ABSTRACT
Much of functional analysis involves abstracting and making precise ideas that have been developed and used
over many decades, even centuries, in physics and classical mathematics. In this regard, functional analysis
makes use of a great deal of “mathematical hindsight” in that it seeks to identify the most primitive features
of elementary analysis, geometry, calculus, and the theory of equations in order to generalize them, to give
them order and structure, and to define their interdependencies. In doing this, however, it simultaneously
unifies this entire collection of ideas and extends them to new areas that could never have been completely
explored within the framework of classical mathematics or physics.
