Chapter 28 - Georg Cantor (1845–1918)

Abstract

This chapter discusses the mathematician Cantor. Georg Cantor was born in St. Petersburg, Russia, in 1854 where his father Woldemar Georg Cantor was a successful merchant. From 1884 Cantor suffered sporadically from mental illness and spent more than four years in hospitals. Nevertheless, he remained active in mathematics and in organizing mathematical congresses, the foundation of the German Association of Mathematicians. His work was finally accepted as fundamental to mathematics, moreover his set theory was regarded as a landmark in human thought. In tradition of discussions on infinity Cantor was a major participant. He turned arbitrary collections of things into mathematical objects and in a very general sense of the word he counted these collections and calculated with the resulting numbers. A possible consequence of this approach could be that mathematics is nothing more than a generalized set theory, which would imply that all foundational problems of mathematics would be reduced to the problems of the foundation of set theory. An important notion in Cantor's set theory is the notion of power. Two sets are of the same power, if there is a one-to-one correspondence between their elements.