Pure versus Applied Mathematics
I just read this fictive interview in Math with Bad Drawings. That is a nice blog by the way which I should include in my blog roll. However, I definitely do not agree with the picture of mathematics that is sketched in this interview.
After reading the blog the reader is left with the following idea of pure mathematics: useless mathematics for its own sake which may or may not become useful in the future. Since we cannot tell the outcome we are bound to finance the pure (poor?) mathematicians and their hobby. I believe that we should not allow this public opinion about our craft.
Along the centuries, including the current one, the best and most important part of mathematics has always been inspired by nature, by applications. Who could deny the influence of physics? In fact, all human sciences influenced mathematical thinking, not only the natural sciences, but also the social sciences, and even philosophy. In all our sciences mathematical thinking is not only useful, but often indispensable for a clear understanding, modelling, checking or counter-checking of a theory. That is not because mathematics is the language of nature, but because we need mathematical methods to order the chaos of nature.
Thus the driving force in mathematics is the outside world, the applications. It is a pity that we nowadays think of applications mostly as money making. This discredits most of our science, not only mathematics. But to try to understand the world around as is a more important and fruitful force behind science than financial rewards.
In this light, saying that pure mathematics must exist because it may become useful in the future is at least misleading. It may happen that some branch of our science, originally developed to explain one phenomenon, was later applied for quite a different purpose. That only shows the power of mathematical thinking. We should be proud of it.
I cannot end this without saying that there are indeed mathematicians which work on the last epsilon. Some ideas are generalized to death. But do not take me wrong. I cannot condemn these mathematicians. It is too often the case that generalizations uncover new insights, either because the idea is surprisingly working in a broader setup, or because it is no longer working when some assumptions are missing. Both are fruitful expansions of our common human knowledge.