"Riemann's third proposition that space is an "n-fold extended multiple" or a "multiply extended aggregate"... The term "Mannigfaltigkeit," as here employed, is a standing puzzle to the readers of Riemann's essay. ...Riemann adopted the term from Gauss, who was probably the originator of its employment for the designation of "space in general" (as distinguished from "flat space," in the metageometrical sense). Gauss, in turn, took the expression no doubt from Herbart... whose philosophy is to a great extent a sort of reproduction of the old Eleatic quandaries about "The One and the Many." Herbart, in fine, had obtained it from Kant, whose disciple he was, or believed himself to be, and whose phrase 'Mannigfaltigkeiten der Empfindung'is variously found... in... his followers. ...space is not a "multiple" or "aggregate" at all, but... its very essence is continuity. This... follows from its conceptual nature as well as from its relativity. ...space itself is not in any intelligible sense a quantity."
January 1, 1970
https://en.wikiquote.org/wiki/Bernhard_Riemann