“Sur une définition géométrique du tenseur d’énergie d’Einstein”; “Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion”; “Sur les espaces généralisés et la théorie de la Relativité”; “Sur les espaces conformes généralisés et l’Univers optique”; “Sur les équations de structure des espaces généralisés et l’éxpression analytique du tenseur d’Einstein”. In Comptes Rendus Hebdomadaires des Séances de L’Academie des Sciences, Volume 174, January-June 1922, pp. 437-439; 593-595; 734-737; 857-860; 1104-1107

Paris: Gauthier-Villars, 1922. FIRST EDITION. Contemporary half morocco and marbled boards, edges worn, otherwise a fine copy. First edition of the five papers that comprise the Einstein-Cartan theory of gravitation. In theoretical physics, the Einstein–Cartan theory is a classical theory of gravitation similar to general relativity. The theory differs from general relativity in two ways: (1) it is formulated within the framework of Riemann–Cartan geometry, which possesses a locally gauged Lorentz symmetry, while general relativity is formulated within the framework of Riemannian geometry, which does not; and (2) an additional set of equations are posed that relate torsion to spin. Einstein became affiliated with the theory in 1928 during his unsuccessful attempt to match torsion to the electromagnetic field tensor as part of a unified field theory.

The second paper, Cartan’s Généralisation de la notion de courbure, “arose from a creative evaluation of the geometrical structures underlying both Einstein’s theory of gravity and the Cosserat brothers generalized theory of elasticity. In both theories groups operating in the infinitesimal played a crucial role. Cartan developed his concept of generalized spaces with the dual context of general relativity and non-standard elasticity in mind. In this context it seemed natural to express the translational curvature of his new spaces by a rotational quantity (via a kind of Grassmann dualization). So Cartan called his translational curvature “torsion” and coupled it to a hypothetical rotational momentum of matter several years before spin was encountered in quantum mechanics.” (Scholz, “E. E. Cartan’s attempt at bridge-building between Einstein and the Cosserats – or how translational curvature became to be known as torsion.” European Physical Jl. H 44, 47–75 (2019).

Cartan (1869-1951) was one of the most profound mathematicians of the last hundred years, and his influence is still one of the most decisive in the development of modern mathematics ... his influence has been steadily increasing, and with the exception of Poincaré and Hilbert, probably no one else has done so much to give the mathematics of our day its present shape and viewpoints.

DSB, III, pp. 95-96.