As a mathematician he is known for a number of contributions: the Cartan-Kähler theorem on singular solutions of non-linear analytic differential systems; the idea of a Kähler metric on complex manifolds; and the Kähler differentials, which provide a purely algebraic theory and have generally been adopted in algebraic geometry. In all of these the theory of differential forms plays a part, and Kähler counts as a major developer of the theory from its formal genesis with Elie Cartan.

His earlier work was on celestial mechanics; and he was one of the forerunners of scheme theory, though his ideas on that were never widely adopted.