the shape of a life This page intentionally left blank shing-tung yau and steve nadis The Shape of a Life one mathematician’s search for the universe’s hidden geometry new haven and london Published with assistance from the foundation established in memory of William McKean Brown. Copyright © 2019 by Shing-Tung Yau and Steve Nadis. All rights reserved. This book may not be reproduced, in whole or in part, including illustrations, in any form (beyond that copying permitted by Sections 107 and 108 of the U.S. Copyright Law and except by reviewers for the public press), without written permission from the publishers. Yale University Press books may be purchased in quantity for educational, business, or promotional use. For information, please e-mail [email protected] (U.S. office) or [email protected] (U.K. office). Illustrations on pages 49, 58, 78, 81, 101, 119, 176, 178, 199, 205, 234, and 235 are courtesy of Barbara Schoeberl, Animated Earth, LLC. Set in Scala and Scala Sans type by Integrated Publishing Solutions. Printed in the United States of America. Library of Congress Control Number: 2018953465 ISBN 978-0-300-23590-6 (hardcover : alk. paper) A catalogue record for this book is available from the British Library. This paper meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). 10 9 8 7 6 5 4 3 2 1 To Our Parents: Yeuk Lam Leung and Chen Ying Chiu Lorraine B. Nadis and Martin Nadis on the centennial birthday of my late father An inspiring life of ups and down, vanquished in a moment. Though his wisdom of East and West still echoes in my heart. I never enjoyed his love enough, which has left me in dismay. The bloom of youth has passed me by, my hair turned to gray. Yet I oft look back to that fateful time when I was just a careless teen. How sad it was when he left that night, so long ago and faraway. What might he have told us, I wonder, if only he could have said? Though I’ll never hear those words, his thoughts are with me, always. —Shing-Tung Yau, 2011 contents Preface ix 1 Itinerant Youth 1 2 Life Goes On 26 3 Coming to America 44 4 In the Foothills of Mount Calabi 75 5 The March to the Summit 96 6 The Road to Jiaoling 117 7 A Special Year 142 8 Strings and Waves in Sunny San Diego 170 9 Harvard Bound 189 10 Getting Centered 211 11 Beyond Poincaré 233 12 Between Two Cultures 261 Epilogue 277 Index 283 Photographs follow p. 141 This page intentionally left blank preface Having no prior experience in committing “the story of my life” to the printed page, I’ll try to keep things simple—for my sake, if not for yours— and start at the beginning. I was born in China in the spring of 1949 in the midst of the Communist revolution. A few months later, my family moved to Hong Kong, where I lived until going to the United States for graduate school in 1969. In the nearly five decades that have elapsed since my first transpacific crossing, I have gone back and forth between America and Asia on countless occasions. At times, it is hard for me say which is my true home or whether it would be more accurate to say that I have two homes, neither of which I’m fully at home in. To be sure, I have carved out a comfortable existence in America without ever feeling truly at one with the society around me. I also have strong emotional and familial ties with China that are deeply engrained and seemingly hardwired into my being. Nevertheless, after many de- cades away, my perspective on my native land has shifted as if I were always observing things from at least one or two steps removed. Whether I’m in America or in China, I feel as if I have both an insider’s view and an outsider’s view at the same time. This sense has left me occupying a rather peculiar place that cannot be located on a conventional map—a place lying somewhere between two cultures and two countries that are separated from each other historically, ix