Singularities *

This article recounts the rather wonderful interaction of topology and singularity theory which began to flower in the 1960’s with the work of Hirzebruch, Brieskorn, Milnor and others. This interaction can be traced back to the work of Klein, Lefschetz and Picard, and also to the work of knot theorists at the beginning of this century. It continues to the present day, flourishing and expanding in many directions. However, this is not a survey article, but a history; the events of our time are harder to see in perspective, harder to marshal into coherent order, and their very multitude makes it impossible to recount them all. Hence this interaction is followed forward in only a few directions. 1 The reader may get a sense of the current state of affairs in singularity theory by browsing in the conference proceedings [Orl83, LSE95]. The focus of this article is singularities of complex algebraic varieties. Real varieties are omitted. Also omitted from this account is the area of critical points of