We summarize how AI can approach mathematics in three ways: theorem-proving, conjecture formulation, and language processing. Inspired by initial experiments in geometry and string theory, we present a number of recent experiments on how various standard machine-learning algorithms can help with pattern detection across disciplines ranging from algebraic geometry to representation theory, to combinatorics, and to number theory. At the heart of the programme is the question how does AI help with mathematical discovery.

Prof. Yang-Hui He is a Fellow at the London Institute for Mathematical Sciences. He also holds honourary positions as lecturer in mathematics at Merton College, University of Oxford, Visiting Professor at City, University of London and Chang-Jiang Chair at Nankai University. Yang read physics and mathematics at Princeton University (BA with Highest Honours), followed by the Mathematics Tripos at Cambridge (MA with Distinction), before earning his PhD in mathematical physics at MIT (NSF scholar and presidential award). After a postdoc at the University of Pennsylvania, he joined Oxford as the FitzJames Fellow and an STFC Advanced Fellow. Authoring more than 200 papers and several books, Yang works on the interface between geometry, number theory and string theory. He was a pioneer using AI to for mathematics in 2017 and wrote the first textbook on the subject (Springer, LNM, 2021). Yang is also a keen science communicator. His public talks have included a Friday Evening Discourse at the Royal Institution.