Paul Sally.

The recent issue of the alumni magazine from my undergraduate alma mater, The University of Chicago, includes a profile of mathematician Paul Sally, who taught the Honors Analysis in Rⁿ sequence I took in my second year. 

Despite the rigorously intellectual image of itself that the University promotes, the alumni magazine is usually as circumspect as an in-flight magazine. Of course the primary purpose of the magazine is to cultivate us as donors, so on-campus controversy, intellectual or otherwise, gets scant attention. The article on Sally certainly follows the magazine’s formula of uncritical boosterism, but I still found it a delight to read: it took me back to what was probably the most intellectually fulfilling experience of my academic career, a time when all the promotional slogans about the life of the mind were very real for me.

Although my enthusiasm for working in a lab led me to choose physics over mathematics, I still have a fondness for pure mathematics. I retain a handful of habits  that are more a part of math culture than physics culture.¹ Sally’s course kept me on the fence between the two disciplines.

Sally delivered his classes entirely without notes, and the course rarely made reference to the assigned book (a cheap Dover reprint and a small volume from Spivak). He led a “discussion session,” Tuesday evenings from 6:30 until 8 or 9, stretching the amount of class time. He told us he expected at least 25 hours per week from us, at one point advising us to make posters which read “Mathematics… is a full time job.” It was mathematics by immersion.

Not every teacher can pull this off so successfully: it’s easy enough to assign lots and lots of work, but the combination of a heavy workload and an uninspiring instructor usually results in lots of incomplete assignments. 

Sally once remarked that, as you continue in mathematics, you get to a point where hard work is not only necessary, but also sufficient, to prove theorems and make progress. He was getting us to develop the sort of attitude and work ethic to reach that point.

There are many things I learned in college that I’ve now forgotten, many problems I can no longer solve. I don’t know how much review it would take for me to be able to solve the problems from Honors Analysis again, but, 15 years on, I feel I still have a well-developed understanding of the structure of the real numbers. 

Here’s another article about Sally, for winning a teaching award.

1. In particular, I can’t stand the common-in-physics habit of using the word “finite” when what is really meant is “non-zero” or “infinitesimal.” [↩]