In 1883, the brilliant German mathematician Georg Cantor produced the first rigorous, systematic, mathematical theory of the infinite. It was a work of genius, quite unlike anything that had gone before. And it had some remarkable consequences. Cantor showed that some infinities are bigger than others; that we can devise precise mathematical tools for measuring these different infinite sizes; and that we can perform calculations with them. This was seen an assault not only on intuition, but also on received mathematical wisdom. In due course, I shall sketch some of the main features of Cantor’s work, including his most important result, commonly known as ‘Cantor’s theorem’. But first I want to give a brief historical glimpse of why this work was perceived as being so iconoclastic. Ultimately, my aim is to show that this perception was in fact wrong. My contention will be that Cantor’s work, far from being an assault on received mathematical wisdom, actually served to corroborate it.
