Claude has just solved a calculation for theoretical physicists that nobody had ever completed. On September 25, Anthropic published a guest post on its official research blog: physicist and science writer Matt von Hippel looked back on a challenge he had issued to AI companies a month earlier — compute the six-particle, nine-loop scattering amplitude in planar N=4 super Yang-Mills theory, on a computing budget an academic could afford. Two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, took up the challenge with Claude. And pulled it off.
A problem nobody had solved
First, how hard is this problem? Scattering amplitudes are the formulas particle physicists use to predict the outcomes of particle collisions; the more precise the calculation, the better experimental results — from machines like the Large Hadron Collider — can be tested. Because the math is brutally complex, physicists usually stop at a "two-loop" approximation, a few reach three loops, and the most precise prediction in particle physics history used only five loops. N=4 super Yang-Mills is a "toy model" — it doesn't describe the real world, but its high symmetry makes it relatively tractable, so amplitude researchers use it to hone new methods. Nine loops means precision nobody had ever touched.
Anthropic's approach was surprisingly simple. In late August, the two physicists first asked Claude which problem it felt most confident tackling, then gave it a single prompt: "The problem is to compute the six-particle (hexagon) amplitude in planar N=4 super Yang-Mills at nine loops." After that, they just kept telling it to continue — "I'm going to sleep and won't be available for another several hours. Keep working on this until I tell you to stop. Give me updates every 4-6 hours." Claude produced the answer via two independent methods (the original "bootstrap" and the indirect "form-factor" approach), at a total end-user cost of roughly one to two thousand dollars; the bootstrap portion, done in Python with SymPy, cost about $100 — the equivalent of 96 CPUs running for a week.
The real news isn't the answer
The result's credibility was double-checked: amplitude expert Lance Dixon helped verify the answer, and — coincidentally — Song He's group at the Chinese Academy of Sciences independently obtained most of the result with GPT-6 assistance. By academic convention, human researchers will write up and publish the paper; Claude's job is done.
The real significance isn't that it was solved, but how. Von Hippel is candid: he had hoped to see AI break a computational bottleneck with methods humans hadn't imagined. What actually happened was different: Claude used known methods — just with more compute than humans had dared to throw at the problem, better software engineering habits, and almost entirely unsupervised autonomous operation. In March, AI could only do "student-level" physics with heavy hand-holding; by September it was independently completing frontier calculations. That pace is itself the answer: this kind of "experts think it's out of reach" low-hanging fruit may be far more abundant than imagined. Nor is this Claude's first solo act in science — Anthropic previously announced that Claude had autonomously discovered ART, a novel enzyme system with CRISPR-like repeat arrays.
Von Hippel does draw a boundary: success on a toy model doesn't mean real-world amplitude calculations will fall as easily — N=4 theory is a small community's testing ground. But he also urges researchers working on real amplitudes to try right now whether AI science tools can one-shot frontier calculations — because if they can, the field's very definition of the frontier will have to be rewritten.
