 At the same time, geometry has posed fundamental epistemological problems, and has been a decisive locus of philosophical debate. One may quickly mention: 1, the problem of certainty and apriority of geometric knowledge, linked to the question – one geometry, or many? 2, the problem of the role of intuition (was Kant right? is the axiom of parallels intuitively grounded?) 3, the problem of idealization, concerning the relation between perfect geometric figures and their real instantiations; 4, the shifting conceptions of the interrelation between mathematics and natural science.