FASCINATING MATHEMATICAL People Albers-Pages.indb 1 5/31/11 10:00 AM Albers-Pages.indb 2 5/31/11 10:00 AM FASCINATING MATHEMATICAL PEOPLE INTERVIEWS AND MEMOIRS Donald J. Albers and Gerald L. Alexanderson, Editors With a foreword by Philip J. Davis Princeton University Press • Princeton and oford Albers-Pages.indb 3 5/31/11 10:00 AM Copyright © 2011 by 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 press.princeton.edu All Rights Reserved Library of Congress Cataloging-in-Publication Data Fascinating mathematical people : interviews and memoirs / Donald J. Albers and Gerald L. Alexander- son, editors ; with a foreword by Philip J. Davis. p. cm. Includes bibliographical references and index. ISBN 978-0-691-14829-8 (hardcover : alk. paper) 1. Mathematicians—Biography. 2. Mathematicians— Interviews. I. Albers, Donald J., 1941– II. Alexanderson, Gerald L. QA28.F37 2011 510.92’2—dc22 2011010624 British Library Cataloguing-in-Publication Data is available This book has been composed in Minion Pro and Eras Printed on acid-free paper. ∞ Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Albers-Pages.indb 4 5/31/11 10:00 AM Contents Foreword by Philip J. Davis vii Preface ix Acknowledgments xiii Sources xv One Eleven Lars V. Ahlfors 1 Fern Hunt 193 Two Twelve Tom Apostol 17 Dusa McDuff 215 Three Thirteen Harold M. Bacon 43 Donald G. Saari 240 Four Fourteen Tom Banchoff 52 Atle Selberg 254 Five Fifteen Leon Bankoff 79 Jean Taylor 274 Six Sixteen Alice Beckenbach 96 Philippe Tondeur 294 Seven Arthur Benjamin 107 Eight Biographical Notes 319 Dame Mary L. Cartwright 129 Glossary 321 Nine Index 325 Joe Gallian 146 Ten Richard K. Guy 165 Albers-Pages.indb 5 5/31/11 10:00 AM Albers-Pages.indb 6 5/31/11 10:00 AM Foreword Philip J. Davis How do the words of mathematicians, dis- Since 1950 modes of communication and cussing their work, their careers, their lives, the possibility of social/technological inter- become known to a larger audience? There changes have grown exponentially (a math- are, of course, biographies and autobiogra- ematical term that pundits like to use). phies of mathematicians going as far back Newspapers, books (e.g., the recent Recount- as Pythagoras. There are letters galore. Some ings: Conversations with MIT Mathematicians), off-the-cuff remarks have been preserved radio, TV, dramatic stage productions, movies, (e.g., those of Lagrange). Thus, authentic e-mail, YouTube, the Internet, and conference words of bygone mathematicians are not dif- reports all record or depict interviews in which ficult to come by, and out of them it would mathematicians often sound off on all sorts of be easy to construct an imaginative mock topics far removed from their narrow special- interview: ties. I myself have interviewed several dozen numerical analysts, with texts now available Interviewer: Academician Euler, with so online, as a part of a Society for Industrial and many children how did you manage to Applied Mathematics (SIAM) project. Thus, separate your professional life from your the time of much singing has come, and the family life? voice of the mathematician is heard in the Euler: I’m glad you asked. I didn’t. I con- land. The question of who is listening is not sider all of them, theorems and children, as beyond conjecture. my results. The variety of subjects, professional values, personal lifestyles, and more, of contempo- Interviews? The word interview originally rary mathematicians are all well depicted in meant simply the meeting of two people. the interviews presented in this third col- Later it came to mean the questioning of lection of Mathematical People. Those of us some notable person by a newspaper reporter. in the mathematical business will find the In the current and wider sense of the word, macro aspect familiar, while the micro aspect interviews with mathematicians start, say, satisfies our natural curiosity as to why and around 1950. We now have interviews that what the next fellow is up to. link mathematical works, lives, and opinions. Perhaps, therefore, the larger value of They are often called oral histories. such collections as this may be found in, say, Foreword vii Albers-Pages.indb 7 5/31/11 10:00 AM twenty-five or fifty years. During this inter- view. A future mathematician may pick up val of time, the very nature of mathematics, this book in a library or in whatever format its contents, its applications, the manner of texts are then the norm and say, “Gosh, that its presentation, and of its support by society was certainly the golden age,” or alternatively, may have changed substantially. The study of and with considerable pride, “How much bet- the history of mathematics confirms such a ter, from all points of view, things are now!” viii Foreword