Claude Formalizes Fermat's Last Theorem in 11 Days

<cite index="41-5,41-6">Claude worked largely autonomously for 11 days and produced a computer-checked proof of Fermat's Last Theorem, with the formalization running to 13 million lines of Lean code and proving 29,500 intermediate theorems, over five times the size of Mathlib, the principal mathematical proof library</cite>. <cite index="44-7">With Prove2Me and a Claude Code-based multi-agent harness, a team of agents completed the proof in a little under two weeks, consuming about six billion output tokens from a general-purpose internal research model roughly comparable to Claude Fable 5.1</cite>. <cite index="41-10,41-11">The run turned on Prove2Me, an open collaborative platform built by Anthropic researcher Tianyi Peng and collaborators at his Columbia University group, which maintains a directed acyclic graph of theorem statements that dozens of Claude agents used in parallel to decide which sub-proofs to attempt next</cite>. <cite index="40-1">First proposed by Pierre de Fermat in 1637, Fermat's Last Theorem went unproven until Andrew Wiles published his groundbreaking solution in 1995</cite>. <cite index="46-14">A job expected to take years was completed in 11 days</cite>. <cite index="40-9">The full proof was independently verified by nanoda, a separate proof kernel written in Rust, which confirmed that all 1,052,234 declarations are correct</cite>. <cite index="41-8,41-9">Kevin Buzzard highlighted the broader implications: "If the automatic formalization of FLT is possible now, then we have taken a big step towards automatic formalization of the modern mathematical literature. Such autoformalization techniques will lead to new tools, rooting out errors in the current mathematical corpus and lightening the load of referees."</cite>