Before I changed gears in my mid-twenties and embarked on an actuarial career, I had been pursuing a doctorate in pure mathematics at the University of Chicago, under the tutelage of the noted group theorist Jon Alperin.

I did manage to publish one academic paper in my mathematician days, although it was actually an outgrowth of a summer research position that I had at Queen’s University right before coming to graduate school.   The paper was called “Properties of Functions Associated with Invariant Theory”, published in Communications in Algebra in 1994, and it was joint work with two of my Queen’s professors, Eddy Campbell and Ian Hughes.  (Eddy has gone on to a career in university administration, serving since 2009 as President of the University of New Brunswick.)   As often happens in mathematics, another mathematician shortly thereafter found a much more efficient proof of our main result; he published a paper called “On a Theorem of Bell-Campbell-Hughes” which I had the pleasure of refereeing.  I should note that, in mathematics (as opposed to most other academic disciplines), it is normal for authors to appear in alphabetical order without regard to their relative contributions to the paper; mine were admittedly modest…

Starting in my sophomore year of university, I had developed an odd study habit for each of my math classes:  After each class, I would re-write my class notes into a more permanent form, in pen in a bound notebook, with changes as appropriate (such as adding to proofs those details that had been glossed over during class).  Towards the end of my first quarter of graduate school, my bound notes from Alperin’s MATH 325 class proved to be quite popular among my classmates studying for the final.  The following summer, and with my professor’s explicit blessing, I spent my time turning my notes into the first draft of a textbook.

Two years thereafter, I found myself the proud co-author (at age 23) of Groups and Representations, Volume 162 in the well-known Springer Graduate Texts in Mathematics series.  (Both Alperin and I were huge baseball fans and hence were very happy that our book ended up in the #162 slot in that series, since 162 happens to be the number of games each team plays in a major league baseball regular season, at least since 1961.)  The book remains in print two decades later, and it still seems to sell maybe a hundred copies a year.

Mind you, the fact that as a graduate student I was more interested in spending my energy to help write a textbook rather than to pursue mathematical research problems was, in retrospect, a very clear indication that mathematician was not the ideal profession for me.  In my opinion the only people who ought to pursue a career in mathematics are those who, having been exposed to it, cannot imagine being happy doing anything else.  I was not one of those special souls, so I left the field, although I continue to have a soft spot for it.

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