Despite his well-known deductivism, in his early (unpublished) writings, Popper held an inductivist position. Up to 1929 epistemology entered Popper's reflections only as far as the problem was that of the justification of the scientific character of these fields of research. However, in that year, while surveying the history of non-Euclidean geometries, Popper explicitly discussed the cognitive status of geometry without referring to psycho-pedagogical aspects, thus turning from cognitive psychology to the logic and methodology of science. As a consequence of his reflections on the problematic relationship between geometrical-mathematical constructions and physical reality Popper was able to get over a too direct notion of such a relationship, cast doubts on inductive inference and started conceiving in a new (strictly non-inductivist) manner the relationship between theoretical and observational propositions.