Foundations of mathematics; some comments

Abstract

The Theory of Sets, which includes the theory of transfinite numbers, was created by Cantor (1845-1918) during the years 1874-5. Much of the work leading up to this theory was done by analytical mathematicians of the 19th Century, among whom were Kummer (1810-1893), Weierstrass (1815-1897), and Dedekind (1831-1916). I have referred to the type of approach adopted by these four as 'Classicist'. At the turn of the century, Russell (1872- ) discovered the paradox in set-theory given at the opening of this thesis. Many modern mathematicians regard this paradox as destroying much of the work of the classicists, and some have tried to set up new systems of mathematics which avoid it.