Peter Lax, Mathematician An Illustrated Memoir Reuben Hersh Peter Lax, Mathematician An Illustrated Memoir AMERICAN MATHEMATICAL SOCIETY http://dx.doi.org/10.1090/mbk/088 Peter Lax, Mathematician An Illustrated Memoir Reuben Hersh Photographic research by Eda Gordon AMERICAN MATHEMATICAL SOCIETY Providence, Rhode Island 2010 Mathematics Subject Classification. Primary 01A60, 01A70, 01A72, 35A21, 35L05, 35L40, 76L05, 65M06, 35C08, 35Q53. Cover photograph courtesy of the New York University Archives. All other photo- graphic permissions and acknowledgments can be found on p. xi. For additional information and updates on this book, visit www.ams.org/bookpages/mbk-88 Library of Congress Cataloging-in-Publication Data Hersh, Reuben, 1927– Peter Lax, mathematician : an illustrated memoir / Reuben Hersh ; photographic research by Eda Gordon. pages cm. Includes bibliographical references and index. ISBN 978-1-4704-1708-6 (alk. paper) 1. Lax, Peter D. 2. Mathematicians—United States—Biography. I. Title. QA29.L422H47 2015 510.92—dc23 2014036520 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Permissions to reuse portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink service. For more information, please visit: http://www.ams.org/rightslink. Send requests for translation rights and licensed reprints to [email protected]. Excluded from these provisions is material for which the author holds copyright. In such cases, requests for permission to reuse or reprint material should be addressed directly to the author(s). Copyright ownership is indicated on the copyright page, or on the lower right-hand corner of the first page of each article within proceedings volumes. c 2015 Reuben Hersh. All rights reserved. Printed in the United States of America. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ 10987654321 201918171615 To my honored and beloved children, Daniel and Eva, and grandchildren, David, Jessica, and Zeev Contents Acknowledgments ix Permissions and Acknowledgments xi Introduction xv Chapter 1. A prodigy and his family have a narrow escape 1 The Holocaust 6 Lax family 6 Chapter 2. Manhattan, NY, and Manhattan Project. An army private among the “Martians” 17 Into the army 19 Manhattan Project. An army corporal among the Martians 20 NYU and the Courant Institute 33 Chapter 3. Family life: Son, husband, father, grandfather 35 Anneli Cahn 35 Jimmy 38 Johnny 42 Lori 45 Chapter 4. Early career 49 The advent of the computer 51 Becoming Peter Lax’s student 55 Chapter 5. The famous CDC 6600 bomb-scare adventure 69 Chapter 6. Later career 79 Chapter 7. The queen of Norway 91 Entr’acte. Peter’s stories 97 Chapter 8. Books 105 Chapter 9. Pure AND applied, not VERSUS applied 113 Computing 118 Partial differential equations and the real world, a beginner’s primer 121 Thinking geometrically about dynamical systems: Phase space 125 Function spaces, functional analysis 126 Nonlinearity 129 vii viii CONTENTS Chapter 10. Difference schemes. Shocks. Solitons. Scattering. Lax-Milgram. P´olya’s curve, etc. 133 Difference equations and computing 133 Shock waves 135 Solitons 142 The nonlinear Schr¨odinger equation occurs in water waves 148 Scattering theory 150 Differentiability of the P´olya function 154 Lax-Milgram lemma 156 Algebraic hyperbolicity 156 Epilogue 159 Appendix 1. Anneli Lax 161 Appendix 2. John von Neumann: The early years, the years at Los Alamos, and the road to computing 167 Appendix 3. The life of Richard Courant 175 Appendix 4. Peter D. Lax curriculum vitae 187 Appendix 5. The closed graph theorem 199 Appendix 6. List of Peter Lax’s doctoral students (from the Mathematics Genealogy Project) 203 John Lax 207 Appendix 7. From A Liberal Education, by Abbott Gleason, pages 314–317 on John Lax 209 Appendix 8. John Lax article on Chicago jazz musicians 213 References 229 Index 233 Acknowledgments Profuse and ardent thanks are due to many. To Peter Lax himself, of course, first and foremost. And to my partner, Veronka. And to Eda Gordon for her brilliant, amazing contribution, finding beautiful, expressive photographs, and ob- taining the needed permissions. Also to Lori Berkowitz Lax and to Anneli, Jimmy, Tommy and Timmy and Dee Dee, to Miriam Helbok and Eleanor Piel, to Carol Hutchins and Al Novikoff and Elena Anne Marchisotto, to Brittany Shields, to Nancy Cricco and the staff of the New York University Archive on the 10th floor of Bobst Memorial Library, to Professors Cathleen Morawetz and Louis Nirenberg and Joe Keller and Chandler Davis and Martin Davis and Fred Greenleaf and Emile Chi, and to Nick Unger and Dr. Robert Wolfe, to Dr. Marnie Greenwood and her partner, David. To Alex Chorin, Jeff Rauch, Mutiara Buys, and Stan Osher and Joel Smoller and Phil Colella. To Dean