Claude breaks nine-loop scattering amplitude record with one prompt and a few thousand dollars

新智元 · wechat · 2026-09-26

Anthropic announced that Claude, running autonomously for days, computed the nine-loop six-particle amplitude in planar N=4 super Yang-Mills — breaking the human record of eight loops. The challenge came from physicist Matt von Hippel, who dared AI companies to solve his field's open problems on an academic budget.

Anthropic physicists used the Claude Science system (Fable 5.1) with a single prompt, then left it unattended with 4-6 hour progress reports.
Claude solved it two independent ways: the bootstrap method (Python + SymPy, Sudoku-like constraint elimination) and the form-factor route via antipodal duality, cutting unknowns from 1.85M to 76K with exact integer arithmetic. One cut expansion alone has 30 billion terms.
Cost: a few thousand dollars total; pure compute was $100 (96 CPUs for a week).
Eight-loop record holder Lance Dixon verified the result over two weeks, calling Claude possibly the deepest reader of his papers besides his coauthors.
Twist: He Song's team at CAS Institute of Theoretical Physics posted two-through-nine-loop skeleton data on Zenodo on Sept 17 — 8 days before Anthropic's announcement — using GPT-6 as partial assistance with a human-built framework.
Dixon: real watershed will be when LLMs propose new physics before humans do.

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Claude breaks nine-loop scattering amplitude record with one prompt and a few thousand dollars

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