The success of the Claude model in solving scattering amplitude equations at the nine-loop level demonstrates the potential of artificial intelligence as a super-computing tool capable of helping physicists break through the walls of arduous mathematical operations.
- Computational breakthrough for Claude in theoretical physics
- Importance of scattering amplitudes and supersymmetric Yang-Mills theory
- Behind the scenes of the experiment and executed computational paths
- Independent verification and simultaneous achievement with a human team
- Horizons of artificial intelligence between computing and theory invention
- Frequently asked questions
Computational breakthrough for Claude in theoretical physics
Anthropic announced on Friday that its artificial intelligence model, Claude, managed to calculate the scattering amplitude for six particles at the nine-loop level within planar four-dimensional maximally supersymmetric Yang-Mills theory, a highly precise and complex mathematical problem at the forefront of theoretical particle physics research, thereby surpassing the previous world record set at the eight-loop level in 2023. This successful work was in response to an open scientific challenge launched a few weeks earlier by science writer and specialized physicist Matt von Hippel, who invited artificial intelligence companies to prove their models’ capability to solve one of the thorny and pending mathematical problems in this scientific specialty, within a modest financial budget similar to the resources available to academic institutions.
Importance of scattering amplitudes and supersymmetric Yang-Mills theory
Scattering amplitudes represent the fundamental mathematical formulas and equations that physicists rely on to accurately predict how subatomic particles interact and collide with one another. Higher mathematical “loop” levels add increasingly complex and branching quantum corrections, which raise prediction accuracy but require in return a computational effort far exceeding normal human calculation capabilities; indeed, the majority of calculated particle scattering amplitudes in the real world have not yet exceeded just two or three loops. The world record specifically registered in this theory was set in 2023 by researcher Lance Dixon from the Stanford Linear Accelerator Center and his colleague Andy Liu at the eight-loop level.
It is worth noting that four-dimensional supersymmetric Yang-Mills theory is not a model representing matter particles in actual physical reality, but rather a carefully designed “simplified gauge theory” serving as a mathematical test environment, which theoretical physicists use to develop and test the robustness of modern mathematical methods and techniques, subjecting them to the harshest degrees of experimentation and analysis. Consequently, completing this calculation represents a valuable theoretical addition to specialized mathematical tools, even though applying the same methodologies to less symmetric physical theories remains a complex future scientific challenge awaiting a solution.
Behind the scenes of the experiment and executed computational paths
This experiment was led by two physicists working at Anthropic, Liam Fitzpatrick and Siddharth Mishra-Sharma, who oversaw guiding the Claude model version 5.1 operating within the specialized platform environment “Claude Science.” The researchers provided the model with concise text instructions explaining the dimensions and goals of the physical problem, with an explicit directive for the model to continue independent computational work throughout the night without stopping. The artificial intelligence successfully completed the complex calculations across two fully independent paths: the first path relied on a direct self-bootstrapping method known as the “bootstrap,” while the second path used an indirect approach based on “form factors.” The total cost to complete the task was estimated between $1,000 and $2,000 USD for each path, with the vast majority of these expenses attributed to the operational cost of the Claude model’s own compute consumption.
Independent verification and simultaneous achievement with a human team
Physicist Lance Dixon spent two full weeks reviewing the outputs of the Claude model and independently verifying their mathematical accuracy, primarily using the nine-loop form factor approach. Dixon described the final result as a “genuine and impressive victory” for large language models, pointing out that Claude was required to program and build all necessary codes and algorithms from scratch, applying a very precise and sensitive calculation recipe such that any minor error at any stage would lead to the collapse of the entire mathematical structure and the failure of the experiment.
However, this mathematical achievement was not exclusive to the Claude model alone; a human research team led by Professor Song He at the Chinese Academy of Sciences managed to calculate the major part of the nine-loop code simultaneously and independently, utilizing some computational assistance from the GPT-6 model. The Chinese team published their completed research data on the open platform Zenodo on September 17. Von Hippel commented on this synchronization by affirming that the Chinese human effort deserves all appreciation and scientific recognition, explaining that these human researchers will be the ones writing and publishing the scientific papers and analyzing the extracted physical results for the international scientific community rather than the artificial intelligence robot.
Horizons of artificial intelligence between computing and theory invention
Von Hippel was keen to place the achievement in its precise realistic context to avoid exaggerations, pointing out that Claude relied on established mathematical approaches and methods well-known to scientists but with a larger processing and computing volume than researchers had previously attempted, and did not invent entirely new physics out of thin air. He wrote in his assessment: “The biggest takeaway for me is that there are low-hanging fruit and research goals closer than we expected in this field, just waiting for someone to pick them.” For his part, Dixon added that the deeper and more fundamental questions in the course of science will emerge when “large language models begin to invent entirely new physical principles and insights and surpass the minds of human scientists.”
Frequently asked questions
Question: What is the specific computational achievement accomplished by the Claude model in particle physics?
Answer: Calculating the scattering amplitude for six particles at the nine-loop level within supersymmetric Yang-Mills theory, outperforming the previous record.
Question: How much was the estimated financial cost to solve this complex problem?
Answer: The cost ranged between $1,000 and $2,000 USD for each computational path, which is a very modest amount for academic research.
Question: Did Claude achieve this mathematical feat alone, or did other scientists precede or coincide with it?
Answer: It was coincided with by researchers at the Chinese Academy of Sciences led by Song He, who published nearly identical results at the same time.