Porter Gerber, Roger Frye, Frank Wimberly, Edward Dunne. To Francoise Ulam. To Richard Courant. I have used quotations from Peter’s previous interviews: in More Mathematical People, by Jerry Alexanderson; The Mathematical Intelligencer, by Istvan Hargit- tai; and in the Notices of the American Mathematical Society, reprinted from the European Mathematics Newsletter, by Martin Raussen and Christian Skau. Espe- cially valuable have been Peter’s interviews with Phil Colella for the Oral History of Numerical Analysis of the Society for Industrial and Applied Mathematics. Colella was a student of Peter’s student Alex Chorin. He became head of the Applied Nu- merical Algorithms Group of the National Energy Research Scientific Computing Center and is a member of the U.S. National Academy of Sciences; he is known for high-resolution adaptive mesh-refinement schemes for partial differential equations. ix Permissions and Acknowledgments The American Mathematical Society gratefully acknowledges the kindness of the following individuals and institutions in granting permission to reprint material in this volume: Donald Albers: Photograph of Peter Lax and brother John, Photograph of R´ozsa P´eter, Photograph of Peter Lax and father Henry, Photograph of Peter Lax with older Jimmy. Gerald L. Alexanderson: Photograph of George P´olya and G´abor Szeg˝o, Berlin, 1924. Archives of the Mathematisches Forschungsinstitut Oberwolfach (Gerd Fischer, Photographer): Photograph of J¨urgen Moser. Michael Atiyah: Photograph of Professors Michael Atiyah, Ralph Phillips, Don- ald Spencer. Norman Bleistein: Photograph of Peter Lax and Burt Wendroff. Esther Brass-Chorin: Photograph of Alexandre Chorin. Mutiara Buys: Photograph of Mutiara Buys. Civertan Grafikai St´udi´o: Photograph of Heroes’ Square, Budapest. Jitze Couperus: Photograph of CDC 6600 computer with console. George Csicsery: Photograph of Paul Erd˝os. Dartmouth College Library, Rauner Special Collections: Photograph of John Kemeny. Virginia Davis: Photograph of Martin Davis. Sarah Gleason: Photograph of John Lax, in Abbott Gleason, A Liberal Educa- tion, Tide Pool Press, 2010, Appendix 7. James Glimm: Photograph of James Glimm. Eda Gordon: Photograph of Lax books. Ruth Harten: Photograph of Amiram Harten, Palo Alto, CA, 1982. Hearst Corporation: Esquire Magazine cover, September 1958 issue; Illustration from “Who Are America’s 54 Outstanding Young Men...And Why,” ibid., p. 33. Heriot-Watt University: Photograph of Soliton Experiment, Union Canal, Au- gust 1995. Geraldine Calisti Kaylor: Photograph of Jeffrey Rauch. Joseph Keller: Photograph of Joseph Keller. Henry Lax (Courtesy of James Lax): Photos of Anneli Lax and of Anneli and Peter Lax at the Courant Institute. James Lax: Photos of Elizabeth Thomas, the Lax family nanny, with Jim Lax on his graduation from Columbia University, 1976; John and Marnie, Greece, 1978; Peter on the phone with the Norwegian Academy of Science and Letters learning of his award of the 2005 Abel Prize, with Lori by his side, 6:30 a.m.; Peter with family and guests at Prince Camp, Loon Lake; Lori and Peter with Pierre at his xi xii PERMISSIONS AND ACKNOWLEDGMENTS college graduation, 2013; Family Thanksgiving, 2013. L-R: Sabah D’Agrhi, Tommy, Timmy, Jim, Pierre, Peter, Nancy Foldi, Lori; Peter’s grandsons Pierre, Tommy and Timmy at the Abel Prize ceremony. Lori Berkowitz Lax: Photograph of Lori Berkowitz playing the viola. Peter Lax: Photos: Peter told his friend and fellow mathematician Louis Niren- berg he was willing to explain the same thing more than once, but not more than ten times; Peter (left) and Enrico Fermi (right) on a hike in the mountains around Los Alamos with a colleague; Niels Bohr (left) and Richard Courant (right); Henry and Klara Lax; Henry Lax with sons Peter and John on an outing in the Grunewald, Hungary, 1931. Materal grandmother Ilka Kornfeld, n´ee Nemenyi, watches in the background; John and Peter Lax at Prince Camp, Loon Lake; Still life painting by Peter Lax; Anneli and Peter at Courant Institute; Peter with his young son Johnny; Peter with his young son Jimmy; Grandma Klara reading to Jimmy, 1957; Grandpa Henry with Jimmy on his knee, 1957; Peter giving Johnny tennis advice; John and James; Anneli Cahn Lax; Anna Lesznai, artist and poet with whom Pe- ter studied painting; Kurt Otto Freidrichs at work with Richard Courant, 1965; excerpt from Lax, John, “Chicago’s Black Musicians in the Twenties: Portrait of an Era”, Journal of Jazz Studies 1 (June 1974), 106-127. Courtesy of Peter Lax. Los Alamos Historical Society Photo Archives (Jack Aeby, Photographer): Pho- tograph of the Trinity Test. Los Alamos National Laboratory Archives: Photograph of John von Neumann, Richard Feynman, Stanislaw Ulam.