The immense sea of the infinite

Abstract

In a celebrated talk Hilbert stated that the infinite was nowhere to be found in the real, external world. Yet from time immemorial the idea of infinity has excited the human mind as no other subject. Beginning with the image of the ocean of the indivisibles and the infinite, evoked by Cavalieri and Fontenelle, to the works by Galilei and Descartes, Kepler and Bruno, Pascal and Leibniz up to the Prize announced by the Berlin Academy in 1784 for a rigorous theory of the infinite, and eventually up to Dedekind’s and Cantor’s theories and beyond, in the talk I will try to offer a picture of various aspects according to which the infinite has been considered by mathematicians, astronomers, philosophers, writers and poets over the centuries.