In this post I discuss general questions regarding the future health of Science and Mathematics in our Universities, both with respect to research and teaching. It seems to me that several aspects of these are in peril, in part because many consider it necessary that subjects of studies or research should have a clear usefulness for some social, technological or economic reasons; and in part because of the growing trend that pushes for an application of the “laws of the market” as a rule-set for allocating resources to and inside Universities. I intend to deconstruct arguments that only rest on such seemingly natural “axioms”, show that they only cover part of the picture, and maybe propose interesting alternatives. In this post, I will first consider some aspects of the “necessity of usefulness” paradigm.
There is no denying that mathematics has a great social, technological and economic impact, and it is undeniable that it plays a crucial role in all sciences, as well as being of absolute necessity in the elaboration of much of our technology. Hence it seems to pass the “usefulness test” with more than flying colors. However, in apparent contradiction with all this, I know of very few mathematicians for which there is any consideration about usefulness in their research, and I believe this to be both natural and healthy. In hindsight, we easily see many instances of this phenomenon, with mathematical notions and theorem finding applications only years, decades, or even centuries after being developed. Moreover, it is often the case that these uses would have been impossible to predict by the mathematicians responsible for them. As a typical (and very often mentioned) example, just think of Fermat’s Theorem whose application to Cryptography has opened the door to Public-Key systems, which are now essential to secure transactions on the web. We could (and maybe should) construct a huge list of such examples. My point here is that even if we often cannot justify many of our current cutting-edge research endeavors using only their potential usefulness, we should strive to better explain to the general public why they are interesting and important. As a corollary, this also goes for the subject matters that we teach.
To make things clearer, it may be good to consider research subjects that are both eminently appealing to most and easy to describe, while being probably of no specific expected usefulness whatsoever, even in the far future. This is a conundrum since it is hard to guarantee true uselessness, but let us try regardless even if to do so we may need to step out (not too far) of the mathematical world. Maybe a good example is the search for planets circling distant stars. The farther the star the better, since the probability that we could ever visit that planet becomes very remote. It seems to me that a significant proportion of our population is easily fascinated by such questions, simply because we naturally wonder about our place in the universe. So, should we stop this apparent waste of time simply because it has no perceivable short or long term social, technological or economic impact. My point is that we should not, and that we could better explain why, as well as making this understood by the general public. In fact, many of the most striking human endeavors are not justified by simple usefulness, but rather by broader needs such as the search for knowledge, a craving to understand our universe, the urge to build our culture, or the need to push back the limits of human thought.