Mathematicians evaluate Claude's 13-million-line proof of Fermat's Last Theorem
Over an intensive 11-day run, a multi-agent swarm generated a verified 13-million-line proof, solving a formal verification challenge once estimated to take years.
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- Following Anthropic's announcement of the first computer-checked formalization of Fermat's Last Theorem, mathematicians have begun evaluating the verified 13-million-line proof.
- The resulting Lean 4 code contains approximately 13 million lines of code and proves 29,511 intermediate theorems across modular forms and elliptic curves.
- The project was made possible by 'Prove2Me,' a collaborative platform that used a directed acyclic graph to provide a shared memory space for parallel agents.
- The proof was fully verified by the Lean kernel using only its three standard axioms, confirming there are no logical gaps in the formalized proof.
Following Anthropic's landmark announcement of the first complete, computer-checked formalization of Fermat's Last Theorem, mathematicians and technology analysts have begun assessing the implications of the 13-million-line proof. While the AI completed the autoformalization autonomously over an 11-day campaign, the broader scientific community is now examining the result. Ars Technica's analysis highlights that this success marks a profound shift in computer-assisted mathematics, showing that AI systems can systematically verify complex, long-horizon proofs once expected to take human teams years.
The AI formalized the celebrated 1995 proof by Sir Andrew Wiles and Richard Taylor, specifically following the modern algebraic exposition by Darmon, Diamond, and Taylor. The resulting Lean 4 code comprises approximately 13 million lines, making it the largest Lean proof ever written and over five times the size of Lean's standard mathematical library, Mathlib. To reach the final proof, Claude's agents had to independently verify 29,511 intermediate theorems spanning elliptic curves, modular forms, and Galois representations. The Lean kernel successfully compiled the entire proof, confirming zero logical gaps.
A critical factor in the project's success was the deployment of 'Prove2Me,' an open collaborative platform developed by Columbia University researcher Tianyi Peng. Previous attempts at large-scale formalization failed because individual agents quickly lost context over complex, multi-week proof chains. Prove2Me resolved this by maintaining a shared directed acyclic graph (DAG) that acted as a collective memory, allowing dozens of Claude agents to collaborate simultaneously without overwriting or repeating each other's mathematical sub-tasks.
The formalization has drawn praise from the mathematical community. Kevin Buzzard, a professor at Imperial College London who has led human efforts to formalize Fermat's Last Theorem since 2024, described the result as an extraordinary autoformalization achievement. While the AI did not discover new mathematical concepts, the sheer speed and autonomy of the process suggest a new era where AI agents can systematically audit and verify complex mathematical and software engineering codebases at a scale impossible for human teams.
This achievement establishes that multi-agent systems, when supported by structured collaborative memory systems like Prove2Me, can solve incredibly complex, long-horizon logic tasks. Moving from short-context generation to a verified 13-million-line formal proof shows that AI can systematically eliminate human error in safety-critical fields, laying the groundwork for autonomous verification of complex software, cryptography, and engineering specs.
Will the mathematical community adopt Prove2Me to accelerate other massive human-led formalization efforts, such as the classification of finite simple groups?
Still open. When the paper finds out, it will say so here and on the open questions page — including if it got this wrong.