Machine-learning mathematical structures

This is the authors' abstract. We don't add key points for this paper.

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. 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.”