Georg Cantor

Georg Cantor was a German mathematician who founded set theory and developed the theory of transfinite numbers, two of the foundational frameworks of modern mathematics. He was born Georg Ferdinand Ludwig Philipp Cantor on March 3, 1845, in Saint Petersburg, Russia, to a Danish-German father and a Russian mother of Roman Catholic background. His family moved to Germany in 1856.

He studied at the ETH Zürich and the universities of Berlin and Göttingen, taking his doctorate in Berlin in 1867 with a dissertation on number theory under Karl Weierstrass and Ernst Kummer. From 1869 he taught at the University of Halle, where he was promoted to full professor in 1879 and remained until his retirement in 1913.

His 1874 paper "On a Property of the Collection of All Real Algebraic Numbers" established for the first time that infinite sets can have different sizes by showing that the real numbers cannot be put in one-to-one correspondence with the natural numbers. The 1891 paper containing the diagonal argument, the development of the cardinal numbers aleph-null and aleph-one, the formulation of the continuum hypothesis, and the construction of the Cantor set are now standard material in undergraduate mathematics. His correspondence with Richard Dedekind documents the development of these ideas in detail.

His work was attacked by Leopold Kronecker, his former teacher, who rejected the actual infinite, and the resulting professional isolation, combined with recurring depressive illness, marked the second half of his life. He suffered repeated breakdowns from 1884 onward and spent long periods in the Halle nervous-disease clinic. David Hilbert later described Cantor's set theory as "the paradise from which no one shall expel us." Cantor died of a heart attack in the Halle clinic on January 6, 1918, during a wartime food shortage.

His name Georg is the German form of George, from the Greek Geōrgios meaning "farmer" or "earthworker" — from gē ("earth") and ergon ("work"). It is a masculine name long current in German-speaking countries.