A challenge, answered in a month
Anthropic said on 25 September that Claude had computed the six-particle amplitude in planar N=4 super Yang-Mills theory at nine loops — a calculation nobody in the field had done. The claim is made in a guest post on the company’s science blog written by Matt von Hippel, the former theoretical physicist who set the challenge in the first place.
Von Hippel posted it on his blog on 7 August. He wanted a test of AI on work he personally knew to be hard, and specifically a test of compute rather than insight: “Show that an AI can take the kinds of computer resources an academic has access to, and solve one of the scattering amplitudes field’s big outstanding problems.” He named two: N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine.
Scattering amplitudes are the formulas that turn particle momenta and energies into probabilities of reactions. They are approximated by cutting the calculation off at a number of “loops”, and the cost rises steeply with each one. Most real-world amplitudes have been done to two loops. A few to three. N=4 super Yang-Mills is a deliberately unrealistic toy theory whose extra symmetry makes it tractable, which is why the field uses it to push technique.
What the previous record was
Lance Dixon, a professor at the SLAC National Accelerator Laboratory, reached eight loops a few years ago, and got there indirectly — via a related object called a form factor, which is easier to compute. He had not done nine, and neither had anyone else. As von Hippel puts it, “If people thought it was possible to just run the usual bootstrap method for one more loop, someone would have done it.”
The bootstrap is the technique in question. Rather than summing every interaction, it starts from the shape the answer must take and eliminates possibilities against every constraint the answer has to satisfy — von Hippel compares it to Sudoku. That structure left Dixon well placed to check a nine-loop answer if one appeared.
One prompt, and “keep going”
At the end of August, two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, told von Hippel they had taken the second challenge. They used Fable 5.1 inside Claude Science, the company’s paid research harness.
After asking Claude which of the problems it was most likely to be able to do, they gave it one instruction: “The problem is to compute the Six-particle (hexagon) amplitude in planar N=4 SYM at nine loops.” Then they left it alone. Von Hippel quotes one of their follow-ups: “I’m going to sleep and won’t be available for another several hours. Keep working on this until I tell you to stop. Give me updates every 4-6 hours.”
Claude did the calculation twice, once by the bootstrap and once by the form-factor route. Anthropic puts the cost to an end user at roughly one to two thousand dollars for either approach, most of it the expense of running the model for that long. The bootstrap itself, done in Python with SymPy, took about $100 of that budget — the equivalent, von Hippel writes, of running 96 CPUs for a week.
Humans were closer than anyone thought
Dixon verified the result. Days later, Song He, an amplitudeologist at the Chinese Academy of Sciences in Beijing, told von Hippel that his group had already obtained the majority of the same result, with some AI assistance based on GPT-6 — but not the near-human-free, one-shot approach Anthropic used. Dixon, He and their collaborators will publish the physics.
Von Hippel’s own reading is deflationary about the method and pointed about the field. “Claude used known methods, with a bit more compute than people had tried to use before,” he writes. His conclusion is that “there is more low-hanging fruit out there than you’d expect”, and that computer scientists who have long told amplitudeologists to hire programmers “should feel vindicated”.
What he does not discount is the autonomy. Claude Science, he notes, did this “in one shot, without any scientific oversight more sophisticated than ‘keep going’”, on calculations he describes as finicky and messy and on which he would expect to make mistakes himself.
What to watch
The harder of von Hippel’s two challenges — whether N=8 supergravity diverges at seven loops — is still open, and nobody has announced having done it. He suggests groups working on real-world amplitudes should test whether a science harness can one-shot a frontier calculation there too, “and they ought to have a plan for how to check the results”.
