Anthropic's Claude Solves 9-Loop Scattering Amplitude in N=4 Super Yang-Mills

Anthropic's Claude Science platform, powered by the Fable 5.1 model, successfully calculated the 9-loop scattering amplitude for N=4 super Yang-Mills theory. This achievement, reported by physicist Matt von Hippel, marks a significant milestone in amplitudeology, as the 9-loop calculation was previously deemed impossible via direct methods due to its extreme computational fragility.

Methodology and Execution

The calculation was performed by Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma using a simple prompt instructing the model to compute the planar N=4 SYM 9-loop 6-particle (hexagon) amplitude. No external scientific supervision was provided during the process. Claude employed two distinct approaches:

• Bootstrap method: Utilizing Python and SymPy, this approach required approximately 96 CPUs running for one week, costing around $100.
• Form-factor connection: An indirect method linking form factors to amplitudes.

The total cost for the final user was estimated between $1,000 and $2,000. The resulting code followed the methodology and formatting of existing research teams, leading Lance Dixon (SLAC) to note that Claude understood his 2019 and 2023 papers better than any non-coauthor.

Verification and Competition

Lance Dixon independently verified the results, confirming that the 9-loop amplitude was correct despite the high risk of small errors collapsing the entire calculation. The verification process also served to validate the research team's previous work on 9-loop form factors.

Concurrently, the Song He group at the Chinese Academy of Sciences reported calculating parts of the 9-loop amplitude using GPT-6 for constraint calculations. However, their approach involved more human intervention compared to Anthropic's "one-shot" method. The author noted being "scooped" by both the AI and the human-AI hybrid team within two weeks.

Implications for AI in Physics

The author emphasizes that this success does not represent AI creating new physical principles, but rather executing known methodologies with superior efficiency and software engineering. The key takeaway is the improved reliability of LLMs in handling complex, fragile computational recipes. While this solves a "low-hanging fruit" previously thought out of reach, the true challenge for AI will be when it begins to propose novel physical insights or principles beyond existing human knowledge.