In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics. The harsh criticism has been matched by later accolades. 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.
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". 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. The objections to Cantor's work were occasionally fierce: Leopold Kronecker's public opposition and personal attacks included describing Cantor as a "scientific charlatan", a "renegade" and a "corrupter of youth". Not all theologians were against Cantor's theory prominent neo-scholastic philosopher Constantin Gutberlet was in favor of it and Cardinal Johann Baptist Franzelin accepted it as a valid theory (after Cantor made some important clarifications). 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. Cantor, a devout Lutheran Christian, believed the theory had been communicated to him by God. Brouwer, while Ludwig Wittgenstein raised philosophical objections see Controversy over Cantor's theory. This caused it to encounter resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Originally, Cantor's theory of transfinite numbers was regarded as counter-intuitive – even shocking. Cantor's work is of great philosophical interest, a fact he was well aware of. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's method of proof of this theorem implies the existence of an infinity of infinities.
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. He played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Georg Ferdinand Ludwig Philipp Cantor ( / ˈ k æ n t ɔːr/ KAN-tor, German: March 3 1845 – Janu) was a mathematician.
0 kommentar(er)
