Anthropic reports that Claude solved a nine-loop scattering amplitude challenge in N=4 super Yang-Mills theory

Anthropic announced that its AI system, Claude, computed a nine-loop scattering amplitude in N=4 super Yang-Mills theory, a task the company described as a frontier challenge in theoretical particle physics. The work was presented in a guest post by physicist and science writer Matt von Hippel, who issued the challenge to AI companies in August 2026.

Von Hippel framed the challenge as a test of whether AI could solve a problem that physicists consider computationally out of reach for typical academic resources. He asked companies to demonstrate that an AI could use compute comparable to what an academic researcher has access to and solve one of the field’s outstanding problems: either N=8 supergravity to seven loops or N=4 super Yang-Mills to nine loops.

N=4 super Yang-Mills is a toy model theory used by amplitudeologists to develop and stress-test new computational techniques. It is not used to model real-world particles but is valued for its mathematical structure, which simplifies certain calculations. Prior to this result, the highest loop calculation in this theory was eight loops, achieved by Lance Dixon at SLAC National Accelerator Laboratory using a bootstrap method.

The bootstrap technique relies on encoding known constraints and symmetries into a computational search, akin to solving a constrained Sudoku puzzle. Dixon noted that the new nine-loop result could be validated using the same bootstrap framework he had previously used for the eight-loop amplitude, providing a pathway for independent verification.

Anthropic stated that Claude produced the nine-loop amplitude using compute resources accessible to academic researchers, though the company did not disclose specific hardware, runtime, or cost figures. The announcement emphasized that the achievement was not merely a scaling exercise but involved nontrivial reasoning steps that aligned with established physics constraints.