I will describe how machine learning can be used as a tool for pure mathematicians to formulate new conjectures. I will initially focus on a discovery of a new connection between two different areas of low-dimensional topology and geometry. My collaborators and I were able to use fairly simple supervised learning to establish that the signature of a knot can be predicted from the knot's hyperbolic invariants. We were able to formulate this relationship as a precise conjecture, that we eventually proved (in a slightly modified form). The method that we used is very general: it is likely to be applicable to many area of mathematics. However, in my talk, I will discuss its limitations, which include the difficulty of interpreting the patterns that machine learning discovers, as well as the tendency for machine learning algorithms to ignore outliers. If there is time, I will describe some new examples where machine learning has been able to find unexpected conjectural connections in low-dimensional topology.
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