  Cartan’s approach to differential geometry is in response to the fact that Euclidean geometry was generalized in two ways resulting in  essentially two incompatible approaches to   geometry.[88]  The first generalization occurred with the discovery of non-Euclidean geometries and with Klein’s (1921) subsequent Erlanger program in  1872, which provided a coherent group theoretical framework for the  various non-Euclidean geometries. The second generalization of  Euclidean geometry occurred when Riemann (1854) discovered Riemannian geometry. 