Although many people contributed to the study of infinity over the centuries it was Georg Cantor in the nineteenth century who established its modern development. Cantor created modern set theory and established the importance of one-to-one correspondence between sets. For example he showed that the set of all integers can be put into one-to-one correspondence with the set of all fractions and so these two sets have the same infinity. But he also proved the remarkable result that there are infinitely many infinities, all of different sizes.

The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and-events/cantors-infinities

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