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How Claude Reached a Nine-Loop Physics Result—and What It Took
Claude calculated the six particle amplitude in planar N=4 super Yang–Mills theory at nine loops, one beyond the previous eight loop result. The calculation used a direct bootstrap and an indirect form factor route; the reported cost was about $1,000–$2,000 per route, mostly for Claude usage.
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Key takeaways
- Claude calculated the six particle amplitude in planar N=4 super Yang–Mills theory at nine loops, one beyond the previous eight loop result.
- The calculation used a direct bootstrap and an indirect form factor route; the reported cost was about $1,000–$2,000 per route, mostly for Claude usage.
- Lance Dixon checked the result, while a separate report describes another nine loop effort involving a GPT 6 team; that report does not establish a human only concurrent result.
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openai.comCreate a landscape editorial hero image for this Studio Global article: How did Anthropic’s Claude calculate the nine-loop, six-particle scattering amplitude in planar N=4 super-Yang–Mills theory in response to M. Article summary: Claude met Matt von Hippel’s challenge by calculating the nine-loop, six-particle amplitude in planar N=4 super-Yang–Mills theory using established techniques, rather than inventing a new way to do the calculation. The r. Topic tags: general, general web, user generated. Style: premium digital editorial illustration, source-backed research mood, clean composition, high detail, modern web publication hero. Use reference image context only for broad subject, composition, and topical grounding; do not copy the exact image. Avoid: logos, brand marks, copyrighted characters, real person likenesses, fake screenshots, UI text, readable text, watermarks, charts with fa
Anthropic reports that Claude computed the six-particle scattering amplitude in planar N=4 super-Yang–Mills theory at nine loops, extending an eight-loop benchmark. The work used established techniques, and Anthropic researchers framed the task and gave Claude guidance during the run. It is a notable example of AI carrying out a demanding research calculation—not evidence that it independently invented a new method or can solve any open problem in physics. 15
Two routes to the nine-loop result
Claude approached the calculation in two ways:
- Bootstrap: This method narrows down an amplitude by assembling possible answers and testing them against known mathematical constraints and predictions. Rather than calculating every possible particle interaction directly, it uses what is already known about the form the answer should take.
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- Form-factor route: This indirect approach calculates a related quantity called a form factor, then uses a known duality to connect it to the amplitude.
Using two routes matters because they provide separate ways to check the calculation. The methods themselves, however, were established techniques; the reported advance was reaching nine loops with them. 15
Researcher guidance and reported cost
Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma set Claude the problem and guided the extended run. The result should therefore be understood as a researcher-directed computation, even if Claude performed much of the work over an extended period. 15
The reported end-user cost was roughly $1,000–$2,000 for either route, largely reflecting the cost of running Claude. The conventional computing component of the bootstrap calculation was reported to be much smaller—about $100 for a week on 96 CPUs. These figures are estimates, not a general price tag for doing theoretical physics with AI. 15
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How it compares with earlier and concurrent work
Lance Dixon and Andy Liu had previously calculated the amplitude to eight loops in 2023 using the form-factor approach. Claude’s nine-loop calculation went one loop further. 15
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A separate report says a team at the Chinese Academy of Sciences using GPT-6 also reached a nine-loop result around the same time. That report describes work involving another AI system; it does not establish a concurrent human-only result. 1
What validation does—and doesn’t—show
Lance Dixon checked Claude’s nine-loop answer, and the agreement between the bootstrap and form-factor routes offers an additional cross-check. These checks strengthen confidence in the reported calculation, but they do not turn it into a new theory or establish that AI can reliably solve unrelated frontier problems. 15
The result shows that an AI system can contribute to a difficult, well-defined research computation when researchers provide the problem, established methods and oversight. It does not show that Claude devised a new calculation technique, worked without human direction, or overcame the broader limits of theoretical physics. Anthropic’s account presents a concrete research milestone; its wider implications for AI’s future capabilities remain uncertain. 15
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What is the short answer to "How Claude Reached a Nine-Loop Physics Result—and What It Took"?
Claude calculated the six particle amplitude in planar N=4 super Yang–Mills theory at nine loops, one beyond the previous eight loop result.
What are the key points to validate first?
Claude calculated the six particle amplitude in planar N=4 super Yang–Mills theory at nine loops, one beyond the previous eight loop result. The calculation used a direct bootstrap and an indirect form factor route; the reported cost was about $1,000–$2,000 per route, mostly for Claude usage.
What should I do next in practice?
Lance Dixon checked the result, while a separate report describes another nine loop effort involving a GPT 6 team; that report does not establish a human only concurrent result.