Claude Successfully Completes 9-Loop Cutting-Edge Physics Calculations, Experts Originally Thought Direct Calculation Would Be Too Difficult

Beating AI Express (Dongcha) News: Anthropic has disclosed that Claude Fable 5.1 completed a nine-loop theoretical particle physics calculation within Claude Science, deriving the six-particle scattering amplitude for planar N=4 super Yang-Mills theory. Scattering amplitudes are used to calculate the probability of particle interactions. A higher loop count means more corrections are added, making calculations more challenging. This specific problem had previously only been solved publicly up to eight loops. No manual human intervention was involved this time: two Anthropic physicists first instructed Claude on the task, then let it operate largely autonomously, with progress updates every 4 to 6 hours. Claude ultimately arrived at results via two distinct approaches. The direct approach used Python and SymPy, running on 96 CPUs for a week at a compute cost of roughly $100; factoring in the cost of repeated Claude API calls, each full approach cost between $1,000 and $2,000. The results were independently verified by Lance Dixon, a physicist at SLAC and Stanford who participated in the earlier eight-loop study. Dixon said he had originally believed a nine-loop amplitude would be too difficult to calculate directly. Claude did not develop new physics methods; it primarily executed the methods, constraints, and extensive tedious calculations established by researchers in prior work. Meanwhile, He Song’s team at the Institute of Theoretical Physics, Chinese Academy of Sciences, has also independently advanced to nine loops with GPT-6 assistance, and obtained the main portion of the results.