Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah

Do you often wonder why your teachers make you study a piece of mathematics that could not possibly ever be useful?

You study mathematics not just to acquire a bunch of techniques that you can use to solve problems arising in your work. Keep in mind that you are going to be working for the next forty years or so and that nobody now can possibly anticipate what part of the mathematics that is now known you will need in the future. It's much more important to learn how to approach new mathematics, how to acquire it, and perhaps how to develop new mathematics.

There are many reasons to study a given piece of mathematics, for example:

• It may be needed to explain a piece of more complicated mathematics that is in fact "useful".
• It may teach you new techniques and principles that you can apply in understanding new pieces of mathematics.
• Believe it or not, but it may be fun, entertaining, exciting, or beautiful.

As a general principle, if you do work with mathematics, the more mathematics you know the larger will be your bag of insights, tools and techniques, and the more successful you will be,

Selecting mathematics to study solely on the basis of its "usefulness" is limiting, stifling, and ultimately self defeating (and I'm saying this even though my colleagues consider me an "applied" mathematician).

Fine print, your comments, more links, Peter Alfeld, PA1UM

[16-Aug-1996]