater than two. Its short statement conceals a proof spanning several advanced mathematical fields, which makes translating the entire argument into a formal language a substantial undertaking.
Kevin Buzzard Reports an Independent Code Check
Imperial College London mathematician Kevin Buzzard says in his September 4 assessment that he compiled the code and ran Lean’s comparator tool successfully. He describes the result as completing the final remaining item in Freek Wiedijk’s list of 100 formalization challenges.
Buzzard also identifies the proof route precisely: it follows the Darmon–Diamond–Taylor exposition of the Wiles–Taylor–Wiles argument, rather than the more modern version his own project has been formalizing. That distinction matters because two formalization efforts can establish the same conclusion while building different mathematical infrastructure.
His assessment leaves a continuing role for human-led work. Buzzard’s project also aims to contribute reusable material to Lean’s mathematics library and create a document through which people can explore the modern proof. Checking a giant body of code does not automatically deliver those educational and organizational benefits.
The Lean project’s background account describes formalization as a way to make advanced number-theory objects available for further research. Its scope includes algebra, geometry, and analysis. Reusable definitions can therefore matter beyond the single theorem that draws public attention to the effort.
Prove2Me Organizes Shared Mathematical Work
The Prove2Me research paper, first submitted August 28, describes a platform where people launch formalization missions and AI agents contribute proofs. The design lets agents reuse completed results and divide larger goals into smaller tasks.
A central design choice separates a theorem’s statement from its proofs. A statement remains a stable object while different agents can supply proofs of it. That creates a common reference point for collaboration, instead of requiring every contributor to manage the same evolving document.
The paper identifies three practical needs for large projects:
- Audit the definitions and claims that determine what is being proved.
- Make completed results easy for other agents to find and reuse.
- Coordinate contributions without making every step depend on one contributor.
The authors also distinguish logical checking from meaning. A proof assistant can accept a proof of a formal statement even if that statement does not faithfully express the intended human claim. Their proposed workflow keeps people responsible for reviewing a curated core of definitions, goals, and milestones.
Public Proof Files Expose the Verification Boundary
Anthropic’s proof repository documents a build on Lean 4.33.1, a comparator check against Mathlib’s statement of the theorem, and verification with a second kernel called nanoda. The repository says its final theorem depends on Lean’s three standard axioms, with no additional assumed theorem or unfinished proof placeholder.
The nanoda run used patches supplied by the team, which the repository describes as progress reporting and performance changes that do not weaken typing rules. These are documented checks of the released artifact; Twokq has reviewed the published evidence and has not rerun the full build.
Reproduction is a significant computing job. The repository reports a build lasting more than five hours at 96 parallel jobs and recommends allowing 300 GB of memory for the comparator stage. Public availability makes scrutiny possible, but it does not make every verification step inexpensive.
The immediate result is a formal artifact that other researchers can inspect and test. Its longer-term value will depend on how readily the community can simplify the generated code, reuse its mathematics, and pair checked arguments with explanations that people can understand. Those tasks remain distinct from generating a successful proof.
