# 'The Calculus of Friendship'

For 30 years, starting in the spring of 1977, Steven Strogatz maintained an occasional correspondence with his high school calculus teacher, Don Joffray. During that time, both Strogatz and Joffray experienced great changes in their lives -- from professional successes to family tragedies -- yet their letters focused almost entirely on mathematics, rarely mentioning personal matters at all.

In a new book, *The Calculus of Friendship* (Princeton University Press), Strogatz shares many of the letters he exchanged with his old teacher, and explains what led him finally to try to learn more about the man he’d hardly known for so many years. In an e-mail interview, Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University, discussed his book and the story behind it.

**Q: The Calculus of Friendship **

**-- though published by a university press -- isn’t exactly a typical academic book (and it stands noticeably apart from your other works). When and why did you decide to write it?**

**A:** It’s been on my mind for a long time. At first I imagined it as a collection of fun math problems, a supplement for teachers or

students looking for something off the beaten track. But as the years went by and I began telling my friends about my ongoing correspondence with my high school calculus teacher, Mr. Joffray, their reactions surprised me: when I’d mention that our letters were almost entirely about math problems, they’d laugh and look a little perplexed. It never occurred to me that there was anything peculiar about this until my wife, Carole, heard about the correspondence for the first time. After all these years, you must know everything about each other, she said. When I told her no, we just write about math problems, she shook her head and said, “That is such a guy thing.”

Carole’s teasing opened my eyes to a puzzle I’d never considered before: Why did I know so little about my teacher? Why had so much gone undiscussed between us? I went back to the thick stack of letters from the past three decades and realized it was more than a collection of math problems; it was the chronicle of a friendship between a teacher and a student. At that point I felt I had to write the book.

**Q: It sounds like you were fortunate enough to have a number of excellent teachers in high school and in college. Why do you think it was Mr. Joffray in particular with whom you ended up having this extraordinary friendship?**

**A:** Mr. Joffray made me feel like I could teach him. That was an incredible gift because more than anything else I wanted to be a math teacher. At a time before I had any students, he was my student. In later years he’d write to me asking for advice about how to solve a problem that had stumped him, typically a question raised by one of his advanced students.

**Q: The bulk of your correspondence – and thus much of the book – consists of the two of you discussing particularly tricky math problems. How would you recommend that readers with little mathematical background approach the book, and what do you hope they can gain from it?**

**A:** Many of my friends and relatives have read the book in one sitting by skipping the equations and just reading the main text. That’s fine. But I hope readers will at least glance at the letters (which contain most of the math), in part because the formulas shown there are beautiful, but also because the letters are where you can hear Mr. Joffray’s voice, and watch the little emotional undercurrents slip out. Plus, the letters are so playful. Many people think of math as cold and impersonal, but by watching two friends playing the game of calculus together, readers may be surprised to see just how warm, intimate, and joyful math can be.

Math also plays a more poetic role in the narrative. Calculus is the mathematics of change, and in a metaphorical way, the book is about the same thing. It’s about the transformation that takes place in a student’s heart, as he and his teacher reverse roles, as they age, and as they get banged around by life. Each chapter begins with a gentle passage about a concept in the mathematics of change (such as chaos, bifurcation, or infinity) and uses it to foreshadow the emotional changes coming next in the story. I hope readers will find these metaphors illuminating and perhaps even poignant.

**Q: You mention that you were not, as a high school junior, particularly impressed with Mr. Joffray’s teaching, but it’s clear that you learned a great deal from him over the years. Can you talk about how this friendship has affected your teaching – if at all – and how you view your own role as a professor?**

**A:** What I now realize was amazing about Mr. Joffray’s teaching was the way he motivated his students. He never competed with us or tried to prove how smart he was. On the contrary, he openly revered his students, past and present, almost to the point of hero worship. He made us want to show him our little insights and discoveries, and he took tremendous pleasure in them. In that way he often acted more like a cheerleader than a teacher. This wasn’t a pedagogical gimmick. He was an amateur in the truest sense, someone who loved math and the challenge of understanding it. Just asking a good question was enough to earn you a spot in his pantheon.

I’ve tried to do something similar with my own graduate students. When it’s time for them to select a thesis project, I give them a great deal of freedom. Rather than assigning a problem, I encourage them to make up their own. It has to be something that grips them irrationally by the imagination, to borrow a phrase from another mentor of mine, Art Winfree, who taught me that this is the only way to have a chance at doing something remarkable. But of course it’s also a risky strategy. Sometimes the student concocts an intractable problem or chooses an area that I know nothing about. In cases like that I try to act like a lifeguard, swimming alongside them, letting them do all the work but not letting them drown either. Whether their resulting discoveries turn out to be impressive or mundane, at least they are their own. In this way math becomes personal, a form of artistic expression.

**Q: You spent much of your undergraduate career preparing for medical school, but your desire to take quantum mechanics led you back to mathematics. Did you always feel that you wanted to be an academic? In what ways has the life of a professor been what you imagined – and in what ways has it not?**

**A:** Yes, I always did want to be a professor. And in most ways it has turned out about how I’d imagined. The one surprise is how much of my time is devoted to research and graduate education. I’d always pictured myself working mainly with undergraduates. In my heart of hearts, what I love most is teaching math to bright-eyed newcomers, which means everyone from undergraduates to the public at large. I’m always looking for more opportunities to do that.

