Symbolic AI for mathematical discovery

Abstract: Small language models, trained from generated data, can be used as tools for mathematical discovery, either by providing new insights on a problem, or by generating interesting mathematical objects. 

This is illustrated in two recent works. Models trained to predict distant elements of the Collatz sequence exhibit a surprising learning pattern, which reveals a deep mathematical property of the sequence. Generative models, trained for next token prediction, can be used to discover competitive solutions of a hard (and well-researched) problem in extremal graph theory: discovering maximal graphs with no 4-cycles.