The paper aims to show how by elaborating the Peircean terms used in the title creativity in learning processes and in scientific discoveries can be explained within a semiotic framework. The essential idea is to emphasize both the role of external representations and of experimenting with those representations ("diagrammatic reasoning"), and to describe a process consisting of three steps: First, looking at diagrams "from a novel point of view" ("theoric transformation") offers opportunities to synthesize elements of these diagrams which have never been perceived as connected before. Second, by forming those observed syntheses to "new objects' of thinking, and by signifying these objects through new signs ("hypostatic abstraction"), new means of thinking and acting are created (to be used for "theorematic deductions"). And finally, by applying these new means — in proofs, for instance — the "intelligibility" of new discoveries and their power to explain problematic facts must be tested.