Mathematical Conversations

There is a remarkable parallel, first explicitly enunciated in the 1960s, between algebraic number theory and 3-dimensional geometry; for example, prime numbers are considered analogous to knots. I will only say a few short words about the substance of this parallel itself: the real point of the talk is to look at three key steps in the evolution of this metaphor, from 1880 to 1960, and observe just how much they depended on blind chance and people stepping outside their immediate disciplines.