Can machine learning identify interesting mathematics? An exploration using empirically observed laws

TL;DR

This paper investigates whether machine learning can identify interesting mathematical structures by analyzing integer sequences with features derived from empirical laws like Benford's and Taylor's, aiming to classify sequences based on their properties.

Contribution

It introduces a novel approach of using empirical laws as features for machine learning classification of mathematical sequences, exploring their effectiveness in identifying sequence properties.

Findings

Machine learning classifiers can distinguish sequence properties with moderate accuracy.

Empirical laws like Benford's and Taylor's provide useful features for sequence classification.

The approach opens new avenues for automated discovery in mathematical research.

Abstract

We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws: Benford's law and Taylor's law and experiment with various classifiers to identify whether a sequence is, for example, nice, important, multiplicative, easy to compute or related to primes or palindromes.