Mathematical People Mathematical People Profi les and Interviews Second Edition Edited by Donald J. Albers and Gerald L. Alexanderson Introduction by Philip J. Davis A K Peters Wellesley, Massachusetts Editorial, Sales, and Customer Service Offi ce Photo and Illustration Credits p. xx, Marguerite Dorian; p. 3 (left), The University of Chicago A K Peters, Ltd. Offi ce of News and Information; p. 16, Daniel Wheeler; pp. 18, 888 Worcester Street, Suite 230 24, John Blaustein; p. 32, James H. White; p. 36, Simon J. Fraser; Wellesley, MA 02482 pp. 37, 38, 39, 40, 41, 42, Richard Guy; pp. 51, 52, 54, 55, 56, www.akpeters.com Dave Logothetti; pp. 58, 64, 70, News and Publications Service, Stanford University; p. 74, Burton Halpern Public Relations; p. 77, Steven Swanson; pp. 79, 83, University Communications, Copyright © 2008 by A K Peters, Ltd. Santa Clara University; pp. 105, 108, 109, 110, 112, Ché Graham; p. 106, Carol Baxter; pp. 156, 158, 161, 167, Adrian N. 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Mandelbrot; p. 229, Richard Voss; p. 254, Stella Pólya; electronic or mechanical, including photocopying, recording, p. 255 (right), Bernadette Boyd; p. 258, Rose Mandelbaum; or by any information storage and retrieval system, without p. 262, City University of New York; pp. 271, 272, Mina Rees; written permission from the copyright owner. pp. 277, 278, 281 (2), Springer-Verlag, Inc.; p. 304, Bill Ray; p. 306, Blanche Smullyan; p. 313, Herbert Kuhn; p. 314, Halmos Collection; p. 316, 318, Blanche Smullyan; p. 320, University of First Edition published in 1985 by Birkhäuser Boston in London; pp. 359, Princeton University; p. 366, Steve Larson; collaboration with the Mathematical Association of America. p. 368, Los Alamos Photo Laboratory; p. 370, HERBLOCK. (All other photographs were supplied by interview and profi le subjects.) Library of Congress Cataloging-in-Publication Data Mathematical people : profi les and interviews / Donald J. Additional Acknowledgements Albers and Gerald L. Alexanderson, editors ; introduction by Several of the interviews and profi les in this volume fi rst ap- Philip J. Davis. -- 2nd ed. peared in the College Mathematics Journal: Birkhoff (March p. cm. 1983), Chern (November 1983), Coxeter (January 1980), Erdős Includes bibliographical references and index. (September 1981), Gardner (Part I, May 2005; Part II, September ISBN-13: 978-1-56881-340-0 (alk. paper) 2005), Halmos (Part I, September 1982, Part II, January, 2004), 1. Mathematicians--Biography. I. Albers, Donald J., 1941- II. Kemeny (January 1983), Kline (June and September 1979), Alexanderson, Gerald L. Knuth (January and March 1982), Pollak (June 1984), Pólya (January 1979), Reid (September 1980), Robbins (January QA28.M37 2008 1984), Tucker (June 1983), and Ulam (June 1981). The profi le 510.92’2--dc22 of Conway fi rst appeared in Math Horizons (Spring 1994). The profi le of Graham fi rst appeared in Math Horizons (November 2007047393 1996). The memoir of Smullyan is an abridgement of Some Interesting Memories: A Paradoxical Life published by Thinker’s Press, Inc., Davenport, Iowa, 2002. Copyright Raymond Smullyan. Published with permission. The memoir of Taussky- Todd is published courtesy of the Archives, California Institute of Technology. Printed in India 12 11 10 09 08 10 9 8 7 6 5 4 3 2 1 Contents Contents ° vii Preface to Second Edition xi Preface to First Edition xv Foreword xix By Ivan Niven Introduction: Refl ections on Writing the History of Mathematics xxvii By Philip J. Davis Garrett Birkhoff 1 Interviewed by G. L. Alexanderson and Carroll Wilde David Blackwell 15 Interviewed by Donald J. Albers Shiing-Shen Chern 29 By William Chinn and John Lewis John H. Conway 37 By Richard K. Guy H. S. M. Coxeter 47 Interviewed by Dave Logothetti Persi Diaconis 59 Interviewed by Donald J. Albers Paul Erdős 75 Interviewed by G. L. Alexanderson Martin Gardner: Defending the Honor of the Human Mind 87 By Peter Renz Martin Gardner: Master of Recreational Mathematics and Much More 93 Interviewed by Donald J. Albers Ronald L. Graham 105 By Donald J. Albers Paul Halmos 115 Interviewed by Donald J. Albers Peter J. Hilton 139 Interviewed by Lynn A. Steen and G. L. Alexanderson viii ° Mathematical People John Kemeny 157 Interviewed by Lynn A. Steen Morris Kline 173 Interviewed by G. L. Alexanderson Donald Knuth 185 Interviewed by Donald J. Albers and Lynn A. Steen Solomon Lefschetz: A Reminiscence 209 By Albert W. Tucker Benoit Mandelbrot 213 Interviewed by Anthony Barcellos Henry Pollak 235 Interviewed by Donald J. Albers and Michael J. Thibodeaux George Pólya 253 Interviewed by G. L. Alexanderson Mina Rees 263 Interviewed by Rosamond Dana and Peter J. Hilton Constance Reid 275 Interviewed by G. L. Alexanderson Herbert Robbins 286 Interviewed by Warren Page Raymond Smullyan 305 Autobiographical Essay Olga Taussky-Todd 321 