Anthropic says its Claude model computed the six-particle (hexagon) amplitude in planar N=4 super Yang-Mills at nine loops, a frontier calculation in the theoretical particle-physics subfield known as amplitudeology. The result is described in a guest post published on 25 September 2026 by physicist and science writer Matt von Hippel, who had publicly challenged AI companies to attempt exactly this problem.
Von Hippel issued the challenge after deciding he wanted to see a model make progress on something he knew was hard because he had tried similar work himself. He asked for N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine loops, on the kind of computing budget an academic would have. Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma reached out at the end of August to say they had tackled one of the two.
This calculation, a scattering amplitude, is a formula that lets the momenta and energies of subatomic particles be used by physicists to work out how likely they are to react in particular ways. More accurate predictions let researchers check whether results from experiments such as the Large Hadron Collider match theory, and a mismatch could point to a new theory. Amplitudeologists almost always approximate, cutting the calculation off at a number of loops, where more loops means a closer answer and a harder computation.
Most scattering amplitude formulas have been calculated only to two loops, with a few at three. Von Hippel writes that he helped calculate a three-loop amplitude for his PhD, saw seven loops before he started losing steam, and that Lance Dixon, a professor at the SLAC National Accelerator Laboratory, managed eight loops a few years back. The nine-loop target was set in a toy model, N=4 super Yang-Mills, which amplitudeologists use to stress-test new techniques because its balance of particles makes it paradoxically easier to calculate with.
How the run was set up
According to the post, the work did not use millions of dollars in computer power. Fitzpatrick and Mishra-Sharma used Fable 5.1 inside Claude Science, a paid platform for scientists that von Hippel describes as a harness — a program that wraps the Claude model in structured rules and prompts to get more robust, scientifically useful behavior.
They first asked Claude which problem it was most likely to solve, then sent a brief prompt requesting that it work out, at nine loops, the six-particle (hexagon) amplitude in planar N=4 SYM. They then repeatedly told it to continue, including a note that they would be away for several hours and a request for updates every 4-6 hours.
Claude produced the calculation two ways, using the original bootstrap method and an indirect form-factor approach. According to the post, either route would have cost an end user roughly one or two thousand dollars, mainly because the model ran for so long. The bootstrap run, written in Python with the SymPy package, accounted for roughly $100 of that budget and corresponded to running 96 CPUs for a week.
The bootstrap technique, von Hippel explains, does not require tracking every possible particle interaction. It starts from roughly what the answer should look like, keeps every possibility in computer files in a specialized alphabet, and then applies known constraints — predictions from other techniques, rules the answer must obey, links to related problems — crossing out possibilities until one survives. He compares it to Sudoku.
Validation and a concurrent human result
Dixon validated the result. In an addendum to the post, he writes that on 1 September he learned the nine-loop MHV six-particle amplitude in planar N=4 super Yang-Mills had been computed by Claude, and he then set about validating it. He says Claude's direct handling of the amplitude impressed him, less for the computation's size than for the setup's fragility: one error in the computational recipe collapses everything, and much of the construction is too mundane for full documentation in a publication, so Claude had to write all the code from scratch.
Dixon also notes that his team had been working toward the nine-loop form factor for a couple of years, and that going back from the amplitude to the form factor made validation easier. He writes that Claude used the methods his collaborators developed over the years and presented the solution in the format the team had already set up.
A few days after von Hippel heard from Anthropic, Song He, an amplitudeologist at the Chinese Academy of Sciences in Beijing, reported that his group had already obtained most of the result. Dixon writes that Song's group computed the symbol piece of the nine-loop amplitude, and that GPT-6 helped with some constraints but not the overall framework. The humans involved — Dixon, Song and their collaborators — will publish the results; the post says Claude's role is done for now.
What the author concludes
Von Hippel writes that he had expected AI to overcome a computational barrier in a surprising way, and instead it did something humans turned out to be able to do as well. In his account, Claude used known methods with somewhat more compute than people had tried, and may have benefited from using Python rather than Maple or Mathematica and from better software engineering practices.
His main takeaway is that there is more low-hanging fruit than he expected: even a simple, well-defined goal can look far less achievable to experts than it is. He also flags that the harness reached the end without scientific oversight more sophisticated than "keep going," on calculations he says are finicky and messy enough that he would almost certainly have needed two weeks of 96 CPUs rather than one.
He is careful about how far the result generalizes. Toy models are the focus of small sub-communities, while real-world amplitude calculations involve many groups competing at the frontier, where there may be less low-hanging fruit. He adds that he would not count on it, and that AI for coding has been increasingly used by people working on those calculations.
On the broader question that motivated the challenge — what current AI implies about future capability — von Hippel writes that he did not get an answer. He had hoped to see new methods for the calculation itself, and instead learned that he had been too naive about where the computational limit was.
Confirmed
- Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma told von Hippel at the end of August that they had tackled his challenge; the post was published on 25 September 2026.
- According to the post, Claude computed the six-particle (hexagon) amplitude in planar N=4 super Yang-Mills at nine loops using Fable 5.1 within Claude Science, a paid harness for scientists.
- Claude produced the result two ways — the bootstrap method and an indirect form-factor approach — at an estimated end-user cost of around one or two thousand dollars, with the Python/SymPy bootstrap run accounting for about $100, corresponding to 96 CPUs for a week.
- Lance Dixon of SLAC validated the result; he writes that he learned of it on 1 September and that his team had been working toward the nine-loop form factor for a couple of years.
- Song He's group at the Chinese Academy of Sciences in Beijing had already obtained most of the result, computing the symbol piece with help from GPT-6 on some constraints, per Dixon's addendum.
- The post discloses that Anthropic invited von Hippel to write it and compensated him, that Anthropic staff gave feedback on drafts, and that Dixon received Claude usage credits.
Unknown
- No independent replication of the nine-loop amplitude beyond Dixon's validation is described; the human groups' write-ups had not yet been published.
- The post does not break down the roughly one or two thousand dollar figure by approach, and the $100 bootstrap figure is given only for that run.
- No pricing, rate limits, or access terms for Claude Science or Fable 5.1 appear in the material.
- Whether the approach transfers to real-world amplitude calculations, rather than toy models, is left open by the author.
Our take
The interesting claim here is not raw compute but reliability: a fragile, under-documented recipe ran end to end without a human collaborator, on a budget an academic group could plausibly spend. That is a narrower result than a new physics method, and the post says as much. The harder question is what happens when the same harness is pointed at fields where many groups race the same target and the low-hanging fruit has already been picked.
