文档介绍：HISTORIA MATHEMATICA 2 /1975), 577-590
THE RELATIONOF FUNCTIONALANALYSIS
TO CONCRETEANALYSIS IN 20~~ CENTURYMATHEMATICS
BY FELIX E, BROWDER, UNIVERSITY OF CHICAGO
Before I begin the main substance of my remarks on the
history and character of functional analysis and its interaction
with classical analysis within twentieth century mathematics,
let me note a significant relationship between what I shall
say and the discussion presented by Professor Dieudonne in yes-
terday’s session on the development of algebra in the twentieth
century. Despite the implicit conflict of emphasis that ap-
pears in the two discussions between algebra and number theory
on the one hand and on the other, the problems of concrete anal-
ysis (particularly those that arose in mathematical physics
and in classical analysis and were the historical origin of
functional analysis), there is an important unity of approach
in the two discussions which would not have existed 25 years ago
This unity contrasts with one of the most forceful trends of
the earlier period of mathematics in this century. This trend,
which has set the tone of much discussion of mathematical prior-
ities and options, has been the emphasis on foundations and the
axiomatization of mathematical reasoning and, through the dis-
cussion of foundations, on the clarification of the content of
various disciplines through their reconstruction on set-theoret-
ical foundations. This emphasis on axiomatics and on structure
was the focal point of a considerable part of the mathematical
world for many decades in the twentieth century; it reached its
peak in the 1940’s and ’s. I suggest that this emphasis has
now suffered a sharp decline in its influence in many of the
most influential branches of mathematical research.
I am presenting a talk about the character, the past, and
(by implication) the future of functional analysis. In 1950,
such