There are phrases that one very often sees and may fall in the habit of using without necessarily spending some time to question them. I am sure to try to do that for all words we use would be unbearable if not impossible, but to do it once in a while for certain words may be an enjoyable activity, at least for the mind. Well, I guess I’ve probably made you wait too much. Here is the conundrum, if one wants to call it that way: I’ve realized two names are used for many math departments; they are named either Department of Mathematics or Department of Mathematical Sciences. At first, I would say there should be something that each name wants to emphasize that the other does not have; otherwise, why then different names? A conjecture is that “mathematical sciences” would be used to encompass the sciences that use mathematics in which case one would expect what is usually called “applied math” would dominate in these departments while “mathematics” would be for departments that would want to emphasize only mathematics without too much involvement with the other sciences. At first, it seems to be a reasonable explanation when I looked up the descriptions of the Department of Mathematical Sciences at the Carnegie-Mellon University and the Department of Mathematical Sciences at Michigan Tech , which seem to emphasize their applied slant, and the description of the Department of Mathematics at the University of Chicago with a history of producing many “pure” mathematicians. However, it doesn’t seem to be that simple: the Department of Mathematics at the Massachusetts Institute of Technology (MIT) emphasizes its focus on both the pure and applied aspects of mathematics; the same can be said for the Department of Mathematics at the University of California at Irvine.

Besides, if one looks more closely at “mathematical sciences,” one may even ask what those sciences are. The immediate ones I think would come up are what are called the “hard” sciences, such as physics and chemistry. However, if one stretches the word “sciences,” as it seems to be done nowadays, and disregards to what extent math and what kind of mathematical methods are used, the list of those sciences becomes even longer. Is it then the case that these departments necessarily consider such an exhaustive list when considering which sciences to focus on? I don’t know, but I have the impression (again it’s an impression for which I have no evidence) that the hard sciences would the first on the list.

Now, to make matters even worse: if some departments do mathematics and are named “mathematical sciences,” would that imply that mathematics is a science? If so, why then would it have this special place among the other sciences to such an extent as to become a qualifier for them? (Why not consider math a physical science, for instance?) If it’s not the case, would that imply that these departments only use mathematics as a tool for the sciences and have no intention to practice mathematics for its own sake? I don’t know again, but I wouldn’t be surprised to see a complicated amalgam of different aspects of these questions in a single department.

So, in this state of confusion, what do you think?