The Calculus of Friendship

I got this book as an early Christmas present from my father-in-law. Over the years, we’ve gotten better and better at selecting appropriate presents for each other. Lately, we’ve settled in to a pattern of buying scotch and excellent books for each other. Last year, I knew that I had picked a good title when I noticed that my father-in-law left for the evening with his finger marking a page in the book I’d just given him. He couldn’t wait to read it.

I mention this exchange of fine books because it’s relevant to The Calculus of Friendship. The book almost exclusively focusses on the exchange of gifts. Strogatz and his highschool teacher Mr. Joffray (“Joff”) exchange calculus problems. For decades, they exclusively interact with one another through calculus. Nice problems, nice solutions.

It is delightful to hear what problems other people like. The book opens with a genre of problems I’ve never really thought about: pursuit and evasion games. In these problems, for example: a duck swims in a circle and is chased by a dog inside the circle which swims directly towards it. What is the path of the dog’s pursuit?

You won’t learn calculus by reading this book. The book is unapologetically mathematical. There is almost no background, no context. It is for calculus connoisseurs. I think it would be interesting reading for someone whose taken (or taught) a calculus course.

There is also a sub-text or narrative reflecting on masculinity. Strogatz wonders why his relationship with Joff is so exclusively mathematical. He regrets not writing about the loss of Joff’s son in early adulthood. Looking back, he feels bad about hiding the difficulties of his marriage from Joff. Here is a thoughtful line in the introduction:

Through all these changes, they are bound together by a love of calculus. For them it is more than a science. It is a game they love playing together — so often the basis of friendship between men — a constant while all around them is in flux.

Another recurring theme of the book is the Gaussian integral. \[ \int\limits_{-\infty}^{\infty} e^{-x^2}\ dx = \sqrt{\pi} \] It seems to come up in almost all of their problems and provides a lovely plot running through the book. Here is the inset from the cover, which shows Joff smiling in front a blackboard showing the clever polar coordinates evaluation of the Gaussian integral. Joff similing in front a blackboard showing the final steps of computing the Gaussian integral.

The Calculus of Friendship

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