Simplicity Is The Point
Dennis Sullivan, Graduate Center, CUNY & SUNY at Stony Brook
4:15-4:45 Friday April 5
There is a famous theory due to René Thom in France and Lev Pontryagin in Russia which can be seen to directly evolve from one simple geometric picture. The feeling one has as a beginning topologist on realizing this is: "Now I know what it means to really understand a part of mathematics."
Mathematicians often feel a mathematical story is not over until one sees the entire structure evolving painlessly from a quite small number of simple starting points.
1) One can research any fertile field of mathematics not so rendered to try to find its simplicity sources. One usually begins by thinking "What is really going on here?"
2) Sometimes some rather sophisticated heights are constructed from which the structure of the desired mathematical landscape is simply revealed.
3) The relative simplicity just described becomes pure simplicity when the sophisticated heights are gently lowered into the foundations by becoming part of any early study of the subject.
4) At this point one may be able to satisfy Hilbert's criterion "Someone only really understands a mathematical subject if they can tell it to the person on the street."
The talk will offer a few more comments/examples.