Claude Completes Complex Physics Computation

On September 25, 2026, Anthropic published a guest post on its research site reporting that Claude computed the nine-loop MHV six-particle amplitude in planar N=4 super-Yang-Mills theory.

Anthropologic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma ran the computation using Fable 5.1 inside the Claude Science platform. The initial prompt given to Claude was: “The problem is to compute the Six-particle (hexagon) amplitude in planar N=4 SYM at nine loops.”

Dual Computational Approaches

Claude performed the nine-loop calculation two different ways: the original bootstrap method and an indirect form-factor approach. Either approach to the nine-loop calculation would have cost an end-user around $1,000 to $2,000 in total.

The bootstrap calculation step, implemented in Python using the SymPy package, cost approximately $100 and corresponded to running 96 CPUs for one week. Fitzpatrick and Mishra-Sharma left Claude running unsupervised with the standing instruction: “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.”

Independent Validation and Prior Work

Lance Dixon, a professor of Particle Physics and Astrophysics at SLAC National Accelerator Laboratory and Stanford University, independently validated Claude’s nine-loop result by checking the nine-loop form factor, spending approximately two weeks on validation.

The challenge that prompted the computation was publicly issued on August 7, 2026 by physicist and science writer Matt von Hippel on his blog 4gravitons.com.

Song He’s group at the Chinese Academy of Sciences in Beijing had already computed the majority of the nine-loop result using AI assistance based on GPT-6, independent of Anthropic’s effort. Song He’s team published their dataset on September 17, 2026.

Scope of the Achievement

Matt von Hippel was invited to write the guest post by Anthropic and was compensated for his time, with Anthropic staff providing feedback on drafts. Von Hippel concluded that Claude used known methods with more compute than physicists had previously tried, rather than discovering a new computational technique.

Source: Anthropic