 The much more significant change came with the arrival of Bernhard Riemann’s great extension of Gaussian differential geometry. Precisely, he found a way to define geometries starting from very general concepts, and gradually leading (through more and more narrow hypotheses) to the known metric geometries. At the risk of sounding anachronistic, it can be argued that Riemann’s “conceptual” style of work is a form of proto-structuralism. What he does is this: first, he introduces the general structure of n-dimensional manifold, to then define a metric in the manifold (with the means of differential geometry, line element and Gaussian curvature). With all this in place, Euclidean and non-Euclidean geometries emerge as particular cases of 3-dimensional manifolds, concrete forms of the general structure. And the “hypothesis” that singles out these geometries, within the general framework of Riemannian manifolds, is the physical assumption that rigid bodies can move freely without deformation.