The Establishment of Functional Analysis

This article surveys the evolution of functional analysis, from its origins to its establishment as an independent discipline around 1933. Its origins were closely connected with the calculus of variations, the operational calculus. and the theory of integral equations. Its rigorous development was made possible largely through the development of Cantor’s “Mengenlehre,” of set-theoretic topology, of precise definitions of function spaces, and of axiomatic mathematics and abstract structures. For a quarter of a century, various outstanding mathematicians and their students concentrated on special aspects of functional analysis, treating one or two of the above topics. This article emphasizes the dramatic developments of the decisive years 1928-1933, when functional analysis received its final unification.