Anthropic Says Claude Computed a Nine-Loop Scattering Amplitude, Beating an Eight-Loop Record

Anthropic published an account on September 25 describing how Claude Fable 5.1 computed, to nine loops, the six-particle scattering amplitude in planar N=4 super Yang-Mills theory (a highly symmetric model physicists use to test calculation methods in quantum field theory). No physicist had reached that level through direct calculation before. The previous result, at eight loops, belonged to Lance Dixon of SLAC National Accelerator Laboratory and Andy Liu, who reached it by an indirect method in 2023. Russian-language AI channels summarized the claim within hours of publication.

The setup deserves close attention. Matt von Hippel, a former theoretical physicist, issued a public challenge on August 7, asking labs to solve a real open problem on the budget of a typical university lab. Two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, gave the model a single instruction and then let it work inside Claude Science, checking in periodically. Anthropic reports about a week of computation on 96 processors, at a cost of $1,000 to $2,000 for each of the two methods used.

Verification here is stronger than in most lab-published science demonstrations. Dixon checked the result himself, and the write-up carries von Hippel's name. Even so, the result is a lab-published account that has not gone through peer review. It also addresses a single problem in a narrow, highly structured corner of theoretical physics, where symbolic manipulation and established bootstrap methods do much of the work.