Georg Cantor
1845–1918, St Petersburg, Russia, Halle, Germany
Russian-born German mathematician who founded set theory, proved that the real numbers are uncountable while the algebraic numbers are countable, and formulated the still-unresolved continuum hypothesis.
Cantor was born in St Petersburg to a Danish father and Russian mother and moved with his family to Germany in 1856. He studied at Berlin under Weierstrass, Kummer and Kronecker before taking up a post at the University of Halle in 1869, where he spent his entire career. Challenged by his colleague Heine to settle an open problem on trigonometric series, Cantor solved it by 1870, and by December 1873 he had proved that the real numbers cannot be put in one-to-one correspondence with the natural numbers, while the algebraic numbers can — showing that 'almost all' real numbers are transcendental.
Between 1879 and 1884 Cantor published a series of papers systematically developing set theory, transfinite numbers and the notion of cardinality, work that met fierce resistance from Kronecker in particular. He formulated the continuum hypothesis — that there is no set of cardinality strictly between that of the integers and the real numbers — and struggled for years, unsuccessfully, to prove it; it was later shown by Gödel (1940) and Cohen (1963) to be independent of the standard axioms of set theory. Cantor suffered recurring episodes of depression from 1884 onward and died in a sanatorium in Halle in 1918.
Workplaces: University of Halle
Russia, Germany