Anthropic's Claude Sets Nine-Loop Physics Record

Anthropic researchers Liam Fitzpatrick and Siddharth Mishra-Sharma used the Claude Science platform, running the Fable 5.1 model, to calculate the six-particle scattering amplitude in planar N=4 super Yang-Mills theory to nine loops. This achievement broke the previous eight-loop record held by Lance Dixon of the SLAC National Accelerator Laboratory. The AI agent completed the multi-day task autonomously, requiring only basic continuation prompts and no scientific corrections from humans during the run.

The challenge was originally issued by physicist Matt von Hippel on his 4gravitons blog. Claude solved the problem using Python and the SymPy library via two distinct mathematical paths: a direct bootstrap and a form-factor route utilizing antipodal duality. The entire run cost between $1,000 and $2,000, with model inference making up the bulk of the expense. In contrast, the underlying numerical bootstrap calculations cost only about $100, a workload equivalent to running 96 CPUs for one week. Dixon later verified the results using his team's independent validation tools.

Shortly after, a team led by Song He at the Chinese Academy of Sciences achieved a similar milestone using GPT-6 to assist human researchers. However, Claude's autonomous execution highlights a major shift for practitioners. Instead of spending months manually coding and debugging complex algebraic loops, physicists can now use AI agents to handle fragile, long-horizon computations. This allows researchers to tackle highly structured mathematical problems that were previously ignored due to a lack of time or specialized tooling.