Appears in collection : FLAIM: Formal Languages, AI and Mathematics

Can machine learning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early computers to help formulate the Birch and Swinnerton-Dyer conjecture and using computer aid to prove the four colour theorem are among the most notable. Up until now there hasn’t been significant use of machine learning in the field and it hasn’t been clear where it might be useful for the questions that mathematicians care about. In this talk we will discuss how working together with top mathematicians to use machine learning to achieve two new results - proving a new connection between the hyperbolic and geometric structure of knots, and conjecturing a resolution to a 50-year problem in representation theory, the combinatorial invariance conjecture. Through these examples we demonstrate a way that machine learning can be used by mathematicians to help guide the development of surprising and beautiful new conjectures.