  Riemann’s separation thesis together with his adoption of the  infinitesimal standpoint, were prerequisite steps for the development of differential geometry as the mathematics of differentiable  geometric fields on manifolds. When interpreted physically, these  mathematical structures or geometrical fields correspond, as Weyl  says, to physical structural fields (Strukturfelder). Analogous to  the electromagnetic field, these structural fields act on matter and  are in turn acted on by matter. Weyl (1931a, 337) remarks: 