Georg Cantor (nonfiction): Difference between revisions
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== Biography == | == Biography == | ||
He invented [[set theory | He invented [[set theory]], which has become a fundamental theory in [[Mathematics (nonfiction)|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. | 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. | ||
Revision as of 07:48, 6 June 2016
Georg Ferdinand Ludwig Philipp Cantor (/ˈkæntɔr/ kan-tor; German: [ˈɡeɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfɪlɪp ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician (nonfiction).
Biography
He 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.
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'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 (nonfiction), and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections.
Cantor, a devout Lutheran, believed that set theory (nonfiction) had been communicated to him by God.
Religious issues
Some Christian theologians (particularly neo-Scholastics) 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 –- a proposition that Cantor vigorously rejected.
Objections and personal attacks
The objections to Cantor's work were occasionally fierce: Henri Poincaré (nonfiction) referred to his ideas as a "grave disease" infecting the discipline of mathematics, and Leopold Kronecker's public opposition and personal attacks included describing Cantor as a "scientific charlatan", a "renegade" and a "corrupter of youth."
Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included in a standard mathematics (nonfiction) curriculum.
Writing decades after Cantor's death, Wittgenstein lamented that mathematics (nonfiction) is "ridden through and through with the pernicious idioms of set theory," which he dismissed as "utter nonsense" that is "laughable" and "wrong".
Cantor's recurring bouts of depression from 1884 to the end of his life have been blamed on the hostile attitude of many of his contemporaries, though some have explained these episodes as probable manifestations of a bipolar disorder.
Later accolades
The harsh criticism has been matched by later accolades.
In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics.
Mathematician David Hilbert defended it from its critics by declaring:
"No one shall expel us from the Paradise that Cantor has created."
Nonfiction cross-reference
Fiction cross-reference
External links
- Georg Cantor @ Wikipedia