Professor Bressoud talks about the MAA, mathematical careers, and teaching mathematics.
After a couple of talks this morning, one technical and incomprehensible, one unexpectedly mind-opening – more about this later – I got to sit down with MAA President David Bressoud.
First, I asked for his understanding of the purpose of the MAA. He reinforced what I’ve been coming to understand: the MAA deals mainly with college-level math. It is therefore focused on teaching math, encouraging the sharing of mathematical ideas through improved exposition and accessibility. Professor Bressoud has been involved in congressional briefings. The MAA does many things with the government, including influencing the support of scholarships and support for REUs.
Professor Bressoud teaches at Macalester College in Minnesota (which is about 1 mile from where I grew up). This is a smaller, liberal-arts college, not a research institution. The difference between smaller colleges and larger universities is mainly a matter of focus, he said. At either, professors are expected to be active researchers and to teach classes, but the focus at universities is usually on the research, whereas the focus at smaller colleges is usually on teaching.
After his undergraduate education, Professor Bressoud found that research was his passion. He went to graduate school, and afterwards felt very suited to a life in academia. More and more, however, teaching seemed to him of paramount importance, hence his position at Macalester College and his activity in (and current presidency of) the MAA. He is personally interested in the history of mathematics. Moreover, he thinks that a good grounding in history is of key pedagogical importance. It motivates the learning of mathematical concepts: the order in which ideas were formulated historically is perhaps an indicator of the order in which they should be taught to modern students. As an example, he pointed out that trigonometry was understood for millennia as relating to circles, and it is only in the last two or three centuries that the formulation of trigonometric concepts in terms of right triangles has been developed. Yet students are often taught SOHCAHTOA long before the definitions of trigonometric functions in terms of circles (which are much more useful for calculus).
More importantly, perhaps, studying the history of mathematical innovation can ease the shift into research. The math that we learn in childhood through undergraduate study is of a much different sort than the math we do as active mathematicians. We might classify the former as pristine. As a result of centuries of work, basic math concepts have been refined and polished repeatedly so that they can be taught to a wide audience in as “finished” a form as possible. This, however, gives an inaccurate picture of how math is actually practiced. Many subjects now seem handed down from the gods; reading the original papers on these subjects, however, makes the authors seem mortal. That is, rather than being scared away from research because it seems to require a spark of rarefied genius, mathematics can be seen as a very human, very accessible endeavor.
Having never done any math research myself, I was very interested about Professor Bressoud’s description of it. The first thing to realize, he said, is that working as a mathematician is (clearly) very different from working as a student. A lot of mathematical work can be simply described as trial and error, repeated over and over again. The main thing, though, is that math is doable. It’s not easy, it’s not simple; but it’s doable. “We’re adding little pieces into the whole.”
His main areas of research are combinatorics and number theory. One application of his work he mentioned was statistical mechanics, which heavily relies on combinatorial ideas. We generally think of physics as taking many ideas from mathematics. However, there are also many ideas and methods that physicists have developed, he said, which have interesting pure mathematical applications. There is a lot of exchange of ideas between the two disciplines, in both directions.
Finally, I had just been to a talk by Dr. Brenda Dietrich, sponsored by SIAM, about her work as a mathematician at IBM. This opened my eyes to the many possible mathematical careers, many of which I am often not conscious of, nor even ever aware of. When asked what I want to do after I graduate from college, I am usually at a loss for words. I tacitly assume that I’ll go to graduate school, end up as a professor, and happily spend my life in academia. But I rarely think about this explicitly, and the wealth of other options for mathematicians often makes me second-guess myself. I talked with Professor Bressoud about this subject, and he mentioned many jobs of which I have never even thought. Basically, there is a demand for people who can “think creatively qualitatively.” Thus, in many areas, mathematicians are those best suited to being analysts. There is an abundance of data nowadays, and there is a pressing need to sift through this quantitative data and obtain qualitative interpretations, a job well-suited to a mathematician.
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