AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever
Anthropic's Claude AI has produced a fully computer-verifiable proof of Fermat's Last Theorem in 11 days, generating 13 million lines of code that eliminates the need for human verification of each logical step. The achievement surpasses a parallel human-led effort at Imperial College London that has been underway since 2024 and remains incomplete, with leading mathematician Kevin Buzzard confirming the AI's work is mathematically sound.
Why It Matters
As mathematical proofs grow increasingly complex, computer-formalized versions become critical for preventing errors and fraud—a problem mathematicians have struggled with for over a century. This demonstration shows AI can efficiently translate existing proofs into machine-checkable form, addressing a bottleneck that currently takes human teams years to complete.
Key Facts
- Time to completion: 11 days for Claude versus ongoing Imperial College project started in 2024
- Proof size: 13 million lines of code, equivalent to 160 novels
- Original theorem date: Fermat proposed the theorem in 1637; first valid proof published by Andrew Wiles in 1995
- Supporting theorems proven: More than 30,000
- Reviewer confirmation: Kevin Buzzard validated the proof uses only basic mathematical axioms
Anthropic announced that Claude successfully formalized a proof of Fermat's Last Theorem, a mathematical conjecture that remained unproven for nearly 360 years. The AI completed the task in just 11 days by deploying dozens of parallel agents that collaboratively wrote definitions, proved intermediate results, and built progressively larger logical structures. A critical tool called Prove2ME coordinated these agents by maintaining a shared task list and organizing files to prevent duplicated work and enable knowledge sharing across parallel processes.
The resulting proof runs 13 million lines of computer code—more than five times larger than Mathlib, the standard shared library mathematicians use for formal verification work. This computer-readable format is fundamentally different from traditional mathematical proofs: while Andrew Wiles's original 1995 proof required expert human review to verify correctness, Claude's version can be checked mechanically by computer, eliminating subjective interpretation and reducing the risk of hidden errors.
The achievement outpaced a competing effort led by mathematician Kevin Buzzard at Imperial College London, which began in 2024 with the same goal of formalizing Wiles's proof using the Lean programming language. That human-directed project, backed by funding through 2029, has not yet reached completion. Buzzard personally reviewed Claude's output and confirmed it holds mathematically sound, requiring only the foundational axioms of mathematics.
While Claude did not discover new mathematics—Wiles established the underlying proof three decades ago—the formalization addresses a growing practical problem in modern mathematics. As proofs become longer and more intricate, human review teams struggle to verify correctness before publication, creating opportunities for errors or invalid claims to propagate. Computer-verified proofs eliminate this verification bottleneck and provide absolute certainty that logical chains remain unbroken.
Anthropmic made the complete 13-million-line proof publicly available on GitHub, allowing any mathematician to independently verify Claude's work without relying on corporate claims. This transparency reflects broader industry recognition that formal verification, rather than institutional authority, will increasingly underpin mathematical credibility.
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