Machine-Learning Mathematical Structures

TL;DR

This paper reviews recent experiments on extracting mathematical structures using supervised machine learning across various fields, highlighting its potential for conjecture formulation and computational efficiency.

Contribution

It provides a comparative analysis of machine learning accuracy in different mathematical problems, emphasizing its utility in mathematical research.

Findings

Supervised machine learning can effectively extract structures from diverse mathematical data.

The paradigm aids in conjecture formulation and discovering hierarchical structures in mathematics.

Machine learning shows promising accuracy across geometry, representation theory, combinatorics, and number theory.

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.