Cantor, Georg Ferdinand Ludwig Philipp (1845-1918)

German mathematician who followed his work on number theory and trigonometry by considering the foundations of mathematics. He defined real numbers and produced a treatment of irrational numbers using a series of transfinite numbers. Cantor's set theory has been used in the development of topology and real function theory.

Cantor was born in St Petersburg, Russia, but went to school in Germany and attended the universities of Zürich and Berlin. From 1869 he was on the staff at Halle University, as professor from 1879. His work gained little recognition, which may have contributed to his depression and mental illness in later life.

Investigating sets of the points of convergence of the Fourier series (which enables functions to be represented by trigonometric series), Cantor derived the theory of sets that is the basis of modern mathematical analysis. His work contains many definitions and theorems in topology. For the theory of sets, he had to arrive at a definition of infinity, and also therefore consider the transfinite; for this he used the ancient term ‘continuum’. He showed that within the infinite there are countable sets and there are sets having the power of a continuum, and proved that for every set there is another set of a higher power.

Cantor considered metaphysics and astrology to be a science into which mathematics, and especially set theory, could be integrated.