Anthropic published a research article on September 25 describing how two of its physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, used Claude to complete a theoretical-physics calculation: the nine-loop result for the six-particle scattering amplitude in planar N=4 super Yang-Mills theory. The previous record was eight loops, set in 2023 by Lance Dixon and collaborators at SLAC National Accelerator Laboratory and Stanford University.
The article's author is Matt von Hippel, a former theoretical physicist who is now a science writer covering amplitude physics on his blog, 4gravitons. The project grew out of a challenge he had posed: show that an AI could use the computing resources available to a single academic to crack an outstanding open problem in scattering amplitudes. He gave two concrete targets — either N=8 supergravity at seven loops, or N=4 super Yang-Mills at nine loops.
How the calculation was done
The two researchers worked on Anthropic's Claude Science platform, running on the underlying model Fable 5.1. The code was written in Python, with symbolic computation handled by the SymPy package.
The calculation followed two separate routes. One was the field's existing bootstrap method, which writes down the constraints an amplitude must satisfy and then solves them; the other was the indirect form-factor method Dixon's team had used in 2023. The two routes agreed. The whole project cost roughly $1,000 to $2,000 in total, and one stretch of the computation ran for about a week across 96 CPUs.
According to the article, Claude worked largely on its own, with the humans giving only simple instructions — something like "Keep working on this until I tell you to stop." Dixon later independently verified the result. He described this kind of calculation as extremely fragile: get any single step wrong, and the whole thing collapses like a soufflé that never rose.
"It's quite a triumph, in my opinion, for a large language model to execute all of the steps in the complicated recipe."
What it didn't achieve
The article is candid about the limitations. Claude relied entirely on known methods and proposed no new physical principles; the jump past eight loops came from better software engineering, not from any algorithmic breakthrough. Von Hippel's summary:
"There is more low-hanging fruit out there than you'd expect."
Put another way, many of the amplitude field's stuck problems have been bottlenecked on manpower and engineering execution, not on a missing method.
A Chinese team got most of the way there too, almost in parallel
There is a China-related twist to this result. A team led by Song He at the Chinese Academy of Sciences independently computed the so-called "symbol" portion of the nine-loop amplitude, and posted the result to the academic data repository Zenodo. Per Anthropic's article, that team used GPT-6 to help with the constraint calculations, but built the overall framework themselves.
The two results are independent, which makes them a useful cross-check on each other. For theoretical-physics groups in China, the interesting reference point is the division of labor: Song He's team had the model handle just the constraint-computation piece, while Anthropic had the model run the entire pipeline — and both approaches reached results at the nine-loop milestone.
The nine-loop result has now been posted publicly in the field's standard format, and Dixon and his collaborators plan to write it up as a formal paper. Until that paper appears, what the outside world can see is mainly Anthropic's article and the published result data.
Sources: Anthropic research article "Yes, Claude can do nine loops," Zenodo public data, CocoLoop; the loop-count record, computation cost, and CPU scale are verified against Anthropic's article.