## If This be Treason...

by Ralph P. Boas, Northwestern University

I claim that there is a place, and a use, even for the solution of
quartics by radicals, or Horner's method, or involutes and evolutes, or
whatever your particular candidates for oblivion may be. Here are problems
that might conceivably have to be solved; perhaps the methods are not the
most practical ones; but that is not the point. The point is that in
solving the problems the student gets practice in using the necessary
mathematical tools, and gets it by doing something that has more
motivation than mere drill.

It is the fashion to deprecate puzzle problems and artificial story
problems. I think that there is a place for them too. Problems about
mixing chemicals or sharing work, however unrealistic, give good practice
and even have a good deal of popular appeal. It is absurd to claim that
only "real" applications should be used to illustrate mathematical
principles. Most of the real applications are too difficult and/or
involve too many side issues. One begins the study of French with simple
artificial sentences, not with the philosophical writings of M. Sartre.
The traditional topics have persisted partly by mere inertia but partly
because they still serve a real purpose, even if it is not their
ostensible purpose. Let us keep this in mind when we are revising the
curriculum.

*Ralph Boas was Professor of Mathematics at Northwestern
University and editor of The American Mathematical Monthly. This
commentary is excerpted from The American Mathematical
Monthly, Vol. 64, 1957, pp. 147-149.*

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