- Claude turned the famous mathematical proof into millions of verifiable lines of code.
- Anthropic claims Claude completed several years of work in 11 days
- The large-scale proof contains 13 million lines of Lean code.
Anthropic used its artificial intelligence system, Claude, to create a fully computer-tested version of a famous centuries-old mathematical proof.
The proof is based on Fermat’s Last Theorem, a hypothesis first proposed by mathematician Pierre de Fermat back in 1637.
Mathematician Andrew Wiles presented the very first complete mathematical proof of the theorem back in 1995, which totaled 129 pages in length.
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Proof, rebuilt for machines
Formalizing a proof simply means converting its mathematical reasoning into code that computers can check automatically, without any human assistance.
Anthropic says it expected the entire task to take several years, based on how mathematicians first described the project.
Instead, the company says its internal research model completed the entire proof in just 11 days of continuous, largely unsupervised work.
The finished proof consists of 13 million lines of specialized code written in the Lean programming language used by mathematicians.
Along the way, Claude’s agents reportedly proved some 30,300 individual theorems, ultimately using 29,500 of them in the final version.
Human input was reported to be limited to occasional high-level guidance rather than any direct hands-on coding throughout the eleven-day process.
The final proof, at 13 million lines, is more than five times the size of Mathlib, the community’s own core proof library.
“This remarkable achievement of autoformalization… proves Fermat’s Last Theorem without any assumptions other than mathematical axioms,” said Kevin Buzzard, a mathematician at Imperial College London.
“Along the way, we see the autoformalization of algebra, harmonic analysis, geometry, and number theory, and we learn that the AI autoformalization artifacts are now robust enough to build on; the proof is multi-layered.”
Anthropic attempted formalization several times before succeeding, and these efforts accounted for approximately 7% of the non-standard lines of the final proof.
Not Anthropic’s first mathematical breakthrough
The formalization comes just a month after Anthropic detailed a separate breakthrough involving the Riemann zeta function, a well-studied mathematical object.
This function is at the very center of the Riemann hypothesis, considered one of the most difficult unsolved problems in mathematics worldwide.
Rival lab OpenAI is also doing similar work, using its latest Astra model to solve several classic Erdős problems.
The same OpenAI effort has also reportedly narrowed down several long-standing open questions in theoretical computer science.
Anthropic says the breakthrough only came after Claude gained access to an open-source software tool called Prove2Me, created by third-party collaborators.
The software helps AI agents choose the most useful next step during a lengthy, multi-step research process and also reduces the cost of inferences.
Anthropic has also expanded free access and research credits for mathematicians working on formalization projects, as well as larger grants.
Despite the record pace set here, the eleven-day schedule still shows how time-consuming full formalization remains even with the most modern systems.
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