Thoughts on math education at Rensselaer

To the Editor:

Wesley Mounts ’12 laments what he views as insufficient attention to utility in mathematics education at Rensselaer in last week’s issue of The Polytechnic, and he cites the Introduction to Differential Equations course in particular.

Applications have spurred the development of mathematics from antiquity to the present time. My colleagues and I in the Department of Mathematical Sciences strongly believe that instruction in mathematics is only enriched by highlighting the connection with applications. The subject of differential equations, in particular, is ideally suited to explore such a connection, given that a number of scientific principles from chemistry to mechanics are expressed in terms of rates of change. I regret, therefore, that Mounts’ experience was less than edifying.

One must, at the same time, caution against an excessive zeal for utility. While a majority of our students may be consumers of mathematics, there are others who are drawn to the subject by its aesthetics, or by a curiosity to explore and advance the elegant structure of mathematics. Mounts may be amused by the following excerpts, the first from G.H. Hardy’s A Mathematician’s Apology and the second from the preface to The Theory of Fourier Integrals by E. C. Titchmarsh. Eminent analysts both, their work has found applications beyond what they might have surmised.

Hardy: “I have never done anything ‘useful.’ No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.”

Titchmarsh: “As exercises in the theory I have written out a few applications as it seemed to me an analyst should. I have retained, as having a certain picturesqueness, some references to ‘heat,’ ‘radiation,’ and so forth; but the interest is purely analytical, and the reader need not know whether such things exist.”

Ash Kapila

Professor of Mathematical Sciences