Anthropic says Claude completed a nine-loop scattering-amplitude calculation

Anthropic says Claude completed a nine-loop scattering-amplitude calculation in N=4 super Yang-Mills theory, a frontier problem in theoretical particle physics that the company describes as work "normally tackled by the top experts in amplitudes." The result, published September 25, followed a challenge issued by physicist Matt von Hippel in August and was validated by amplitudes researcher Lance Dixon on September 1.

What's new

According to Anthropic's post, Claude approached the problem twice, using different methods: "Claude ended up doing the calculation two different ways: the original bootstrap, and the indirect form-factor approach." Scattering amplitudes describe the probability of specific outcomes in particle collisions, and pushing a bootstrap calculation to nine loops of quantum corrections represents a substantial jump in complexity over prior manual and computer-assisted results in the field.

Anthropic disclosed the computational cost in concrete terms: "Either approach would have cost an end-user around one or two thousand dollars," with the bootstrap method alone consuming "around $100 of the budget, corresponding to running 96 CPUs for a week." The team's operating method was less about new algorithms than about giving the model long, uninterrupted stretches of compute time. One team member's instruction captures the approach: "I'm going to sleep and won't be available for another several hours. Keep working on this until I tell you to stop."

Anthropic frames the achievement plainly: "This is a real frontier calculation, the kind of thing normally tackled by the top experts in amplitudes."

Context

N=4 super Yang-Mills theory is a simplified but mathematically rich model that particle physicists use as a testing ground for techniques later applied to the real-world Standard Model. Amplitude bootstrapping — reconstructing a scattering amplitude from its known mathematical properties rather than computing it term-by-term from Feynman diagrams — is a specialized technique with a small community of practitioners. Getting an outside challenge from a working physicist, then independent validation from another expert in the field before publication, gives the result a level of external scrutiny that AI-for-science claims don't always receive.

Why it matters

The post's own conclusion is notably restrained: the author attributes the result to more available "low-hanging fruit" than experts expected, rather than to a fundamentally new method, and credits improved coding practices and raw compute access over any algorithmic breakthrough. That framing matters as much as the result itself. Anthropic is not claiming Claude invented new physics or a new technique; it's claiming that sustained, long-running agentic work on a well-defined hard problem, with enough compute and enough patience from a human collaborator, can reach a research frontier that specialists consider difficult. For a lab racing to demonstrate real scientific utility beyond benchmark scores, an externally challenged, externally validated result carries more weight than an internal eval — and the price tag, one to two thousand dollars in compute, is a data point for what that kind of frontier-adjacent research assistance now costs.