Anthropic says its Claude models have computed a result in theoretical particle physics that no one had published before: the six-particle scattering amplitude in planar N=4 super Yang-Mills theory at nine loops. The calculation goes one loop beyond the eight-loop record set in 2023 by SLAC's Lance Dixon and a collaborator, and it was checked by Dixon himself.
The result, described in a guest post on Anthropic's research site on September 25, is being held up as one of the clearest demonstrations yet of an AI system carrying a frontier scientific computation from start to finish on a modest budget — while also coming with important caveats about what kind of discovery it really is.
A Public Challenge, Answered
The work began with a dare. On August 7, 2026, Matt von Hippel, a former theoretical physicist who writes the 4gravitons physics blog, publicly challenged AI companies to show their systems could tackle genuine frontier problems using roughly the computing resources available to an academic. He named two targets: determining whether N=8 supergravity diverges at seven loops, or computing the N=4 super Yang-Mills hexagon amplitude at nine loops.
Anthropic researchers Liam Fitzpatrick and Siddharth Mishra-Sharma took up the second. After first asking Claude which problem it was most likely to crack, they gave it a one-line prompt describing the nine-loop hexagon calculation — and then, by their account, mostly told it to keep going.
How the Calculation Was Done
The team ran Fable 5.1 inside Claude Science, Anthropic's paid research harness that wraps the model in structured rules and prompts to make its behaviour more robust for scientific work. Claude wrote and ran Python code, including the SymPy symbolic mathematics library, and completed the calculation two independent ways:
- The amplitude bootstrap, which constrains the answer using known mathematical and physical properties
- An indirect form-factor approach, linked to the amplitude through a relationship known as antipodal duality
The costs were strikingly low. The post puts the bootstrap computation at roughly $100 of compute — about 96 CPUs running for a week — and each full route at around $1,000 to $2,000 for an end user, mostly in Claude usage.
Verified — With Caveats
Dixon, a professor at SLAC National Accelerator Laboratory and Stanford, reviewed the result and said Claude had used the full toolbox of methods his collaborators developed over many years, executing a long, fragile chain of calculations reliably.
But von Hippel and Anthropic are careful about the framing:
- No new method was invented. Claude applied established techniques with more compute than humans had previously thrown at the problem.
- Humans got there too. A group led by Song He at the Chinese Academy of Sciences reached most of the same result in the same weeks, using GPT-6-based AI assistance for some constraints. On September 17 that team posted a Zenodo dataset of six-gluon MHV amplitude symbols through nine loops.
- Publication belongs to physicists. Von Hippel wrote that Dixon, He and collaborators will publish the results with full analysis, and that Claude's role is complete for now.
Why It Matters
Scattering amplitudes in N=4 super Yang-Mills are a proving ground for the mathematics used to understand particle collisions, and each additional loop has historically demanded years of expert effort. Seeing an AI system finish such a calculation in about a week, for the cost of a conference trip, changes the economics of a whole class of research.
The more interesting shift may be in who can do this work. Von Hippel's challenge was explicitly about academic-scale resources. If a harnessed model can reliably execute long symbolic computations using published methods, then smaller research groups — and scientists outside elite institutions — could attempt problems that previously required rare, specialised teams.
At the same time, the result sharpens an ongoing debate about what counts as AI "discovery." Executing a known recipe at a new scale is valuable, but it is different from inventing the recipe. The near-simultaneous human result also shows that the frontier is moving quickly on both sides, with AI increasingly acting as a force multiplier for human physicists rather than a replacement.
Part of a Pattern
The nine-loop calculation follows Anthropic's report earlier this week that Claude flagged a previously uncharacterised enzyme system in phage DNA, and a steady stream of AI-for-science claims from rival labs. Together they suggest that 2026's competition among frontier labs is expanding from coding and agent benchmarks into verifiable scientific output — results that outside experts can check line by line.
For researchers, the practical takeaway is that AI research harnesses such as Claude Science are becoming credible tools for long-horizon computational work, provided the results are independently verified the way Dixon verified this one.
