Claude Reportedly Formalizes Fermat’s Last Theorem in 11 Days

Introduction

Fermat’s Last Theorem was solved mathematically in the 1990s, but converting that proof into a program that a computer can check line by line is a separate engineering challenge. Anthropic says a team used Claude to complete an end-to-end formalization in Lean in roughly 11 days. The claim should be understood precisely: Claude did not discover a new proof of the theorem. It helped translate a human-readable proof into a formal system where omitted steps and informal appeals to intuition are not allowed.

What was completed

The theorem states that no positive integers a, b and c satisfy aⁿ+bⁿ=cⁿ when the integer exponent n is greater than 2. Andrew Wiles completed the landmark human proof in the 1990s. A conventional mathematical paper can compress routine arguments or say that a step is obvious. Lean requires definitions, types, lemmas and dependencies to be made explicit, then checks whether every conclusion follows from accepted foundations.

According to Anthropic, the project produced roughly 13 million lines of Lean code and more than 30,000 intermediate theorems, with about 29,500 used in the final proof. The reported codebase was more than five times the size of Mathlib, Lean’s core mathematical library. Anthropic also said the formalization relied on three standard Lean axioms and that a programmatic comparison confirmed that the theorem statement matched the version in Mathlib. These are project-reported figures, not evidence that the model discovered a new mathematical result.

Why the harness mattered

The early multi-agent setup could generate local results quickly, but it struggled with global coordination. Agents lost track of dependencies, repeated work and had difficulty combining partial proofs. The decisive change was the use of Prove2Me together with a Claude Code-based multi-agent harness.

The platform represents the proof as a directed acyclic graph of theorem nodes. It tracks prerequisites, completed results and reusable lemmas, while separating theorem statements from proof scripts. Natural-language descriptions help agents search the growing library, and faster Lean compilation makes it practical to test many candidate steps. Different agents can handle definitions, intermediate lemmas, higher-level arguments and final integration, while the human supervisor mainly offers high-level prioritization. The project reportedly consumed about six billion output tokens.

Broader implications

The significance is less about replacing mathematicians than about showing that AI can manage parts of formal mathematics as an engineering workflow. A capable model can propose definitions, split a proof into tasks, invoke a checker, repair errors and reuse earlier results. If this pattern scales, large bodies of mathematical literature may become easier to formalize than before.

There are also clear limits. Lean verifies the submitted formal derivation under its foundations; it does not independently judge whether the modeling choices are useful or whether the original theorem captures the intended mathematical idea. The deeper lesson is that progress in mathematical AI will depend not only on model reasoning, but also on reliable memory, dependency graphs, compilers and collaboration harnesses.

Source: QbitAI