Humans using one of Cloud’s artificial intelligence models built A computer-verifiable version of an extremely complex mathematical proof.
Image source: anthropopic.com
As part of the project, Anthropic examined evidence supporting a study called Fermat’s Last Theorem – It was proposed in 1637 and is related to the properties of positive integers. The proof of the theorem was proposed by mathematician Andrew Wiles in 1995; it took up 129 pages and took several months to verify. The Anthropic Research Project was able to formalize Wiles’ proof, that is, convert it into a form that could be verified on a computer.
The formal proof is code written in Lean programming language – its size is 13 million lines, which is the largest amount in history. Formalization is difficult because the proof is often very terse – it lacks some of the explanations that the computer needs to understand, and they need to be added manually. Arguments in proofs are often interrelated, which means that one line of error in Lean can invalidate all subsequent code.
Mathematicians had expected Wiles’ proof to take years to formalize, but Anthropic’s research model completed the task in 11 days, and the algorithm is comparable to the publicly available Claude Fable 5.1 model. The model accomplished its task using only a limited amount of high-level data. It launched dozens of agents, generated 6 billion output tokens, and proved 29,500 intermediate theorems in the process. The first attempt failed, but a breakthrough came when Claude gained access to the Prove2Me platform.
“We saw automatic formalization in algebra, harmonic analysis, geometry and number theory and realized that automatic formalization tools are now reliable enough to use; multi-level proofs”“A month ago, Anthropic made progress in proving the Riemann Hypothesis,” said Kevin Buzzard, a mathematician whose work was used in the project.
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