Claude Independently Computes Complex Theoretical Physics Challenge

Anthropic's Claude has independently computed the nine-loop six-gluon scattering amplitude in planar N=4 super Yang-Mills theory, demonstrating a new benchmark for autonomous scientific problem-solving. The calculation, verified by Stanford physicist Lance Dixon, was achieved with minimal human intervention and a total cost of approximately $1,000 to $2,000, challenging assumptions regarding AI limitations in high-complexity physics. The breakthrough originated from an open challenge issued by science writer Matt von Hippel, a former collaborator of Dixon's research group. Hippel questioned whether AI could surmount computational barriers in amplitude theory. Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma accepted the task, utilizing the Fable 5.1 interface to run Claude. Provided only with a single initial prompt, the model operated autonomously over several days. Claude pursued two strategies: a replication of the established antipodal duality method and a direct bootstrap approach in hexagon function space that Dixon considered infeasible. Both pathways converged, producing results that matched all 107,053 non-zero coefficients of the expected solution. Validation occurred rapidly. Dixon confirmed Claude's output by reverse-calculating the corresponding shape factor, finding exact agreement. The efficiency of the result contrasts with the factorial growth of computational complexity in loop expansions; Dixon's team previously required years to reach eight loops using indirect techniques. Anthropic published the full amplitude data and symbolic representations on September 16, enabling the community to audit the findings. Dixon noted that Claude exhibited a grasp of the methodology's nuances, potentially exceeding that of non-coauthors, and adhered strictly to the group's established data formats. Parallel developments highlighted the accelerating role of AI in this domain. In mid-September, a team led by He Song at the Institute of Theoretical Physics, Chinese Academy of Sciences, released nine-loop amplitude data via Zenodo. While He's framework was primarily human-driven, the team employed GPT-6 to assist with specific constraint conditions. The simultaneous achievements indicate that large models are becoming viable tools for tackling problems previously restricted by resource constraints. Matt von Hippel emphasized that while Claude replicated human-derived strategies rather than generating novel physical insights, its success in executing compute-intensive workflows alters the landscape of theoretical research. Dixon and von Hippel agree that AI currently excels at precision execution and optimization but has not yet surpassed human capabilities in formulating new theoretical principles. The physics community is now urged to test AI frameworks against their own computational bottlenecks. Research focus shifts to systematic analysis of the nine-loop results, with projections suggesting AI could assist in advancing calculations to the tenth loop within existing budgets.