At four distinct stages in the development of modern society, a mathematical development changed — in a fundamental, dramatic, and revolutionary way — how people understand the world. (A fifth such change may be taking place during our lifetime, but only history will say if this is really the case.) Those advances occurred around 5,000 B.C.E. and in the 13th, 16th, and 17th centuries. I will look at how human life and cognition changed on each of those four occasions.
Based in part on Devlin's recent book The Unfinished Game: Pascal, Fermat and the Seventeenth Century Letter that Made the World Modern, Basic Books 2008.