Anthropic's Claude Finished the First Machine-Checkable Proof of Fermat's Last Theorem in 11 Days

On September 4, Anthropic released the first end-to-end, machine-checkable proof of Fermat's Last Theorem, the 358-year-old conjecture that no positive integers x, y, z can satisfy x^n + y^n = z^n for n greater than 2. The proof is roughly 13 million lines of Lean code, a line-by-line re-statement of Andrew Wiles and Richard Taylor's 1994 argument. A multi-agent Claude system, running under a harness built by Tianyi Peng's Columbia University team, finished the run in about 11 days.

The mathematics is the same mathematics Wiles and Taylor wrote down in 1994. The engineering is what changed: a translation the formalization community had scoped as a multi-year project, completed in eleven days under AI orchestration.

Lean is a proof assistant: a program that checks every logical step and refuses to accept "this is obvious" as a substitute for a written argument. To say a proof is "formalized" means a reader, or another mathematician, can re-run the check without taking any step on faith. The translation has been on the community roadmap since Kevin Buzzard, a number theorist at Imperial College London, published an 86-page blueprint for the first phase in 2024.

The mechanism that compressed the timeline is a project-management layer called Prove2Me, built by Peng's Columbia group. Prove2Me splits the proof into a directed acyclic graph of theorem nodes, the way a build system decomposes a large software project. Dozens of Claude agents work on those nodes in parallel; Peng's team provides the high-level direction, including which branches of the graph to attempt and which intermediate results are admissible.

The first attempt did not survive. According to Anthropic's research post and the public repository, an early multi-agent run lost track of project state and stopped collaborating productively. Roughly 7% of the non-boilerplate code in the final repo is the wreckage of that earlier run, code that did not make it into the proof but had to be cleaned up. The current harness, with Prove2Me wired in, is what finished the work.

Verification did not rely on Anthropic alone. The repo's build manifest targets Lean 4.33.1. Two independent checkers re-ran the proof: leanprover/comparator v4.33.0, which prints "Your solution is okay!" on success, and nanoda 0.4.13, a community-maintained Rust reimplementation of the Lean kernel that reports "Checked 1052234 declarations with no errors." The final proof depends only on Lean's three standard axioms: propext, Classical.choice, and Quot.sound. There are no sorry placeholders, no added axioms, and no native_decide shortcuts.

The repository logs the size and the structure: 30,300 intermediate theorems proved along the way, 29,500 of which feed into the final proof. The whole corpus is more than five times the size of Mathlib, the community's existing library of formalized mathematics.

Buzzard, who has run the FLT-Lean community project since 2024, called the result "an extraordinary autoformalization achievement" and noted that AI-generated formalization artifacts are now robust enough to build on, spanning algebra, harmonic analysis, geometry, and number theory.

The contribution is the workload shift, not the discovery. Fermat's Last Theorem is a useful test case because the underlying mathematics is settled and public, and because the formalization community had already mapped the route in the Buzzard blueprint. If a result this large, this dependent on existing mathematics, can be machine-checked in eleven days, the bottleneck on formalizing the rest of the literature moves from human proof engineering to AI orchestration.

Anthropic says the internal research model sits at roughly the capability level of its Claude Fable 5.1 series, per qbitai's summary of the announcement. Roughly six billion output tokens were consumed across the run. Peng's group plans to open the harness and the build tooling in the coming weeks; the next watch item is whether the same pipeline holds on a proof the formalization community has not already blueprinted.