Tales of (mathematical) paradise

Abstract

Around 100 years ago, Hilbert stated his famous words that “nobody shall expel us” from the Cantorian paradise. The theory of sets had emerged rather suddenly, exactly 150 years ago, with a surprising paper of Cantor that has a peculiar inner story. In this history talk, I presented three vignettes from the early history of set theory. They represent three key moments: 1874, marking the birth of transfinite cardinalities under funny circumstances; 1905, a highly polemical moment when the schism between constructivists and “formalists” emerged; and 1925, the high time of the foundational debate between critics (Weyl, Brouwer, Skolem) and partisans of the higher infinite. I will not follow the obvious chronology; the narrative will be like those movies that include flashbacks.