 The five-year period 1868–1872 saw a mushrooming of set-theoretic proposals in Germany, so much so that we could regard it as the birth of set-theoretic mathematics. Riemann’s geometry lecture, delivered in 1854, was published by Dedekind in 1868, jointly with Riemann’s paper on trigonometric series (1854/1868b, which presented the Riemann integral). The latter was the starting point for deep work in real analysis, commencing the study of “seriously” discontinuous functions. The young Georg Cantor entered into this area, which led him to the study of point-sets. In 1872 Cantor introduced an operation upon point sets (see below) and soon he was ruminating about the possibility to iterate that operation to infinity and beyond: it was the first glimpse of the transfinite realm.