My good friend and colleague Leah Gordon often likes the same books that I do. From time to time we make recommendations to each other. One of these is Francis Su’s Mathematics for Human Flourishing, which I have just finished reading—thanks, Leah!
“Flourishing” in this context definitely does not mean making a lot of money because you have a STEM-related job. If definitely does not mean applying traditional mathematics to investment banking or running a hedge fund. So what does it mean? A part of what it does mean appears in this pair of sentences in the first chapter:
To miss out on mathematics is to live without an opportunity to play with beautiful ideas and see the world in a new light. To grasp mathematical beauty is a unique and sublime experience that everyone should demand.
Yes, I know—claims like these can be found in many math popularizations. So how is this book different from all other books?
In a lot of ways, actually. The most obvious ones have to do with the organization of the material. There are three threads running throughout the book, which is organized into 13 chapters:
- The principal thread has to do with the Big Ideas (see below) along with related personal stories. A few of these personal stories are about growing up Chinese-American in Texas, of all places; some are about his unexpected difficulties as a grad student in mathematics.
- Secondarily, each chapter is followed by one or more interesting problems. Near the end of the book you can find a hint or two if you’re stuck. And after that you can find actual solutions—not just answers, but explanations.
- Finally, between the chapters are letters from Christopher Jackson to Su. You’ve probably been wondering about the photo above; it shows Su on the left and Jackson on the right. Having received excessively long prison sentences for drug offenses, Jackson has been in federal prisons since age 19 and is clearly a brilliant mathematician, having taught himself higher math from the ground up and being a living example of the Big Ideas, with help from Su.
“At every opportunity,” observes Su, “we need to counter the idea that math is memorization, and replace it with the idea that math is exploration.” Yes indeed. But what he doesn’t address is the extreme opposition one can get to this view, especially from students who want to be told what to do and how to do it! Oh well, that’s another book; this one isn’t really intended as advice for teachers. But Su does stress an important value that I have tried to follow since Day One of my teaching career in September of 1969: “[with mathematics] you are not resigned to a life of conformity and blind trust in authority. You are better able to tell if someone is trying to fool you. And mathematical reasoning and sense-making cultivate in us the virtue of thinking rigorously: the ability to handle ideas well and to craft clear arguments with those ideas.”
I have referred twice now to Su’s Big Ideas, which are not the usual ones in popular math books. On the right here is his Table of Contents:
Right away you know that you will be getting an unusual experience. Is this mathematics????? Yes, and you will see why I was struck by a certain comparison. One of my most popular posts in this blog has been Attributes of a Good Mathematician, which has been read by over 8000 unique visitors in the six years since it first appeared. I list there what we considered nine attributes of a good mathematician, to be explored by high-school freshmen at a rate of one per month, as created by Weston’s math department in one of our most useful professional development workshops. I still think it’s a really good list and a really good plan. Anyway, a useful exercise for the reader would be for you to compare Su’s list with ours, even though they had very different intentions. This is what we had in 2015:
A mathematician values…
- Critical thinking
Where does competition fit into this list? It doesn’t—at least not directly. Indirectly, of course, it does, as any math team that practices for meets is going to have to engage in all nine values. However, as Su says, such activities can “sometimes encourage an unhealthy competitiveness, especially if the competition is not well designed, or if it rewards speed (a computational skill, not a mathematical skill) over ingenuity.” This is exactly why I have mixed feelings about math competitions.
If you think about competitiveness, you automatically think about grading. Su points out that “grades are a measure of progress, not a measure of promise.” That’s one of the reasons why I prefer describing a student’s work as something like “not yet proficient” rather than “unsatisfactory.”
Under these circumstances, you may wonder how Su manages to keep politics out of this book. Well, he doesn’t quite manage that, though he comes close. Aside from the question of Jackson’s excessively long prison sentence—purely political in a federal system that doesn’t even have paroles—we do have the occasional observation like this one:
The world I see today is being upended by political instability, stoked by misinformation. Truth is obscure. People are endorsing blatant falsehoods that comport with their worldview rather than accepting complicated truths. We live in filter bubbles that reflect our own biases back at us. Falsehoods are routinely shared within these bubbles, sometimes maliciously.
Finally, I need to comment on an odd point of contrast between Su’s academic experiences and my own. In his case, it was an undergraduate topology professor, Michael Starbird, who rekindled his confidence in mathematics at the University of Texas. Su writes:
To my delight, Starbird was teaching in an “inquiry-based learning” format. There were no lectures. Instead, we were given a list of theorems and provided the challenge of discovering their proofs for ourselves. Through guided interaction with him and with one another, we learned how to present our ideas and subject them to constructive scrutiny by peers. But the underlying strength of the course was how the professor used this format to encourage a different classroom culture. He created an environment where questions were praised and unusual ideas were welcome. He was giving us the freedom to explore.
“Drawing pictures was very important in this course,” says Su. In contrast was my own experience with an undergraduate topology course at a certain well-known university (where Su ended up doing his graduate work). Professor M did nothing but lecture, and he refused to draw any pictures! Well, he drew them in the air, but never on the board. This class, as I have told my own students, was the only one I ever started taking and then dropped.
I wish I had had Francis Su as a college professor. But he is still inspiring my work as a high school teacher.
Go read his book!