Anthropic’s Claude solves nine-loop amplitude challenge in theoretical physics

Physics has a category of problems that are technically straightforward to describe and brutally hard to solve. Scattering amplitude calculations fall squarely in that category. They tell physicists what happens when particles collide, and the more precision you want, the more computational loops you have to work through. Each additional loop multiplies the complexity by an almost absurd factor.

Anthropic’s Claude just cleared nine of them.

On September 25, 2026, Anthropic announced that its physicists Liam Fitzpatrick and Siddharth Mishra-Sharma had used Claude to compute the six-particle scattering amplitude in planar N=4 super Yang-Mills theory at nine loops. That sentence is a mouthful, but the short version is this: the AI completed a calculation that represents the current frontier of a subfield that has occupied some of the world’s sharpest theoretical minds for decades.

What was actually computed, and why it matters

N=4 super Yang-Mills is a theoretical model physicists use as a kind of sandbox. It shares structural features with the theories that describe real particle interactions, but it’s clean enough to be mathematically tractable. Scattering amplitudes in this model tell you the probability of specific particle collision outcomes.

The “loop” number refers to a perturbative expansion, essentially how many rounds of quantum corrections you’re accounting for. Think of it like approximating a curve with a polynomial: one term gets you close, five terms gets you closer, nine terms gets you very close but requires an enormous amount of algebra. Each additional loop doesn’t just add a step, it multiplies the symbolic complexity of everything that came before.

The previous record in this specific calculation sat at eight loops, set in 2023 by physicist Lance Dixon and Andy Liu. Fitzpatrick and Mishra-Sharma, working with Claude, moved that needle to nine.

The computation used two independent methods: a direct bootstrap of hexagon functions, and an indirect route through the nine-loop form factor using a technique called antipodal duality. Running two separate paths to the same answer is the standard way to verify you haven’t made an error, and the results agreed. Dixon himself later verified the findings.

The challenge that set this in motion

This wasn’t a project that Anthropic dreamed up internally. It was a response to a public dare.

On August 7, 2026, Matt von Hippel, a former physicist and science blogger, issued an open challenge to the AI community. The premise was direct: use AI systems and standard academic resources to tackle longstanding problems in scattering amplitude calculations.

Fitzpatrick and Mishra-Sharma took on the challenge. Claude ran largely unsupervised for several days, working through the computation with minimal human intervention. The total cost came to a few thousand dollars in compute. By late August or early September 2026, the nine-loop result was complete.

The data files from the computation, more than 100 megabytes of computer-readable output in a format consistent with previously published six-, seven-, and eight-loop results, were released publicly on Zenodo on September 16, 2026.

What Claude did, and what it didn’t do

The important qualifier here is that Claude didn’t invent new physics. No novel theoretical methods were developed in the course of this computation. The bootstrap techniques applied at nine loops are established tools in the amplitudes toolkit. What changed was the ability to apply them at a scale and for a duration that strains human patience and error-correction capacity.

The fact that the computation ran largely unsupervised is also notable. Fitzpatrick and Mishra-Sharma weren’t babysitting Claude line by line. The model operated with enough autonomy to run a multi-day symbolic calculation, catch or avoid its own errors well enough to produce a result that passed external verification, and output data in a format compatible with existing literature.

The specific Claude version involved was Fable 5.1, running on Anthropic’s Claude Science platform, a setup aimed at extended scientific computation tasks rather than conversational use.