Shing-Tung Yau - The Shape of a Life: One Mathematician’s Search for the Universe’s Hidden Geometry

THE SHAPE OF A LIFE

SHING-TUNG YAU
AND STEVE NADIS

ONE MATHEMATICIANS SEARCH FOR THE UNIVERSES HIDDEN GEOMETRY

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.

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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.

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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 Ill never hear those words, his thoughts are with me, always.

Shing-Tung Yau, 2011

Having no prior experience in committing the story of my life to the printed page, Ill try to keep things simplefor my sake, if not for yoursand 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 Im 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 decades 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 Im in America or in China, I feel as if I have both an insiders view and an outsiders view at the same time.

This sense has left me occupying a rather peculiar place that cannot be located on a conventional mapa place lying somewhere between two cultures and two countries that are separated from each other historically, geographically, and philosophicallyand through rather profound differences in cuisine. I have a home in Cambridge, Massachusetts, not far from Harvard University, which Im happy to say has been my employer since 1987. I also have an apartment in Beijing, which Im delighted to make use of when Im in town. But there is a third home Ive had much longer, and that is mathematicsa field I have been fully ensconced in for almost a half century.

For me, mathematics has offered a kind of universal passport that has allowed me to move freely throughout the world at the same time I ply its formidable tools toward the task of making sense of that world. Ive always found mathematics to be a fascinating subject with seemingly magical properties: It can bridge gaps of distance, language, and culture, almost instantly bringing onto the same pageand onto the same plane of understandingpeople who know how to harness its power. Another thing thats magical about mathematics is that it doesnt take much, if any, money to do something significant in the field. For many problems, all you need is a piece of paper and a pencil, along with the ability to focus the mind. And sometimes you dont even need paper and pencilyou can do the most important work in your head.

I feel lucky that ever since finishing graduate school, and even before obtaining my PhD, I have never stopped pursuing research in my chosen field. Along the way, Ive made some contributions to this discipline that Im proud of. But a career in mathematics was by no means assured for me, despite a fascination with the subject that took hold of me during childhood. In fact, early in my life, the path I currently find myself on appeared to be well beyond reach.

I grew up poor in terms of the standard financial metrics but rich in the love my mother and father bestowed upon my siblings and me, and in the intellectual nourishment we received. Sadly, my father, Chen Ying Chiu, died when I was just fourteen years old, throwing our family into dire economic straitswith no nest egg to fall back on and mounting debts from all sides. My mother, Yeuk Lam Leung, was nonetheless determined for us to continue our educationa wish that was consonant with that of my father, who had always encouraged us toward scholarly pursuits. I became serious about my studies and found my calling in mathematicsa subject I was drawn to in middle school and high school in Hong Kong.

A big break came during my college years in Hong Kong upon meeting Stephen Salaff, a young mathematician from the University of California, Berkeley. Salaff arranged for me to pursue graduate studies at Berkeley, enlisting the services of a powerful member of the schools math department, Shiing-Shen Chern, who was then the worlds foremost mathematician of Chinese descent.

I dont know whether I would have gotten far in my field had it not been for the fortuitous chain of events that brought me to California. But I am certain of one thing: I never would have been able to secure such a career had it not been for the sacrifices that my mother made for all of her children and for the love of learning that my father instilled in all of his progeny. I dedicate this book to my parents, who made it possible for me to live out the story told here. I also thank my wife Yu-Yun and my sons, Isaac and Michael, who have put up with me over the past several decades, and to all of my brothers and sisters.

I have spent innumerable hours indulging my obsession for shapes and numbers, as well as for curves, surfaces, and spaces of any dimension. But my work, as well as my life, has also been enriched, immeasurably so, by my relationships with peoplefamily, friends, colleagues, professors, and students.

This is the story of my odysseybetween China, Hong Kong, and the United States. I have traveled the world in my pursuit of geometrya field that is crucial to our attempts to map out the universe on both the largest and smallest scales. Conjectures have been made during these excursions, open problems raised, and various theorems proved. But work in mathematics is almost never done in isolation. We build upon history and are shaped by myriad interactions. These interactions can, on occasion, lead to misunderstandings and even fights, which I have, unfortunately, been caught up in from time to time. One of the things Ive learned through these incidents is that the notion of pure mathematics can be hard to realize in practice. Personalities and politics can intrude in unexpected ways, sometimes obscuring the intrinsic beauty of this discipline.