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An alternative title for this talk could be "Learning Hardness." To see why, we will explore some long-standing open problems in mathematics and examine what makes them hard from a computational perspective. We will argue that, in many cases, the difficulty arises from a highly uneven distribution of hardness within families of related problems, where the truly hard cases lie far out in the tail. We will then discuss how recent advances in AI may provide new tools to tackle these challenges. Based in part on the recent work with A.Shehper, A.Medina-Mardones, L.Fagan, B.Lewandowski, A.Gruen, Y.Qiu, P.Kucharski, and Z.Wang.

This talk will be held jointly with the Geometry/Topology Seminar.