Georg Cantor was a German mathematician. He is best known as the creator of set theory, which has become a foundational theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers, and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware. Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive—even shocking—that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L.E.J. Brouwer, while Ludwig Wittgenstein raised philosophical objections. Christian theologians (particularly Neo-Thomists) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God, on one occasion equating the theory of transfinite numbers with pantheism. Cantor's recurring bouts of depression from 1884 to the end of his life were once blamed on the hostile attitude of many of his contemporaries, but these bouts can now be seen as probable manifestations of a bipolar disorder. (Read more...)