Opinion 2: People who believe that Applied Math is Bad Math are Bad Mathematicians

By: Doron Zeilberger

Written: May 2, 1995.

I was just kidding. They are not bad mathematicians, because they are not mathematicians at all. A true mathematician has respect for all parts of mathematics, and does not believe in arbitrary divisions into `Pure', `Applied', `Theoretical',`Practical', `Conceptual', `Computational'. Mathematics is a Web, an infinite dimensional tapestry with everything intertwined.

Some people, like G.H.Hardy and Paul Halmos, deceive themselves, like Plato and Aristotle, that `pure', whatever it means, is purer than `applied', whatever it means. The fate of Platonic mathematics is nowadays quickly joining the fate of Platonic, a priori, non-experimental, physics.

My ranting and raving is a propos Halmos's article `Applied Mathematics is Bad Mathematics' reproduced in his`Selecta' volume. Paradoxically, as Peter Doyle pointed out to me, the example of pure math he gives there: Tutte et. al's `squaring the square', was motivated by `applied' math, i.e. Electrical Circuits.

On second thought, both Hardy and Halmos are mathematicians. Hardy, in spite of his philosophical errors, is still a great mathematician, even in the broad sense of the word. Halmos is also a good mathematician, he just sometimes says nonsense.

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