Albers-Pages.indb 8 5/31/11 10:00 AM Preface The best-known recent biographer of math- the Scientific American, came to know hun- ematicians is Constance Reid, the San Fran- dreds of mathematicians, many of whom had cisco writer, whose life of David Hilbert was been inspired by his work. He corresponded highly praised when it was published in 1970. with some of the best mathematicians in the Her sister Julia Robinson was a distinguished world, who regularly sent him news of mathe- University of California, Berkeley mathema- matical developments that he often fashioned tician married to Raphael Robinson, also a into wonderful columns that were enjoyed Berkeley mathematician. Julia’s marriage to by thousands of readers every month. One of Raphael and Berkeley’s close proximity to us interviewed him a few years ago, and he San Francisco brought Constance in frequent had this to say about mathematicians: “There contact with many mathematicians, and she are some traits all mathematicians share. An found that she enjoyed their company and the obvious one is a sense of amazement over the culture in which they were embedded. Her infinite depth and the mysterious beauty and interest in them eventually reached the point usefulness of mathematics.” that she decided to write the Hilbert book, Both of us have interacted with large followed by volumes on Richard Courant, numbers of mathematicians in our profes- Jerzy Neyman, and E. T. Bell. After observing sional lives as professors, journal editors, mathematicians for some time, she summa- and officers of the Mathematical Association rized her impression of them: “Mathematics of America. We have interviewed dozens of is a world created by the mind of man, and mathematicians over the last thirty years, and mathematicians are people who devote their our conversations with and personal observa- lives to what seems to me a wonderful kind tions of scores of mathematicians lead us to of play!” It’s true—if you’re around a group strongly agree with the descriptions of math- of mathematicians excitedly talking about ematicians provided by Reid and Gardner. mathematics, you come away with a sense Historically mathematics has often been that whatever they’re doing, it’s fun. motivated by questions in astronomy, mechan- Martin Gardner, the most widely read ics, the physical and biological sciences, and, expositor of mathematics of the twentieth more recently, in economics. It is therefore century, during the twenty-five years that he widely appreciated because it works. It tells wrote a monthly column on mathematics in us about phenomena that are otherwise hard Preface ix Albers-Pages.indb 9 5/31/11 10:00 AM to explain and yet are important to society. ideas in the early grades, and others did not Modern, so-called abstract, mathematics is come to the subject until high school, college, not so easy to justify on the grounds of utility or graduate school. As you read these inter- because much of it is developed from within views, profiles, and memoirs you will come to the discipline of mathematics itself, just the conclusion that there is no such thing as a because it is interesting. But then the miracle typical mathematician. But all of them share a occurs—suddenly recondite properties of passion for mathematics (and, in many cases, seemingly useless prime numbers, for exam- other fields as well). ple, become essential as your ATM machine One common myth about mathematicians communicates safely with its central bank. is that they are especially interested in music. Modern-day mathematics is certainly an It is true for some but not for others, although example of the remark of the eminent physi- mathematics and music both deal with pat- cist Eugene Wigner on “the unreasonable terns. Scanning the mathematicians in our effectiveness of mathematics.” Some abstract three volumes of Mathematical People inter- forms of mathematics seem far removed from views, we find no evidence of a strong music- practical scientific questions, and then some- mathematics connection. Mathematics is one times we find these ideas popping up in appli- of a very short list of disciplines where we find cations when we least expect them. some child prodigies. We don’t see historians Who then are these people who devote who are child prodigies. To write good his- their lives to mathematics? Like other people, tory one needs a lifetime of experience, some- they come in a variety of shapes, sizes, and thing unnecessary in observing some deep temperaments. Some are gregarious and out- pattern in the whole numbers, for example. going, others reserved. In these interviews Of course, not all successful mathematicians we see a wide range of people drawn to this were prodigies, either.