In an Oct. 1 paper, Harvard physicist Matthew Schwartz reports that BootLoops, an open-source toolkit pairing a language model with scientific software, calculated 15 Feynman integrals for which he found no earlier calculation at the specific mass and momentum settings studied. These mathematical quantities help predict what particle colliders will observe; difficult cases can slow attempts to match precise theory with measurements.
BootLoops lets Claude plan and run programs that manipulate equations and calculate numerical results. Schwartz sets what to calculate and what counts as success; the software, rather than the language model's generated text, supplies the mathematical answers. The toolkit gathers reusable methods from physics, mathematics and computer science.
The paper reports 30 Feynman-integral calculations of varying complexity. Fifteen reproduce known results as a test; Schwartz calls the other 15 new under the mass and momentum conditions listed in the paper. He says he found no earlier calculations checked against independent numerical values at those settings. Some results apply only to those specific conditions, not every possible particle collision.
For each result, the paper provides an explicit formula or a differential equation with the conditions needed to solve it, plus standalone code. The authors compared the formulas with independent numerical values—usually from AMFlow, a solver for these integrals—at test points not used to derive the results. All met a threshold requiring relative agreement better than one part in 1030. This is a stringent computational check, but not a formal mathematical proof that the formulas are identical to the integrals or an independent replication by another group.
BootLoops is an open-source research workbench, not a new AI model or autonomous scientist. Schwartz says human researchers chose the targets and experts helped judge which cross-field results mattered. Anthropic hosted his guest post and funded the project, but disclaims it as its own: Schwartz owns and maintains BootLoops. The reported calculations used Claude; the toolkit is designed to work with other models.
Sources
- Matthew D. Schwartz, “Polylogarithmic, elliptic, and Calabi–Yau Feynman integrals from a hybrid bootstrap” (Oct. 1, 2026), the calculation paper.
- Anthropic, “Claude-shaped science”, a guest post by Matthew Schwartz.
Image: “Feynman diagrams for propagators and interactions in perturbative QCD,” by Zephyr the west wind, CC BY-SA 4.0. Source and license details. General illustration; not a figure from the BootLoops paper.
