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\centerline {FOR THE SAKE OF MATHEMATICS}
\centerline{Darren D. Wick (circa 1997)}
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Consider the following sentence: (which should probably be encased
in quotations, but I'm not sure to whom credit is due)
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Mathematics is the language of science.
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I'm certainly not prepared to argue the validity of this statement,
so let me pose the following question:
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Is mathematics itself a science?
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Well, I'm in no mood to tackle this question either, so I'll
cut to the chase and make the following proposition:
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The aim of mathematics should be the development of pure mathematical
theory, completely removed from all practial applications. In other
words, mathematics should be pursued for the sake of mathematics.
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Now, certainly the practical uses of mathematics are what have driven
its development in the past. Indeed, mathematics was originally 
devised as a tool for counting and measuring. Pretty harmless 
endeavors, I'd say.  But as harmless and beneficial as counting and
measuring may seem, many of the more current applications of 
mathematics are arguably destructive and ethically suspect. I'm 
thinking in particular of biological weapons, chemical weapons,
and nuclear weapons.
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But mathematics should not be condemned merely because of unethical
applications. I would argue that the purely aesthetic aspects of
mathematics alone are sufficient justification for its study. And 
it is
these aspects that are in danger of becoming casualties to the 
predominant view of mathematics as the language of science. 
As my colleague Mark Lynch pointed out, "If the Unabomber had actually 
been doing mathematics, nobody would have been hurt. What he was
doing was chemistry."
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Unfortunately, the exposure of many students to what one might call
advanced mathematics begins and ends with the calculus.
Certainly, we reason, every working scientist must have a basic
understanding of calculus. But in this desire to service the 
sciences, we sacrifice the opportunity to expose students to really
beautiful mathematics. Mathematics which is easily accessible, but
is not seen as useful. Mathematics which is not at all intuitive
and maybe even contradictory to our senses. For example Gabriel's
Horn, a perfectly legitimate geometric construction that has finite
volume yet infinite surface area. One can fill it with paint, but
one cannot paint it.
Mathematics for the sake of mathematics.
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Lest I offend all of my colleagues, let me go on record as stating
my firm belief that the majority of the practical uses of 
mathematics are beneficial to mankind. However, many of these 
fruitful applications may not have been possible without the 
dilligent work of pure mathematicians. Bernhard Riemann's abstract
theories of geometry were developed in the mid-ninteenth century
as a direct response to the concerns of mathematicians over the
validity of the very foundations of their discipline. Mathematics
for the sake of mathematicians.
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And some sixty years later, Albert 
Einstein found Riemann's abstract geometry to be a suitable setting
for his theory of general relativity. 
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So focusing on the purely theoretical aspects of mathematics need
not hinder the advancement of science. Perhaps it would just shift
the blame. In fact, you may think that this entire essay is merely
a charge to mathematicians to "wash their hands", as it were. 
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Maybe it is.
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O.K., it is.
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But I do feel that mathematicians need first and foremost to tend
their own discipline, and leave the applications to the applicators.
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"Look. Here is this beautiful theory I've developed which I call
the theory of expositons" the mathematician might say.
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"Oh," might the phycisist reply, "expositons may be just what I need 
to develop my theory of extraordinary spin-attractor cycle patterns."
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"So be it" sighs the mathemati cian. 

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