05 February, 2006


If you read my one-line entry two Mondays ago, you're aware that I'm not experiencing total job satisfaction, to put it mildly. There are a number of reasons for this. The one I least expected is that I miss research. I spent six years at my PhD-granting institution cursing research and longing for the day when I could devote myself to teaching. Imagine my shock when I realized last semester that I had fallen in love with research, and ached to work on it again!

Natural question; should I look for work at a more research-oriented school? or in industry? Here we encounter the possibility of a contradiction.

It's true that I have little time for research at the College, and they aren't very interested in the sort of research that I do. My employer would almost certainly smile with pleasure on something that directly helps me (or the school) fulfill its teaching mission better. Research into Gröbner bases may be admirable, but quite frankly, it is not going to do much to bring students to a small, private, liberal-arts college. This is where those Java applets I've mentioned come in handy.

On the other hand, I have no pressure to "produce" research. By this, I mean — the research I do, I can do in a relatively relaxed fashion, because I don't feel the pressure to produce something that would be highly valued. I don't think it's an accident that I have discovered two fascinating results in the months since graduation, when I knew that my job at the College would not stand or fall on whether I had any results. Compare this to the two years it took me to discover the result that led to the PhD thesis! More, if you count the two years I spent working on another problem, until we realized I had to solve this one first.

In addition, at the college I can experiment with something I find fun: writing libraries for symbolic computation in the Eiffel language, without worrying that none of my colleagues in the field (and I do mean none) thinks this is a worthwhile endeavor. I freely admit that they're right, insofar as the libraries will not be terribly useful for the world at large; I program what I need (S-polynomials, term orderings), and what piques my curiosity (Gaussian integers, finite fields, maybe polynomial factorization and gcd computation). However, the project has been immensely worthwhile to me; the result that led to my dissertation, I discovered by studying some computations of a more primitive version of the current library; and the most recent result, I discovered after taking up this project again in December.

That's an interesting phenomenon in itself; discoveries often come at the most unexpected times. The point is, however, that in industry I would certainly not be encouraged to study or pass time on the things I study; I am reliably informed by several people that industry hires mathematicians to research the problems that they need, which are not always the same problems that most interest the mathematician. Fair enough; the problems are still interesting enough in their own right. (A huge amount of good research in symbolic computation has come from industry; for instance, I have read papers written by authors employed by IBM or Bell Labs.)

Similarly, a research-oriented university would hire a mathematician that they thought would do research the mathematics community would find valuable, at least in the mathematician's own field, and publicly recognize through publishing in journals. Here, at least, my work on Gröbner bases would provide a start, but probably not the Eiffel programs, unless I managed to figure out some interesting questions that I've answered and wring some publications by writing about them.

There's an important problem: how does one find a question? That is sometimes more difficult than, how does one find the answer? Especially if the answer is already known, but not the question. Seriously :-)

The Eiffel libraries would prove useful at my current institution if they had a computer science program; they would make excellent projects for a CS student. Alas, my current institution has no CS program. They do have a "computer information systems" major containing the kernel of a CS major, but a professor told me that they are considering re-orienting it away from that.

This makes for an interesting quandary. The biggest strength my current institution possesses is that my fellow math professors are competent and supportive. The area is pleasant; after six months here, I could see myself raising a family in this area, especially if the town implements its downtown revitalization plans successfully.

As research goes, however, my current institution is far less appealing. There is no research environment, no adequate technical support (for example, e-mail went down for ten days last semester), and ... I could go on. I have to weight in the balance where the line separates "learning to reach for what you want" from "learning to want what you have reached."

Hence the quandary.

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