Anthropic’s Claude Computes a Nine-Loop Physics Result With Known Methods

A particle-physics calculation that had stopped at eight loops now has a reported nine-loop result. Anthropic researchers used Claude Science to compute it, and a physicist checked the answer. The feat tests whether AI can carry out difficult research with accessible computing resources. It does not show that Claude invented a new technique or broke through a fundamental computing limit.

What nine loops means

The result is a scattering amplitude: a formula physicists use to calculate how likely particles are to react in particular ways. A “loop” marks another level of complexity included in the calculation. More loops can make a prediction more precise, but the work gets harder.

This particular calculation concerns six particles in planar N=4 super-Yang-Mills. That theory is a simplified testing ground, not a description of particles in the real world. Physicists use it to develop and check techniques that may help with harder calculations. The nine-loop answer is therefore a research result worth studying, not a new prediction about an experiment.

Science writer and former theoretical physicist Matt von Hippel had challenged AI companies to solve a frontier problem in this field on resources an academic could reasonably obtain. He expected the next loop to be difficult: the eight-loop answer had come through an indirect route, rather than a straightforward extension of the usual calculation. Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma took up his nine-loop challenge.

Two routes to the same answer

The researchers used Fable 5.1 inside Claude Science, a system that pairs the model with structured instructions for scientific work. They gave it the calculation to do and then largely urged it to keep working. Von Hippel describes no scientific guidance during the run more sophisticated than those prompts; the result was checked afterward.

Claude produced the calculation in two ways. One was the established “bootstrap” method: start with possible forms of an answer, then rule them out using known constraints until a solution remains. The other used a related, easier-to-calculate object called a form-factor to reach the amplitude indirectly. Using both routes makes the account more substantial than a single unexplained output, although physicists still have work to do interpreting the result.

A frontier result, not a broken barrier

The smaller figure in that cost breakdown is for the bootstrap’s computing run, not the whole AI-assisted effort. Its program used Python and SymPy over a week on 96 CPUs. Von Hippel’s larger estimate includes the much greater cost of keeping Claude running. The distinction matters to his original challenge: the work was affordable by the standard he set, but it was not free or effortless.

Nor was Claude alone near the answer. According to von Hippel, a group led by Song He at the Chinese Academy of Sciences had independently obtained most of the result with some GPT-6-based assistance. That effort was human-led, unlike the more hands-off Claude run. Its progress narrows the claim that AI accomplished something researchers could not: people were already getting there, too.

Von Hippel’s conclusion is narrower, and more useful: Claude applied known methods with more computing effort than researchers had tried, rather than finding a way around a fundamental limit. Physicist Lance checked the result with the Anthropic researchers. Lance, Song He and their collaborators are expected to publish and analyze the calculations, work that should make the answer more useful to other physicists.