This has always bothered me: it would seem that the concept of Euclidean space and real numbers themselves arose out of necessity for describing the physical universe that we live in. Mathematics, on the other hand, has become more broad than this and has generalized itself to adapt to any field, of which real numbers are only one. It is unclear to me whether or not we would even have reason to conceptualize the idea of real numbers if we lived in a universe without them. Furthermore, geometry is probably a requisite for every physical theory in existence, although I could be wrong on that point. Stochastic (as opposed to physical) chemistry comes to mind as a weak counter-example. This also brings to mind the fact that I don't know what makes something a physical theory, as opposed to... something else. I think that ideally all physical theories and models are intended to approximate a real world system, but isn't that true for all geometry branches?!
What valid logical criteria exists (if any) to classify geometry in mathematics as opposed to physics?