Georg Cantor (1845 – 1918)
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician. He 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 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. The
objections to his work were occasionally fierce: Poincaré referred to Cantor's ideas as a "grave disease" infecting the
discipline of mathematics, and Kronecker's public opposition and personal attacks included describing Cantor as a
"scientific charlatan," a "renegade" and a "corrupter of youth." 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.
The harsh criticism has been matched by international accolades. In 1904 the
Royal Society of London awarded Cantor its Sylvester Medal, the highest honor it can confer. Today, 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. Cantor believed his theory of transfinite numbers had been communicated to him by God.
In the words of David Hilbert: "No one shall expel us from the Paradise that Cantor has created."