Mathematical Data Science

TL;DR

This paper introduces 'mathematical data science', a paradigm that uses machine learning on datasets of mathematical objects to discover new structures, demonstrated through case studies in number theory and combinatorics.

Contribution

It proposes a novel approach to mathematical research by applying machine learning to study collections of objects rather than individual cases.

Findings

Identified patterns in murmurations in number theory

Analyzed loadings of partitions related to Kronecker coefficients

Showed potential of machine learning in mathematical discovery

Abstract

Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than individually, by creating datasets and doing machine learning experiments and interpretations. After an overview, we present two case studies: murmurations in number theory and loadings of partitions related to Kronecker coefficients in representation theory and combinatorics.