Élie Cartan

Élie Cartan (1869–1951) was a French mathematician who completed the classification of simple Lie groups and developed the differential-geometric machinery — connections, curvature, and symmetric spaces — that underpins modern physics from general relativity to gauge theory. Building on the earlier work of Wilhelm Killing, Cartan classified all finite-dimensional simple Lie algebras and introduced the concepts of root systems, weights, and the Killing-Cartan classification that would later become the foundation for Chevalley's construction of the Chevalley groups. His work on differential geometry provided the mathematical language for Einstein's general relativity and for the gauge theories of the Standard Model.