Nonlinear Relationships

From Seed:

In mathematician Steven Strogatz’s recent book, friendship and integrals collide, yielding a math story of unusual poignancy.

Long after Steven Strogatz had become a professor at MIT and Cornell, he was still writing letters to his high school calculus teacher, Don Joffray. The two started swapping word problems and logic puzzles when Strogatz, who studies chaotic systems, was in college. Their jovial mini-treatises form the body of Strogatz’s most recent book, The Calculus of Friendship. But they always managed to keep a certain distance from each other, demonstrating, perhaps, the natural reserve for which mathematicians are known. Mr. Joffray, as Strogatz still refers to him, sent his congratulations on Strogatz’s engagement in a brief preface to a calculus problem, but Strogatz’s reply makes no acknowledgement. When he heard from secondhand sources that Joffray’s son had died, Strogatz wondered why Joffray never mentioned it, but never brought it up. After thirty years of omissions, it took a string of tragic events to bring their friendship into three dimensions.

Seed editor Veronique Greenwood spoke with Strogatz about the nature of friendship, why math isn’t about right and wrong, and how an elliptical swimming pool helped launch his teaching career.

Seed: How did this remarkable correspondence begin?

Steven Strogatz: When I was a junior in high school, I took calculus with Mr. Joffray. People often assume that he must have been my mentor, but I wouldn’t call him that. Mr. Joffray was not one of the three or four teachers that influenced me the most in high school. And in my senior year, I lost touch with him, because I had finished the available math courses and was working on my own. So it was especially peculiar that I would happen to write to him, starting my freshman year of college. But something about my relationship with him worked—it kept on going. About once a year, I would write to him about something I’d learned in college that I thought he might like—a problem or a proof—and it went on like that for several years. Things really got rolling when I was a junior in college, and he asked me a question that he didn’t know the answer to that had come up in one of his advanced placement courses. I could even tell you the question: He was imagining an elliptical pool with a 1-foot-wide border around the outside, and he wanted to know if the border would also be an ellipse. I mean, it’s certainly some kind of oval, but is it specifically the kind of curve that to a mathematician would qualify as an ellipse? Now it was no longer just me showing him things I was learning—he was actually asking for help. And, boy, I loved that! That was very exciting. It was very generous of him. I wanted to teach—I always wanted to teach—but I was a kid, and I didn’t have anyone to teach! Who would sit there listening to me? Well, he would.

Seed: You describe one of your first math teachers at Princeton, a renowned topologist—“he was so shy that he slithered along the wall when he entered the lecture room, as if hoping to become invisible.” And you tell the joke—How can you tell if a mathematician’s an extrovert? He looks at your shoes when he’s talking to you.

More here.