Claude cracks a nine-loop physics barrier on a budget

Pushing particle physics past human limits just got a lot cheaper.

Physicists predict subatomic particle behavior using complex equations called scattering amplitudes. Because the math is punishing, researchers rely on approximations measured in layers called "loops." Each extra loop increases precision while causing the required computation to explode. Most particle calculations stop at two or three loops. The extreme frontier—achieved in an idealized "toy model" called planar N=4 super-Yang-Mills—was eight loops, set years ago by SLAC theorist Lance Dixon.

Last month, theoretical physicist turned science writer Matt von Hippel threw down a gauntlet on his blog: could an AI push this calculation to nine loops, using only the modest computing budget available to an everyday academic?

Anthropic accepted the bet. On September 25, the company announced that Claude cracked the nine-loop amplitude—and did it largely unsupervised.

A prompt and a good night's sleep

Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma ran the project using Fable 5.1 inside Claude Science, a structured research harness for technical workflows.

After asking Claude which theoretical target it felt capable of tackling, they handed it a single prompt defining the six-particle nine-loop problem. Then, they stepped back. At one point, the researchers told the model: "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 ran for days, ultimately delivering the answer through two completely different mathematical routes: the traditional bootstrap approach and an indirect form-factor method. The bootstrap phase wrote Python scripts using the SymPy library and ran on 96 CPUs for a week, racking up just $100 in compute. Total API costs landed between $1,000 and $2,000 per route.

Dixon independently verified the results. Around the same time, Song He's group at the Chinese Academy of Sciences in Beijing independently derived most of the solution using GPT-6 assistance, though Anthropic's run required remarkably little human hand-holding.

Why it matters

We think this run is a major proof point for agentic science, precisely because it was done on a shoestring budget.

For working scientists, theoretical bottlenecks aren't always a lack of ideas; often, researchers know how a calculation should proceed in principle, but the algebraic bookkeeping would swallow years of human effort. Claude proved that a modern LLM, wrapped in the right harness, can act like a self-directed postdoc: writing code, executing symbolic math, checking edge cases, and pushing past human records for a couple thousand dollars.

Anthropic's approach is clever because it targeted a problem uniquely suited to LLMs—the bootstrap method works like an enormous game of Sudoku, eliminating possibilities against mathematical constraints until only one survives.

Still, it's worth keeping the caveats in view. N=4 super-Yang-Mills is an artificial sandbox, far removed from the messy particles observed at the Large Hadron Collider. Claude didn't invent a new branch of physics; it executed known human methods faster and cheaper than humans ever could. It is an extraordinary computational lever, but real scientific creativity remains human territory for now.