One of the nice things about having evolved in a universe with three spatial dimensions is that we have developed problem solving skills pertaining to objects in space. Thus, for example, we can think of a triplet of numbers as a point in 3-d and hence computation about triplets of numbers as computation about points in 3-d, which can then be solved using our intuition about space. This seems to suggest that it should be possible at times to solve a completely non-geometric problem using techniques from geometry. Does anyone know of such examples?
Of course, the terms 'geometric' and 'non-geometric' are slightly vague here. One can argue that any geometric problem is actually non-geometric if you replace all points with their co-ordinates. But intuitively, the definition is clear. Let's just say that we call something geometric if we would consider sending a paper about it to SoCG.