Anthropic's Claude Computes Nine-Loop Yang-Mills Amplitude

Two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, report that Claude computed the six-particle (hexagon) scattering amplitude in planar N=4 super Yang-Mills theory at nine loops, one loop past the eight-loop record SLAC's Lance Dixon published in 2023.

The run answers a public challenge from science writer and former theoretical physicist Matt von Hippel, posted August 7, that asked AI labs to "Show that a computational limit everyone expected to be a problem doesn't actually matter. Give us N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine loops."

The setup was cheap and mostly unsupervised. Anthropic ran Claude inside a harness it calls Claude Science, driving Python with SymPy across the equivalent of 96 CPUs for a week, at a total cost of "one or two thousand dollars," with roughly $100 of that going to the underlying bootstrap step. Fitzpatrick and Mishra-Sharma left the model running through their off-hours with a standing instruction: "I'm going to sleep and won't be available for another several hours. Keep working on this until I tell you to stop. Give me updates every 4-6 hours."

Dixon, who spent years building out the bootstrap recipe Claude followed, validated the output. "It's quite a triumph, in my opinion, for a large language model to execute all of the steps in the complicated recipe we laid out, and to organize the computational horsepower," he told Anthropic. A separate group led by Song He at the Chinese Academy of Sciences in Beijing reached most of the same nine-loop result days later using AI assistance based on GPT-6, though not the largely hands-off approach Anthropic described. It caps an unusually busy stretch for the company on our tracker.

Von Hippel's own read sits with the harness, not the model itself. "I don't know how many mistakes Claude made internally on the way," he said, "but the harness got it to the end without an outside collaborator's input."