| 翻訳と辞書 |
| Georg Cantor ： ウィキペディア英語版 |
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor ( ; ; – January 6, 1918〔Grattan-Guinness 2000, p. 351〕) was a German mathematician. 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. 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's work is of great philosophical interest, a fact of which he was well aware.〔The biographical material in this article is mostly drawn from Dauben 1979. Grattan-Guinness 1971, and Purkert and Ilgauds 1985 are useful additional sources.〕
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〔Dauben 2004, p. 1.〕 and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections. Cantor, a devout Lutheran, believed the theory had been communicated to him by God.〔Dauben 2004, pp. 8, 11, 12–13.〕 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〔Dauben 1977, p. 86; Dauben 1979, pp. 120, 143.〕 – on one occasion equating the theory of transfinite numbers with pantheism〔 – a proposition that Cantor vigorously rejected.
The objections to Cantor's work were occasionally fierce: Henri Poincaré referred to his ideas as a "grave disease" infecting the discipline of mathematics,〔Dauben 1979, p. 266.〕 and Leopold Kronecker's public opposition and personal attacks included describing Cantor as a "scientific charlatan", a "renegade" and a "corrupter of youth."〔Dauben 2004, p. 1; Dauben 1977, p. 89 ''15n.''〕 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 curriculum. Writing decades after Cantor's death, Wittgenstein lamented that mathematics 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,〔Dauben 1979, p. 280: "...the tradition made popular by Arthur Moritz Schönflies blamed Kronecker's persistent criticism and Cantor's inability to confirm his continuum hypothesis" for Cantor's recurring bouts of depression.〕 though some have explained these episodes as probable manifestations of a bipolar disorder.〔Dauben 2004, p. 1. Text includes a 1964 quote from psychiatrist Karl Pollitt, one of Cantor's examining physicians at Halle Nervenklinik, referring to Cantor's mental illness as "cyclic manic-depression".〕
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.〔 David Hilbert defended it from its critics by declaring: "No one shall expel us from the Paradise that Cantor has created."〔: "Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können." (Literally: "Out of the Paradise that Cantor created for us, no one must be able to expel us.")〕〔
==Life==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Georg Cantor」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|