Wednesday, September 23, 2009

Dispassionate Mathematics

Rick Cleary - Bentley University

I am coming clean. I do not have a passion for mathematics. And I don’t think that’s a bad thing. Here’s why.

I was recently reading an article about a friend who solved an interesting open problem and was rewarded with some well deserved publicity. This mathematician is quoted as saying, “I get a problem like this and I don’t sleep at night.” Articles about mathematics and interviews with mathematicians seem to always include comments like this. There is an indication of a passion for problem solving and a related inability to function in the rest of the world while the math question remains open. I do not recall ever reading an article where a mathematician discusses a recently solved problem and simply says, “Yes, that was a nice result. A good day at the office. That’s what I’m supposed to do. It’s my job.”

Does a person have to possess an extreme level of commitment to be a good mathematician? To choose mathematics as a major in college, should one feel that it is a calling? How about for success in graduate school in one of the mathematical sciences? Can a person forge a happy career in our subject without passion, or is something approaching devotion a vital ingredient?

I think in many circumstances we have, sometimes almost unwittingly, made passion a pre-requisite to entering the major, much to the detriment of the field. There are some of us who have had successful and rewarding careers in mathematics and related fields without having been on the high school math team, without taking the Putnam exam as undergraduates, and without losing sleep over problems. I enjoy mathematics, and I think a day at a math meeting with interesting talks is a great way to spend my time. But at the end of that day when I’m at dinner and a colleague grabs a pencil and a napkin and says, “Here’s a cute problem,” count me among those who try to change the subject.

Of course passion for mathematics can be a wonderful thing and it may be a necessity for the giant steps that move the field forward. The truly great mathematicians have that trait and I recognize its value. I enjoy reading mathematical history and I delight in accounts of the single minded tenacity shown in solving hard problems, and the euphoric feeling of triumph when successful. Anyone who has watched the wonderful Nova episode about Andrew Wiles and his solution of Fermat’s last theorem can see the great interaction between a scientific breakthrough and a personal victory. But tremendous devotion is demonstrably neither a necessary nor sufficient condition for building a successful career in the mathematical sciences. To use a baseball analogy, it might be necessary for a “Hall of Fame” career, but those of us making contributions as utility infielders have a place too.

Making passion a requisite part of our culture has costs. Here are a few of them:

Requiring passion discourages talented students from studying mathematics.
Recruiting students to mathematics is like a political party trying to decide whether to appeal to a committed base or expand a point of view to broaden participation. A common theme among colleges that have large and successful math majors is that they have put up the ‘big tent’ and allowed lots of students in. Does this hurt the quality of their top majors? It doesn’t appear to. For one thing it gives them enough students to offer required and elective courses more than once every other year!

Passion makes for poor advising.
Advisors who want passion as a pre-requisite often see graduate school as the only winning outcome for students with talent in mathematics. This runs counter to one basic goal of a liberal arts education, namely to encourage people to be thoughtful, adaptable and open-minded in career choices. Mathematics majors can go on to be wonderful accountants, machinists or landscapers and perhaps make unexpected contributions in those areas thanks to their point of view.

Faculty may quit research sooner than they should.
When faculty members insist that their research must be elegant, ground breaking and the result of a deep commitment, a common mid-career result is to give up completely. But there are myriad open problems in other disciplines where we can be of great help. There are plenty of opportunities for pedagogical research. There are consulting opportunities in business and industry. My PhD is in statistics, so finding these opportunities might be easier for me than for people in more abstract fields, but there are dozens of underpublicized success stories of people who make contributions in this more mundane way.

I feel fortunate to have an enjoyable, rewarding and I hope useful career in mathematics and statistics. My nonmathematical friends see me as a math nerd who sees the world differently than they do, and some of my mathematical colleagues probably see me as a slacker who doesn’t really ‘do’ math. That’s a balance I like.