Why Maths :d

Most research mathematicians are quite passionate about their subject. Yet they are aware that their enthusiasm is not shared (to put it mildly) by the public at large, and even, in many cases, by research scientists. Is this just a case of "love is blind", or is it possible that mathematicians are aware of something about mathematics that outsiders are not? I`d like to investigate this matter in this article. I hope that in doing so I will stimulate others, both mathematicians and non-mathematicians, to think about these questions, and maybe even contribute their thoughts to later issues of the newsletter.

I think it`s very important to start by asking the right question. Typically, academic disciplines are defined by their subject matter. So, to ask what a geologist does is more or less the same thing as to ask what a geologist studies. Thus, for the Oxford English Dictionary, it is "the science which has for its object the investigation of the earth`s crust, of the strata which enter into its composition, with their mutual relations, and of the successive changes to which their present condition and positions are due". Similarly, for the OED, biochemistry is "the science dealing with the substances present in living organisms and with their relation to each other and to the life of the organism". Moving away from science, we have the OED`s definition of architecture, "the art or science of building or constructing edifices of any kind for human use"; economics, the study of "the development and regulation of the material resources of a community or nation"; and linguistics, "the study of languages". These examples were chosen at random. In every case I expect that the reader`s definition would be very similar to the one given by the dictionary.

Well, if such definitions are so easy for other disciplines, why not for mathematics? Like most people, the OED assumes that mathematics too can be defined by its subject matter and tries "the abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra; and, in a wider sense, so as to include those branches of physical or other research which consist in the application of this abstract science to concrete data". A good effort, but one gets the strong impression that whoever wrote it was struggling! The "spatial and numerical relations" obviously cover geometry and arithmetic, but then algebra had to be added because it wasn`t dealt with. However, that`s nowhere near good enough. Important "divisions" like analysis, probability, set theory and operational research are completely ignored by this definition, so clearly it`s very inadequate. Should we compensate by listing the titles of, say, all mathematics modules taught at NUS, in the hope that we`ll cover the subject that way? That attempt is doomed too, because a glance at the list soon reveals courses on topics like filter banks, chaos and fractals, cryptography, game theory, etc., that weren`t there ten or twenty years ago. If the subject is to be defined by a list constructed at a certain time, then after that time, no newcomers can ever join. However, it`s clear that mathematics is continuing to grow, its tentacles finding their way into areas of investigation previously thought beyond its reach.