Anthropic says Claude computed a nine-loop physics amplitude

Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma said that, given a single prompt describing the problem, Claude Fable 5.1 ran largely unsupervised over several days on Anthropic’s Claude Science platform and computed a nine-loop scattering amplitude in a simplified model of particle physics known as planar N=4 super Yang-Mills theory — one loop beyond the previous record. Physicists use “loops” to describe successive corrections to a scattering-amplitude calculation: each additional loop sharpens the prediction but multiplies the computation required, and the eight-loop record had stood since 2023 work by Lance Dixon of SLAC and a collaborator.

The task answered a public challenge that physicist and science writer Matt von Hippel had set AI companies in an August 2026 blog post, asking whether an AI system could push past eight loops using only the compute budget an academic researcher could reasonably access. Fitzpatrick and Mishra-Sharma had the model work through the calculation using two established methods developed by Dixon and colleagues — a direct bootstrap and an indirect route through a related quantity called a form factor — arriving at consistent results for a total cost Anthropic put at roughly $1,000 to $2,000. Dixon reviewed and independently verified the nine-loop result, and von Hippel — compensated by Anthropic, which said it gave feedback on drafts but left “the content and opinions” his own — wrote up the episode as a guest post on the company’s research site.

The claim is narrower than headline framing might suggest: this was an extension of an established, well-defined calculation technique by one loop, not an open-ended discovery, and it was Anthropic’s own staff who set up and ran the task rather than an outside researcher. What it demonstrated was a model working autonomously and correctly through a long, technically demanding, multi-day symbolic calculation with minimal human steering, at a cost small enough for an individual academic to reproduce.