Steven Strogatz - The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math

The Calculus of Friendship

What a Teacher and
a Student Learned

about Life

While Corresponding
about Math

Steven Strogatz

PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD

Copyright 2009 by Steven Strogatz
Requests for permission to reproduce material from this work should
be sent to Permissions, Princeton University Press

Published by Princeton University Press, 41 William Street, Princeton,
New Jersey 08540

In the United Kingdom: Princeton University Press, 6 Oxford Street,
Woodstock, Oxfordshire OX20 1TW

All Rights Reserved

Library of Congress Cataloging-in-Publication Data
Strogatz, Steven H. (Steven Henry)
The calculus of friendship: what a teacher and a student learned about life
while corresponding about math = Steven Strogatz.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-691-13493-2 (hardback: alk. paper) 1. Strogatz, Steven H.
(Steven Henry)Correspondence. 2. Joffray, Don, 1929
Correspondence. 3. MathematiciansCorrespondence.
4. Calculus. 5. Differential equations. 6. Chaotic behavior
in systems. I. Joffray, Don, 1929 II. Title.
QA29.S698A4 2009
510.922dc22 2008049339

British Library Cataloging-in-Publication Data is available

This book has been composed in

Printed on acid-free paper.

press.princeton.edu

Printed in the United States of America

1 3 5 7 9 10 8 6 4 2

Dedicated to Mr. Joffray,
and to teachers like him everywhere

For the past thirty years Ive been corresponding with my high school calculus teacher, Mr. Don Joffray. During that time, he went from the prime of his career to retirement, competed in whitewater kayak at the international level, and lost a son. I matured from teenage math geek to Ivy League professor, suffered the sudden death of a parent, and blundered into a marriage destined to fail.

Whats remarkable is not that any of this took placesuch ups and downs are to be expected in three decades of lifebut rather that so little of it is discussed in the letters. Instead, our correspondence, and our friendship itself, is based almost entirely on a shared love of calculus.

It never occurred to me how peculiar this is until Carole (Im happily remarried now) teased me about it. Youve been writing to him for thirty years? You must know everything about each other. Not really, I said. We just write about math problems. That is such a guy thing, she said, shaking her head.

Her question got me thinking. What did I really know about my teacher? Why had so much gone undiscussed between us? On the other hand, we both enjoyed our correspondence the way it was, so was there any problem here?

Questions like these have kept nagging at me. Im not sure how to go about answering them or if I should even try. All the while, I find myself looking for clues in a green Pendaflex folder in my office, stuffed four inches thick with letters about math problems.

I was 15 when I took calculus from Mr. Joffray. One thing about him was unlike any other teacher Id ever had: he worshipped some of his former students. Hed tell stories about them, legends that made them sound like Olympian figures, gods of mathematics. In my own case, he was more a fan than a teacher, always marveling at what problems I could invent and solve. It felt slightly strange to be so admired by my own teacher. But I cant say I minded it.

After I graduated, something in me wanted to stay in touch with him. My first letters were about math problems that I thought hed enjoy, gems Id picked up in my college courses. The letters were infrequent, about one a year. I suppose he must have written back to me, but none of his responses have survived. It never occurred to me to save them.

It was only a decade later, when I was just starting my career as a professor, that our correspondence began to flourish. The pattern was always the same: Mr. Joffray would write to ask for help with a problem that had stumped him, typically a question raised by one of his seniors in the most advanced math class at the school. When one of these letters arrived in the mail, I stopped whatever I was doing to see if I could help. For one thing, they posed fascinating little questions, beautiful excursions off the beaten track of calculus. But maybe more importantly, they gave me a chance to explain math to someone who loved learning it, the best student any teacher could have, someone with perfect preparation and an evident sense of delight and gratitude.

With his retirement a few years ago and no more students to stimulate him, our correspondence began to wane. Not in frequencyin fact, he wrote to me more than everbut in intensity and reciprocity. It got to the point where I simply couldnt keep up with him. Yes, he reassured me, he understood all that, and urged me not to worry; he knew how busy I must be in my career and with all the new obligations that come with raising a family. But it still felt like we were drifting apart. Ironically, I was now the same age that he was when he taught me in high school.

In January 2004, yet another letter arrived. But this time I felt anxious when I saw the envelope. The uncharacteristically tremulous handwriting reminded me of my dads after his Parkinsons had set in.

Sat. January 17, 2004

Dear Steve,
Eek! I had a mild stroke Thurs. noon and lost all sensation in my right (writing) hand. Several hours later I managed to open and close my fingers and get some strength back into my grip, but, alas, no dexterity! X@#! A one-handed piano player isnt in demand, so Ill miss my gig with our jazz quartet tomorrow....

This glimpse of mortality awakened me to how much Id been overlooking all these years. I felt compelled to visit Mr. Joffray at his home, to come to know the man behind the math.

Calculus is the mathematical study of change. Its essence is best captured by its original name, fluxions, coined by its inventor, Isaac Newton. The name calls to mind systems that are ever in motion, always unfolding.

Like calculus itself, this book is an exploration of change. Its about the transformation that takes place in a students heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. 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 togetherso often the basis of friendship between mena constant while all around them is in flux.