# Georg Cantor

[https://en.wikipedia.org/wiki/Georg\_Cantor](https://en.wikipedia.org/wiki/Georg_Cantor)

Georg Cantor (1845-1918) was a German mathematician who invented set theory, which has become a fundamental theory in mathematics.

Cantor established the importance of _one-to-one correspondence_ between the members of two sets, defined _infinite_ and _well-ordered_ sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the _cardinal_ and _ordinal numbers_ and their arithmetic.

Cantor spent his entire career at the University of Halle. In 1879, with his 34 years, Cantor became full professor there. Attaining this position at his age was a notable accomplishment, but Cantor desired a chair at the university of Berlin, which was the leading German university at the time. Unfortunately, his work encountered too much opposition for that to be possible.

Cantor's former professor, Leopold Kronecker, was the head of mathematics at Berlin's university and a well-established figure in the math community, and he despised Cantor's work, even publically attacking Cantor, caling him a "corrupter of youth" and "scientific charlatan". Even worse, Kronecker intentionally delayed the publication of Cantor's first major publication in 1874.

Kronecker, who was one of the founders of the constructive mathematics, disliked Cantor's set theory because it asserted the existence of sets satisfying certain properties, without providing examples of such sets.

Cantor's work between 1874 and 1884 is the origin of set theory.
