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Keeping Your Research Alive
In 1978, Fred Gehring of the University of Michigan surveyed all of the Michigan mathematics Ph.D.s. Among the things that this survey showed was that less than half of the survey group ever published anything (even their own dissertation work); of those that published something, less than half published more than one paper beyond their dissertation work; but all of those who published at least five papers continued to have a lengthy and rich publishing record (twenty or more publications). This says to me that
the first few years after graduate school are a critical period in the professional life of a mathematician and that creating a beachhead in the publishing world is both necessary and sufficient for a generous professional career.
Below I'll make a few brief comments about my own experience and then end with three specific suggestions.
This period was characterized by traditional publication work: learning, reading papers, thinking, writing up results, submitting papers, revising papers, learning to use Typits.
My own career began at Western Illinois University with the usual stuff. I published most of my dissertation results and began attending research conferences in real analysis. At these conferences I met many of the researchers who would become my fast friends and frequent collaborators.
Five Years Out
'More of the above, but with some important additions: refereeing, editing, symposia organizing, grant writing. I also learned to use the IBM Symbol Ball.
In addition I worked on my first two ``applied'' problems; one a design of plowshares for John Deere and the second some Operations Research.
Ten Years Out
My research in real analysis continued and ``applied'' problems became a periodic part of my life. I began attending the weekly Real Analysis Seminar at the University of Minnesota, something I've continued ever since. But there was something quite new, curriculum reform. After my move to St. Olaf I became involved with the calculus reform ideas, ran conferences, discussed the issues with Evans and Jerry Uhl (another ancient real analysis colleague), learned SMP (a precursor to Mathematica) and Maple, worked on several calculus reform committees, wrote grants by the score and became acquainted with a new and enthusiastic crowd. I also ``learned'' TROFF-NROFF-EQN and TeX.
And so it goes; I continue to be active in real analysis research. Editing takes much more time now that I serve as a Managing Editor of the Real Analysis Exchange and as a consequence, I have about shut out refereeing and reviewing. I'm not as involved in calculus reform as I once was, but I still maintain an active interest. I have now ``learned'' LaTeX and use it almost exclusively for technical work.
If I had some hints for others, what would they be? I think these.
There are those who have claimed this won't work, but it works for me. I treat my research time the same way I treat my class time. It's high priority and I don't cancel my research time unless I would cancel a class for the same reason.
If you have a problem, you can work on it whenever you have a spare minute. In my experience, research takes some long periods of concentrated work, but it helps a great deal to have some aspect of your problem to think about when you have a free minute or two, when the party becomes dull, or your lunch date fails to show up or . My friend Gyuri Petruska once said that
when I was young I'd spend five minutes ``warming up'' and then I was ready to work. When I was a bit older I had to spend twenty minutes warming up before I was back into my work. Now it seems I spend all my time with warm ups!For Gyuri this is not true at all, but there is truth in his very Hungarian view of himself. If you keep something on the burner you'll minimize your warm up time.
Small conferences are attended by those who are active in your area. You'll get to know them and become acquainted with the lore of your discipline. You'll also discover the topics of current interest and some open problems; that's always helpful. Trivial problems and impossible problems are both a dime a dozen; good problems are more difficult to find. I find I'm always ``fired up'' by a real analysis conference and that motivation often translates into a result or two.