Édouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his Cours d'analyse mathématique, which appeared in the first decade of the twentieth century.

Goursat's work was considered by his contemporaries, including G. H. Hardy, to be exemplary in facing up to the difficulties inherent in stating the fundamental Cauchy integral theorem properly.

Goursat, along with Möbius, Schläfli, Cayley, Riemann, Clifford and others, was one of the 19th century mathematicians who envisioned and explored a geometry of more than three dimensions.

[4] The Goursat tetrahedra are the fundamental domains which generate, by repeated reflections of their faces, uniform polyhedra and their honeycombs which fill three-dimensional space.

He derived a formula for the general displacement in four dimensions preserving the origin, which he recognized as a double rotation in two completely orthogonal planes.

is a p-form in n-space and S is the p-dimensional boundary of the (p + 1)-dimensional region T. Goursat also used differential forms to state the Poincaré lemma and its converse, namely, that if

Élie Cartan himself in 1922 gave a counterexample, which provided one of the impulses in the next decade for the development of the De Rham cohomology of a differential manifold.