Subject: [HM] pathological functions
From: Robert Tragesser (RTragesser@compuserve.com)
Date: Thu Aug 24 2000 - 06:53:17 EDT
I have a question about the other direction. When did the monsters become
gods? (As a fractal theorist once put it.) Was Norbert Wiener's
"discovery" that everywhere continuous, nowhere differentiable functions
were at the core of the theory of Brownian motions the first?
More generally, G-C Rota once characterized mathematical
development thus (in paraphrase): mathematics at any moment is like the
circus. There is the Big Top. And then there is the Side Show. Part of the
Side Show is the Freak Show. The thing about the Freak Show is that we do
not know whether these are the monsters they appear to be, or the beginning
of an altogether new and splendid form of life.
What other "freaks" of the late 19th/20th century have turned out
to be real performers?
Most curiously: Have there been other periods in the history of
mathematics when there have been clusters of "freaks" appearing? What were
they, how were they "redeemed"? (Besides the old standbys such as
incommensurable magnitudes, negative numbers, zero, roots of negative
numbers...)
robert tragesser
wet west(running)brook, connecticut
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