Yes, Claude can do Nine Loops

Matt von Hippel, a former theoretical physicist, issued a challenge: could AI compute a frontier scattering-amplitude problem that looked computationally out of reach? The target was the six-particle (hexagon) amplitude in planar N=4 super Yang-Mills at nine loops, a toy-model calculation amplitudeologists use to test methods. Researchers at Anthropic used Claude via the Claude Science harness (Fable 5.1) and ran two independent approaches - the standard bootstrap and an indirect form-factor route - automating long-running symbolic work in Python/SymPy. The runs cost on the order of $1-2k overall, with the bootstrap step roughly $100 worth of compute (about 96 CPUs for a week). A separate group led by Song He had already obtained most of the result with GPT-6-assisted work; human collaborators will publish and analyze the final answers.

The substantive takeaway is that Claude did not invent a new mathematical trick but executed known, finicky techniques reliably and affordably, benefiting from sustained compute, better software engineering, and a simple “keep working” harness instruction. This demonstrates that apparently hard computational bottlenecks in amplitudeology are often low-hanging fruit when paired with programmer-level tooling and LLM orchestration. The episode signals practical, near-term gains for computational physics from LLM-driven automation rather than evidence of mystical superintelligence.