Anthropic announced on 25 September that Claude had computed the nine-loop six-particle scattering amplitude in planar N=4 super Yang-Mills. The previous eight-loop record had belonged since 2023 to SLAC's Lance Dixon, who has now validated the model's work himself. A week earlier, though, a Chinese Academy of Sciences team published the same result independently.
Key takeaways
- The run used Fable 5.1 on the Claude Science platform, not the newer Opus 5.5
- End to end, the work would cost an end user one to two thousand dollars
- The Python and SymPy bootstrap alone took about $100 of budget, or 96 CPU cores for a week
- Human oversight amounted to prompts like “keep working, give me updates every four hours”
- Song He's group posted the same symbols to Zenodo on 17 September
What the model actually did
The prompt was literal: compute the six-particle MHV amplitude?MHV amplitude: A maximally helicity violating gluon scattering amplitude — the case where exactly two particles carry helicity opposite to the rest. in planar N=4 SYM?planar N=4 super Yang-Mills: A maximally supersymmetric quantum field theory taken in the large-colour limit, used by physicists as a testing ground for calculation methods. at nine loops. Claude attacked it two ways — a classic bootstrap?bootstrap: A method that pins down an amplitude from consistency conditions and symmetries instead of summing Feynman diagrams. written in Python with SymPy, and an indirect route via the form factor and antipodal duality?antipodal duality: A relation linking a scattering amplitude to the so-called form factor, letting one be computed from the other.. The raw data is public, but Anthropic did not release the code.
A record that fell twice
There is a second layer. Song He's group reached the same result that month, leaning on GPT-6 for part of the constraint work but never handing it the whole framework. The boundary Claude pushed was within human reach anyway.
Matt von Hippel, the theoretical physicist who wrote Anthropic's post, puts it plainly: the model used known methods, just with more compute than anyone had tried.
| Result | Who | Date | Tooling |
|---|---|---|---|
| 8 loops | Lance Dixon, SLAC | 2023 | — |
| 9 loops | Song He’s group, Chinese Academy of Sciences | 17 September, Zenodo | GPT-6 for part of the constraints |
| 9 loops | Claude | 25 September, Anthropic announcement | Fable 5.1 on Claude Science |
Dixon spent two weeks checking it, and rates it highly.
I would assert that Claude understands our 2019 and 2023 papers better than any human, aside from my co-authors.
Lance Dixon, professor at SLAC National Accelerator Laboratory and Stanford University.
Why it matters
The result does not prove the model can do things humans cannot. It shows something harder to dismiss: a multi-hour symbolic computation run with no scientific oversight, for a sum that fits inside a single grant. That shifts the question from “can AI do this” to “how much researcher time is still worth spending here”. The sponsored framing warrants caution.
What's next
- Dixon and Song He's team plan formal publications, but as of 27 September there is still no arXiv preprint
- Claude Science remains in beta as a paid platform for researchers
- Von Hippel's August challenge, N=8 supergravity at seven loops, is still open
Sources
- Anthropic — Yes, Claude can do Nine Loops
- Siddharth Mishra-Sharma — Cosmic nine loops
- Zenodo — The Symbols of Six-Gluon MHV Amplitudes through Nine Loops
- arXiv — An Eight Loop Amplitude via Antipodal Duality
- 4gravitons — It got to my field
