Nine-loop record broken with two independent methods – code written from scratch by Claude
Anthropic announced on September 25 that Claude has completed the nine-loop calculation of six-particle scattering amplitudes in planar N=4 super Yang–Mills — breaking the record held by Lance Dixon's SLAC team for three years.
Anthropic announced on September 25 that Claude has completed the nine-loop calculation of six-particle scattering amplitudes in planar N=4 super Yang–Mills theory — breaking the record held by Lance Dixon's SLAC team for the past three years. All of this, according to the company, happened with a one-sentence task description, a "continue" button, and a total cost of roughly $1,000–$2,000 per method.
What is claimed to have happened
According to Anthropic's announcement, as reported by BigGo Finance, the company's language model Claude completed the nine-loop calculation of six-particle scattering amplitudes in planar N=4 super Yang–Mills theory on a research platform operating "with almost no supervision." In doing so, the eight-loop record fell — a record held for three years by a team led by physicist Lance Dixon at SLAC National Accelerator Laboratory in the United States.
It is worth underscoring what is what here: that the record was broken, that the workflow was near-supervision-free, and that the task description was a single sentence are all company claims. What stands on firmer ground is that Dixon himself — according to the same source — has independently verified Claude's computational results.
What the calculation actually is
Scattering amplitudes describe the probability that particles collide and scatter in particular ways. In planar N=4 super Yang–Mills — a highly simplified but famous mathematical model in theoretical physics — these are computed order by order: "loops" represent increasingly precise quantum corrections beyond the simplest level. Each additional loop dramatically increases the complexity, and the nine-loop level for six particles has long been considered extremely demanding.
Dixon's SLAC team held the previous record at eight loops. According to BigGo Finance's reporting, Dixon had previously believed that completing the calculation directly at nine loops was too difficult, and his team had been preparing for the task for years.
The challenge that started it
The assignment did not come from Anthropic itself, but from an August 7 blog post by Matt von Hippel, a former theoretical physicist and science communicator. He challenged AI companies to solve an open problem in scattering amplitudes using computing power affordable to a single academic. He suggested two options: computing N=8 supergravity to seven loops, or computing the six-particle amplitude in planar N=4 super Yang–Mills to nine loops.
Anthropic chose the latter option — and reportedly stayed within von Hippel's budget constraint for individual researchers, according to the reporting.
Two independent methods — and the price tag
Claude reportedly performed the calculation twice, using two different methods: the direct bootstrap approach, and Dixon's team's indirect route via form factors. The agreement between results from two independent approaches is a classic form of internal cross-checking in this field.
The costs — drawn from information provided by Anthropic researchers and von Hippel's own account, as relayed by BigGo Finance — are strikingly low: approximately $1,000–$2,000 per method in end-user costs. Of that, only about $100 went to the actual numerical computation, corresponding to 96 processors running continuously for one week. The rest of the cost therefore lies in the model runs themselves — the development of code and strategy, not the heavy arithmetic.
The workflow: one sentence and "continue"
According to information relayed by BigGo Finance, researchers gave Claude only a brief one-sentence task description. After that, the guidance consisted almost entirely of the word "continue." A typical instruction reportedly went something like: "I'm going to sleep and am not available for the next few hours. Keep working until I tell you to stop, and report progress every four to six hours."
This too is researcher disclosure and company account, not something independently verified. But it points to what may be the real point: not a new algorithm, but a model capable of driving a long, multi-step computational process with minimal human steering.
What Dixon's verification actually establishes
Dixon reportedly verified the results independently, and is said to have expressed surprise that Claude could run the entire workflow in a single pass. In a postscript to the verification, he wrote — as BigGo Finance relays it — that if any single component of the recipe had contained an error, the whole result would have collapsed like a failed soufflé. Yet Claude reportedly built all the code from scratch.
What the Dixon check establishes, then, is this: the results check out, the code was written from scratch, and any single error would have collapsed the result. What it does not establish is a fully independent reproduction: no published paper is described, and no reproduction of the calculation by anyone other than Dixon. The verification rests on one physicist's check, known only through secondary reporting.
The sober counterweight
Von Hippel himself tempers expectations. He acknowledged, according to BigGo Finance's account of his guest blog, that the effort did not deliver the kind of "unexpected breakthrough past a computational barrier" he had hoped for. Claude used known methods — just with somewhat more compute than humans had previously been willing to invest.
That is an important frame for reading the news: this is not a new physics breakthrough, but a breakthrough in how much long-running, precision-demanding work a language model can perform with almost no supervision — at a price a single academic can bear.
Same month: a wave of AI-mathematics claims
The announcement lands amid a series of related company statements in the same month. Anthropic stated that Claude has raised the lower bound on the proportion of zeros of the Riemann zeta function satisfying the Riemann hypothesis, from 41.6 to 67.2 percent, and completed a full Lean formalization of Fermat's Last Theorem in 11 days with largely autonomous operation. OpenAI reported that one of its internal models had solved more than 100 long-unsolved mathematical problems — but the evidentiary basis for that last claim is sparse in available reporting, and its contents cannot be established in more detail here.
All of these figures and claims are the companies' own, relayed via the same source, and none of them is documented through primary sources in the available evidence.
What remains open
Three things remain before the result can be securely placed in the field's history: a primary source from Anthropic or a published paper documenting the calculation, an independent reproduction by someone other than Dixon, and an assessment of whether this kind of near-autonomous long-running computation can generalize to other problems in the field. For now, the safe framing is the one von Hippel himself pointed to: no unexpected physics, but a remarkable feat of execution — known methods, more compute, and a human who mostly just pressed "continue."