From pi to QFT: Symbolic Discovery at Scale

For centuries, formulas for mathematical constants such as pi and e appeared sporadically, discovered by figures like Newton, Euler, Gauss, and Ramanujan. Inspired by experimental physics, the Ramanujan Machine collaboration was established - a program of experimental mathematics that discovers formulas at scale, including new identities for pi and for Riemann zeta-values. This effort runs on a global volunteer network contributing CPU time, enabling the discovery of thousands of formulas - now surpassing the total found by humans over centuries. In the colloquium, Ido will demonstrate how combining these symbolic mathematical capabilities with large language models produced the first example of automated unification of mathematical knowledge, revealing deeper organizing structure among constants. The talk will then outline potential applications to theoretical physics: efficient computation of hypergeometric functions and broader families of D??'finite functions, with implications for computing Feynman integrals. As another application of massive symbolic computation to fundamental physics, Ido will describe the recent contribution to modern toolkits for automated effective field theory. As a proof of concept, the presentation will cover a massive automated scan for UV completions of gravity, showing how one-loop contributions can reproduce general relativity as emergent curvature from flat - space QFTs, and reporting new beta-functions for quantum corrections to gravity.

Speaker: Ido Kaminer, Stanford University