Mathematics as a Scholarly Field

I have been known to be critical of the attitudes of the math community, but I want to be very clear about my feelings about mathematics. As an applied mathematician, the ideas and techniques I’ve picked up from other math folks and the more mathy researchers in the science community constitute my toolbox. When I come across an interesting problem, the tools I reach for are differential equations, statistics, numerical methods, and others. I don’t necessarily want to prove theorems about these tools, but I definitely understand how crucial those proofs are to the usefulness of the tools for people like me. The theoretical advances in mathematics provide the rest of the sciences and engineering fields with the tools they use to formulate their problems carefully, and then solve them analytically. This is not a justification for the existence of mathematics, only the basis of my appreciation for the role of mathematics in the lives and work of nonmathematicians.

The majority of mathematics that is created has no direct link to any current physical problem, and this is what makes math its own field. The same thing can be said about every other area of human study. Most of current physics research has no direct tie to biology, for instance, and we don’t expect it to. When the two fields coincide, we celebrate the consistency of our approach to understanding the universe, but otherwise we don’t complain. The point of my writing here is that we should extend the same courtesy to mathematics. Perhaps theoretical physics and computer science suffer from the same odd bias.

The cliche within the math community is that “we never know what math will be applied to in 100 years.” I say that it’s a cliche only because a lot of pure math folks sometimes find themselves in a position where they need to justify funding their work, say to their mechanic or whatever. Of course, this is true. But it’s also beside the point. Research is done to increase our capabilities and understanding as a species, not just to conquer the world we live in or make our lives easier. And on occasion, that research that seemed like a fun game turns out to be extremely useful, such as classification of prime numbers or binary arithmetic.