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For 30 years, starting in the spring of 1977, Steven Strogatz maintained an occasional correspondence with his high school calculus teacher, Don Joffray. During that time, both Strogatz and Joffray experienced great changes in their lives -- from professional successes to family tragedies -- yet their letters focused almost entirely on mathematics, rarely mentioning personal matters at all.

For 30 years, starting in the spring of 1977, Steven Strogatz maintained an occasional correspondence with his high school calculus teacher, Don Joffray. During that time, both Strogatz and Joffray experienced great changes in their lives -- from professional successes to family tragedies -- yet their letters focused almost entirely on mathematics, rarely mentioning personal matters at all.

In a new book,

The Calculus of Friendship(Princeton University Press), Strogatz shares many of the letters he exchanged with his old teacher, and explains what led him finally to try to learn more about the man he’d hardly known for so many years. In an e-mail interview, Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University, discussed his book and the story behind it.Q:The Calculus of Friendship-- though published by a university press -- isn’t exactly a typical academic book (and it stands noticeably apart from your other works). When and why did you decide to write it?A:It’s been on my mind for a long time. At first I imagined it as a collection of fun math problems, a supplement for teachers orstudents looking for something off the beaten track. But as the years went by and I began telling my friends about my ongoing correspondence with my high school calculus teacher, Mr. Joffray, their reactions surprised me: when I’d mention that our letters were almost entirely about math problems, they’d laugh and look a little perplexed. It never occurred to me that there was anything peculiar about this until my wife, Carole, heard about the correspondence for the first time. After all these years, you must know everything about each other, she said. When I told her no, we just write about math problems, she shook her head and said, “That is such a guy thing.”

Carole’s teasing opened my eyes to a puzzle I’d never considered before: Why did I know so little about my teacher? Why had so much gone undiscussed between us? I went back to the thick stack of letters from the past three decades and realized it was more than a collection of math problems; it was the chronicle of a friendship between a teacher and a student. At that point I felt I had to write the book.

Q: It sounds like you were fortunate enough to have a number of excellent teachers in high school and in college. Why do you think it was Mr. Joffray in particular with whom you ended up having this extraordinary friendship?A:Mr. Joffray made me feel like I could teach him. That was an incredible gift because more than anything else I wanted to be a math teacher. At a time before I had any students, he was my student. In later years he’d write to me asking for advice about how to solve a problem that had stumped him, typically a question raised by one of his advanced students.Don Joffray (left) and Steven Strogatz at Joffray's retirement party

Q: The bulk of your correspondence – and thus much of the book – consists of the two of you discussing particularly tricky math problems. How would you recommend that readers with little mathematical background approach the book, and what do you hope they can gain from it?A:Many of my friends and relatives have read the book in one sitting by skipping the equations and just reading the main text. That’s fine. But I hope readers will at least glance at the letters (which contain most of the math), in part because the formulas shown there are beautiful, but also because the letters are where you can hear Mr. Joffray’s voice, and watch the little emotional undercurrents slip out. Plus, the letters are so playful. Many people think of math as cold and impersonal, but by watching two friends playing the game of calculus together, readers may be surprised to see just how warm, intimate, and joyful math can be.Math also plays a more poetic role in the narrative. Calculus is the mathematics of change, and in a metaphorical way, the book is about the same thing. It’s about the transformation that takes place in a student’s heart, as he and his teacher reverse roles, as they age, and as they get banged around by life. Each chapter begins with a gentle passage about a concept in the mathematics of change (such as chaos, bifurcation, or infinity) and uses it to foreshadow the emotional changes coming next in the story. I hope readers will find these metaphors illuminating and perhaps even poignant.

Q: You mention that you were not, as a high school junior, particularly impressed with Mr. Joffray’s teaching, but it’s clear that you learned a great deal from him over the years. Can you talk about how this friendship has affected your teaching – if at all – and how you view your own role as a professor?A:What I now realize was amazing about Mr. Joffray’s teaching was the way he motivated his students. He never competed with us or tried to prove how smart he was. On the contrary, he openly revered his students, past and present, almost to the point of hero worship. He made us want to show him our little insights and discoveries, and he took tremendous pleasure in them. In that way he often acted more like a cheerleader than a teacher. This wasn’t a pedagogical gimmick. He was an amateur in the truest sense, someone who loved math and the challenge of understanding it. Just asking a good question was enough to earn you a spot in his pantheon.I’ve tried to do something similar with my own graduate students. When it’s time for them to select a thesis project, I give them a great deal of freedom. Rather than assigning a problem, I encourage them to make up their own. It has to be something that grips them irrationally by the imagination, to borrow a phrase from another mentor of mine, Art Winfree, who taught me that this is the only way to have a chance at doing something remarkable. But of course it’s also a risky strategy. Sometimes the student concocts an intractable problem or chooses an area that I know nothing about. In cases like that I try to act like a lifeguard, swimming alongside them, letting them do all the work but not letting them drown either. Whether their resulting discoveries turn out to be impressive or mundane, at least they are their own. In this way math becomes personal, a form of artistic expression.

Q: You spent much of your undergraduate career preparing for medical school, but your desire to take quantum mechanics led you back to mathematics. Did you always feel that you wanted to be an academic? In what ways has the life of a professor been what you imagined – and in what ways has it not?A:Yes, I always did want to be a professor. And in most ways it has turned out about how I’d imagined. The one surprise is how much of my time is devoted to research and graduate education. I’d always pictured myself working mainly with undergraduates. In my heart of hearts, what I love most is teaching math to bright-eyed newcomers, which means everyone from undergraduates to the public at large. I’m always looking for more opportunities to do that.