In a famous article entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” the well known physicist Eugene Wigner wrote:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
— Eugene Wigner
Of course many people do mathematics to solve concrete problems (just as Dr. White), many other people do math because it is enjoyable and interesting and just plain fun!
The remarkable thing is that mathematics done for its one sake may turn out to be just the thing to solve a concrete, real world problem years later! In case you don’t believe it (or if you need to convince your practical minded Senator that a little money and time invested in math research can have big payoffs) we direct your attention to a recent article in the journal Nature. In it they discuss a seven big examples of math done for math’s sake which ends up being crucial later on.
As a child, I read a joke about someone who invented the electric plug and had to wait for the invention of a socket to put it in. Who would invent something so useful without knowing what purpose it would serve? Mathematics often displays this astonishing quality. Trying to solve real-world problems, researchers often discover that the tools they need were developed years, decades or even centuries earlier by mathematicians with no prospect of, or care for, applicability. And the toolbox is vast, because, once a mathematical result is proven to the satisfaction of the discipline, it doesn’t need to be re-evaluated in the light of new evidence or refuted, unless it contains a mistake. If it was true for Archimedes, then it is true today.
— Peter Rowlett in the Nature article.