Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. Petersburg – January 6, 1918, Halle) was a German mathematician who is best known as the creator of set theory. 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 work encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré, and later from Hermann Weyl and L.E.J. Brouwer. Ludwig Wittgenstein raised philosophical objections. His 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.

Nowadays, the vast majority of mathematicians who are neither constructivists nor finitists accept Cantor's work on transfinite sets and arithmetic, recognizing it as a major paradigm shift. In the words of David Hilbert: "No one shall expel us from the Paradise that Cantor has created."

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