Claude computed a nine-loop particle physics amplitude for around $2,000
Anthropic's Claude Fable 5.1 beat the human eight-loop record in theoretical physics, answering a public AI challenge set in August 2026.
On 25 September 2026, Anthropic published a report describing something that most theoretical physicists would have considered implausible a few years ago: an AI model computed the six-particle scattering amplitude in planar N=4 super Yang-Mills theory at nine loops, beating the previous human record of eight loops set in 2023, and doing so for a total compute cost of roughly $1,000 to $2,000.
The researchers behind it were Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma. The model was Claude Fable 5.1, running on Anthropic’s Claude Science platform. The verification came from Lance Dixon at SLAC National Accelerator Laboratory, the same physicist whose team held the eight-loop record.
What are scattering amplitudes, and why does loop count matter?
Scattering amplitudes are the mathematical expressions physicists use to calculate how likely subatomic particles are to interact in specific ways. In quantum field theory, computing them precisely requires summing an infinite series of contributions, each represented diagrammatically as a “loop”. More loops mean a more accurate answer and a vastly harder calculation.
Most amplitude calculations in physics stop at two loops. A handful reach three. Eight loops, before this result, was as far as anyone had taken the six-particle amplitude in N=4 super Yang-Mills, a theoretical model physicists use as a mathematically cleaner stand-in for the theories that describe real particle interactions.
Nine loops is not a trivial increment. The difficulty scales steeply.
The challenge, and how Claude answered it
On 7 August 2026, Matt von Hippel, a former theoretical physicist who writes about physics at 4gravitons.com, issued a public challenge to AI companies. He asked them to demonstrate that an AI, using resources comparable to what an academic group might have access to, could solve one of two open problems: the seven-loop divergence question in N=8 supergravity, or the nine-loop six-particle amplitude in N=4 super Yang-Mills.
Fitzpatrick and Mishra-Sharma told von Hippel on 1 September 2026 that Claude had done the second one. They asked him to validate the result. He did.
The actual computation used two independent methods. The first was the hexagon bootstrap, a technique that constrains the amplitude by imposing known physical properties until only one consistent answer remains. The second was an indirect route using the nine-loop form factor combined with antipodal duality, the same approach Dixon’s group had used to reach eight loops. The two methods agreed on every coefficient, across all 107,053 nonzero coefficients in the nine-loop symbol.
The bootstrap calculation alone cost around $100, corresponding to running 96 CPUs for approximately one week. The full project, including the indirect cross-check, came to $1,000 to $2,000 in total compute.
The prompt that started it was a single sentence: “The problem is to calculate the six-particle (hexagon) nine-loop amplitude in planar N=4 supersymmetric Yang-Mills theory.” After that, Fitzpatrick and Mishra-Sharma mostly sent one word back: “continue.”
What Claude actually did, and what it did not do
Von Hippel’s own assessment is worth quoting directly: “Claude used known methods, with a bit more compute than people had tried to use before.”
That framing matters. Claude did not invent new physics. It did not develop novel mathematical methods or theoretical insights. The bootstrap techniques it applied are established tools in the amplitudes community. What changed was the ability to apply them at a scale and for a duration that strains human patience and error-correction capacity. Writing, debugging, and running the required Python and SymPy code across days of continuous execution, with little human intervention, is exactly the kind of sustained, low-glamour technical work where automated systems have a clear advantage.
Claude Science, the platform Fitzpatrick and Mishra-Sharma used, pairs the underlying language model with structured prompts, tool access, persistent task state, and long-horizon execution. That means the model can write and run code, inspect outputs, recover from failed approaches, and continue working across sessions without a human needing to supervise every step.
The full result, eight files totalling over 100 MB, was deposited on Zenodo on 16 September 2026 in the same computer-readable format used for six-, seven-, and eight-loop results, making it directly usable by other researchers.
What this means for you
If you work in theoretical physics or adjacent areas of mathematics, the immediate implication is that several amplitude problems with known higher-loop extensions may now be tractable without waiting for a team willing to spend months on them. Von Hippel notes that researchers have often lacked the time or tooling to pursue those extensions, not necessarily the ideas.
If you work in AI or technology more broadly, this is a concrete data point about what the current generation of frontier models can do when given a well-scoped technical problem, the right infrastructure for long-running tasks, and a clear verification target. The cost figures are striking: a calculation that extends the frontier of a specialised field of physics cost less than a mid-range laptop.
The wall at ten loops is still there. Whether it falls depends on whether the methods that worked at nine loops scale further, or whether someone has an idea that changes the approach entirely. That is an open question.
What is no longer open is whether an AI system can reach the cutting edge of theoretical physics calculation using established methods, modest compute, and a one-sentence prompt.