Anthropic's Claude AI Breaks Three-Year Computational Record in Theoretical Physics

Anthropic's Claude AI has successfully computed the nine-loop six-particle scattering amplitude in planar N=4 super-Yang-Mills theory, breaking a three-year-old computational record in theoretical physics. Operating largely autonomously within the Claude Science platform, the Fable 5.1 model completed the calculation over several days for roughly $1,000 to $2,000, answering a public challenge issued to AI companies just a month earlier.[1][3][5]

Scattering amplitudes are the mathematical formulas physicists use to predict the probabilities of specific outcomes when subatomic particles interact. To make these calculations manageable, physicists use a perturbative expansion, adding successive layers of quantum corrections known as loops. Each additional loop refines the prediction but increases the algebraic complexity factorially, requiring an integration over unconstrained virtual momenta.[5]

Because real-world particle interactions are overwhelmingly complex, researchers test new mathematical techniques on simplified toy models like planar N=4 super-Yang-Mills theory. Its exceptional symmetry makes calculations tractable enough to push the boundaries of computational methods. Most standard amplitude formulas are only known to two or three loops; the most precise prediction in particle physics, the electron's anomalous magnetic dipole moment, required five.[1][3]

The standing record in this specific toy model was eight loops, established in 2023 by Lance Dixon of the SLAC National Accelerator Laboratory and his collaborator Yu-Ting Liu. They achieved that milestone by calculating a related, simpler quantity called a form factor and converting it to an amplitude using a mathematical symmetry called antipodal duality. Dixon's team had spent the subsequent years preparing to tackle the nine-loop problem using the same indirect path.[1][4]

The catalyst for the AI breakthrough came on August 7, 2026, when former theoretical physicist Matt von Hippel published a challenge on his blog, 4gravitons. He dared AI companies to solve either an N=8 supergravity amplitude at seven loops or the N=4 super-Yang-Mills amplitude at nine loops using only the computing resources typically available to an academic researcher.[1][3]

Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma took up the challenge, providing Claude with a single-sentence initial prompt: "The problem is to compute the Six-particle (hexagon) amplitude in planar N=4 SYM at nine loops." The researchers then left the model to run, instructing it to keep working and provide updates every four to six hours while they slept.[1][5]

Claude did not invent new physics to reach the solution. Instead, it utilized established bootstrap methods, constraining the mathematical space of possible answers using known symmetries and consistency conditions until a unique candidate emerged. The model successfully found the result through two separate routes, including a direct amplitude calculation that Dixon had previously considered too difficult to attempt.[1][4]

Dixon spent two weeks independently validating Claude's output before confirming its accuracy. The total cost of the project was strikingly low: the numerical computing portion required 96 CPUs running for a week at a cost of about $100, while the total API and compute expenses fell between $1,000 and $2,000. "I would assert that Claude understands our 2019 and 2023 papers better than any human, aside from my co-authors," Dixon noted after reviewing the work.[4][5]

The AI did not cross the finish line entirely alone. On September 17, 2026, a research group led by Song He at the Chinese Academy of Sciences published a dataset on Zenodo containing the symbol data for the same nine-loop amplitude. He's team utilized a human-led mathematical framework, assisted by the GPT-6 model on certain constraints, demonstrating that specialist physicists were already on the verge of solving the problem.[4][5]

The nine-loop result proves that current large language models can carry a fragile, multi-step calculation from a brief prompt to a validated frontier result with minimal supervision. However, applying these same autonomous bootstrap methods to the less symmetric theories that govern real-world particle physics remains an open challenge for both human researchers and their AI counterparts.[1][5]