In plain words: Mathematical data labeled with known answers is fed to machine-learning models, and this review compares how accurately they predict across geometry, representation theory, combinatorics, and number theory. The approach can suggest conjectures, speed up computations, and hint at a hierarchy of mathematical structures.

Abstract

We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from different fields ranging from geometry to representation theory, from combinatorics to number theory, we present a comparative study of the accuracies on different problems. The paradigm should be useful for conjecture formulation, finding more efficient methods of computation, as well as probing into certain hierarchy of structures in mathematics.

Yang-Hui He
arXiv:2101.06317 · cs.LG, hep-th, math.HO, physics.hist-ph · submitted Jan 15, 2021 · updated Apr 8, 2021
abstract · pdf · html · 32 pages. Based on various colloquia, seminars and conference talks in 2020, this is a contribution to the launch of the journal "Data Science in the Mathematical Sciences."