and founder of set theory. Born in St Petersburg, Cantor studied at Berlin under Weierstrass, and taught at the university of Halle from 1872. His celebrated diagonal argument proving the different cardinality of the reals and the rationals was first used in a paper of 1874. This demonstrated the existence of infinite sets of differing cardinality: the fundamental result of the modern theory of sets. Cantor’s work was much misunderstood, and attacked by his contemporaries for its unfettered use of the notion of a completed infinity. Although suffering from problems of mental health, he devoted the major part of the remainder of his academic career to the mathematical (and philosophical) defence of the world of mathematical objects that he had opened up. He was also the first to pose and to attempt to prove the continuum hypothesis.