AI-assisted mathematical discovery: murmurations of elliptic curves

Abstract

Elliptic curves have been studied for a long time for their importance in number theory and applications in cryptography. In this talk, I will explain how interpretable machine learning techniques led to the discovery of a new phenomenon from the dataset of elliptic curves, called "murmuration", which shows a striking oscillating pattern. Understanding this new phenomenon has been a challenge to the number theory community, resulting in a recent hot-topics workshop at ICERM and several papers on the subject. This talk is mainly based on the paper https://arxiv.org/pdf/2204.10140.pdf and it is a collaboration with He, Oliver, Pozdnyakov and Sutherland.