Claude reaches nine-loop physics benchmark

Anthropic said Claude completed the nine-loop calculation of six-particle scattering amplitudes in planar N=4 super Yang-Mills theory on its Claude Science platform using the Fable 5.1 model. The result surpasses the eight-loop record held for three years by Lance Dixon’s team at SLAC, and Dixon independently verified the output after working backward from the amplitude to easier-to-check form factors.

The work followed a public challenge from Matt von Hippel to solve a scattering-amplitude problem using resources affordable to an individual academic. Anthropic researchers gave Claude a brief one-sentence task description and mostly prompted it to continue. Claude ran both a direct bootstrap calculation and an indirect route based on Dixon’s earlier form-factor method, with all 107,053 non-zero coefficients matching term by term. The end-user cost for each method was approximately $1,000 to $2,000, with the numerical computation portion about $100.

Other AI-linked math and physics claims are advancing in parallel, including work from He Song’s team at the Chinese Academy of Sciences, OpenAI disclosures, and an anonymous Goldbach-related claim. Terence Tao and 24 other Fields Medalists also warned that counting solved problems may undervalue understanding, originality, attribution, and knowledge transmission.