Claude has completed a nine-loop scattering-amplitude calculation that particle physicists had treated as a frontier problem, according to a guest account published by Anthropic. SLAC and Stanford physicist Lance Dixon independently checked the result, while a separate human-led team had been working toward much of the same answer.
The calculation concerns the six-particle amplitude in planar N=4 super-Yang-Mills. That name is forbidding, but the distinction matters: this is a deliberately simplified theory that physicists use to test mathematical techniques. It is not a direct model of known particles, nor does the result itself predict something new at the Large Hadron Collider.
Scattering amplitudes are formulas used to calculate the likelihood of particle interactions. Physicists often approximate them by adding increasingly detailed corrections called loops. More loops generally mean a more precise result and a much harder computation. Most real-world calculations stop at two or three loops; the previous record in this particular testing ground was eight.
Two routes to the same result
Physicist and science writer Matt von Hippel issued the nine-loop challenge in August after looking for a problem that was difficult because of the required computation, rather than because nobody knew how to approach it. Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma then gave Claude a short description of the problem inside Claude Science and periodically told it to keep working.
The account says Claude reached the answer in two ways. One used a direct “bootstrap” method, which narrows the possible formula by applying known mathematical constraints. The other worked through a related object called a form factor, following a route connected to Dixon’s earlier research.
Either route would have cost an end user roughly $1,000 to $2,000, according to von Hippel. The direct bootstrap also ran a Python and SymPy workload across 96 CPUs for a week, accounting for about $100 of that budget.
Dixon says he validated the result mostly through the form factor. He described the setup as fragile because a small error in the computational recipe can invalidate the entire calculation, and noted that Claude reconstructed many implementation details that had never been fully documented.
A frontier calculation with important limits
The result did not come from an unknown physical principle or an unexpectedly powerful new algorithm. Von Hippel writes that Claude used established techniques, supported by more computation and stronger software engineering than researchers had previously applied to this exact problem.
There was also a concurrent human result. A group led by Song He at the Chinese Academy of Sciences had already computed most of the nine-loop amplitude with some GPT-6 assistance. The researchers, rather than Claude, will publish and analyze the work for the field.