Autobiographical Essay Albert Tucker 353 Interviewed by Stephen B. Maurer Stanislaw M. Ulam 367 Interviewed by Anthony Barcellos Biographical Data 375 Index of Names 379 Preface to Second Edition Preface to Second Edition ° xi n 1985 when Philip Davis wrote the introduction to stream publishers, and to name just a few, biographies I this book he lamented the low esteem in which math- of Abel, Cayley, R. L. Moore, Sylvester, Bourbaki, Erdős ematical history was held by the general public and (two, no less), Wiener, Nash, Coxeter, Tarski, Turing, and even by professional historians. He pointed out, rather Bolyai, some clearly aimed at professionals but some, whimsically, that the “average person hardly thinks that like Gleick’s Newton, for a wide public. During the same mathematics has a history, rather, that all of it was re- time we have seen whole books written about math- vealed in a fl ash to some ancient mathematical Moses ematical constants ( e.g., the golden ratio, Euler’s con- or reclaimed from a handbag at the left luggage room stant), on mathematical objects like the Möbius strip, in Waterloo Station.” He points out that an admired text on gigantic problems—four books on the Riemann in world history at the time devoted 20 of its 900 pages hypothesis alone, one on the classifi cation of the fi - to the history of science. In some ways this probably nite simple groups, one on the four color problem, and has not changed very much, in spite of the best eff orts even on the Langlands program (!). And almost all of of the mathematical community. these were written for a more or less general audience, We decided to check out a currently popular world some more successfully than others, of course. We have history textbook. It has more pages than the one Davis also seen a novel about d’Alembert, another on the pointed out, almost 1000, and that’s not surprising Goldbach conjecture. These publications would have because a lot of history has happened since 1985. But been unimaginable in 1985. the authors have even less to report about science and Nevertheless, when we looked back at our own mathematics. The word “mathematics” does not even early eff ort to make mathematicians seem a bit more appear in the index of the second volume (post 1450). approachable to a general audience, we found that There is brief mention of Arab, Babylonian, Chinese, there were some remarkable disclosures here not read- Greek, Indian, Islamic, and Sumerian mathematics, but ily available in other literature. So we concluded that it for the authors of this text mathematics seems not is time to reissue these interviews and profi les. With the to exist beyond that early time, though Archimedes , passing of time some statements made then now seem Euclid , and Pythagoras are mentioned, and only much less than prescient, and some predications did not later do we fi nd the names of Copernicus and Kepler . come to pass. Some of the participants are no longer Descartes gets four short lines (the format is double col- with us, and Persi Diaconis is no longer 35 years old. But umn), and Newton gets 21. Beyond that there is noth- we have decided not to tamper with the interviews and ing—no Euler, no Gauss, nor anyone else. Computer profi les themselves. They should be read in the context science fares no better. There is brief mention of the of the mid-1980s. We have appended some notes to in- Internet at the end of the second volume and a long dicate what has happened to subjects after the original story about someone seeing a cell phone in the Côte interviews, and the biographical notes at the end have d’Ivoire. That takes care of science, a total of maybe four been updated. or fi ve pages out of 1000. From reviews of the fi rst edition of the book in While mathematics is largely ignored in texts on 1985, it was clear that people saw a need for something world history, something striking has been happening: to make mathematicians appear more accessible to an explosion of new books each year aimed at non- the public. And our title is much used, almost always specialists in mathematics and devoted to the biogra- in reference to this volume. To avoid confusion a sec- phy of mathematicians or to history, often of specifi c tion of the Notices of the American Mathematical Society problems or even specifi c formulas in mathematics. now has to be called “Mathematics People,” not nearly One expects to see occasional scholarly biographies of as euphonious. mathematicians, usually published by university press- Though the range of personalities described es, but in recent years we have seen, even from main- here is wide, we still believe that the people we include xii ° Mathematical People come across as interesting and attractive people, not Acknowledgments the withdrawn or clinically ill people who were pre- sented in popular art forms in the late 1990s.