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The Rise of Abstraction: From Cantor to Bourbaki to Category Theory

by

Professor Kimmo Rosenthal
Union College

February 18, 2014
5:00 pm
Bailey Hall 207

Refreshments will be served in Bailey Hall 204 4:45pm


Abstract:

As Math 199 (perhaps later abstract algebra) begins to unfold many students feel as if they have been dropped into hostile territory without a parachute or reinforcements. Why does abstraction make people uncomfortable? What is the appeal of abstraction? This talk will be an olio of history, personal reflection, and mathematics (a very modest introduction to category theory accessible to Math 199 students) taking us through reimaginings of how to view the mathematical world, from Georg Cantor to Bourbaki in the 1950’s, and finally the burgeoning of category theory in the 1960’s. Time permitting, we will ponder why Cantor was called “a corrupter of youth”, and subsequently Bourbakism was dismissed as “arrogance” and category theory called “abstract nonsense”. When “relevance” and “connections with other disciplines” are currently being touted as paramount, is there still a place for purely abstract mathematics as an aesthetic intellectual art form, to be valued for its beauty alone? Is it the case, as J.L.Borges said, that “mathematics, like music, can dispense with the universe”? “An explorer’s task is to postulate the existence of a land beyond the known land. Whether or not he finds that land and brings back news of it is unimportant. He may choose to lose himself in it forever and add one more to the sum of unexplored lands.” Gerald Murnane, The Plains


For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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