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 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 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, geographically, and philosophically—and through rather profound differences in cuisine. I have a home in Cambridge, Massachusetts, not far from Harvard University, which I’m happy to say has been my employer since 1987. I also have an apartment in Beijing, which I’m delighted to make use of when I’m in town. But there is a third home I’ve had much longer, and that is mathematics—a 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. I’ve 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 page—and onto the same plane of understanding—people who know how to harness its power. Another thing that’s magical about mathematics is that it doesn’t 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 don’t even need paper and pencil—you 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, I’ve made some contributions to this discipline that I’m 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 straits—with 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 education—a 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 mathematics—a 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 school’s math department, Shiing-Shen Chern, who was then the world’s foremost mathematician of Chinese descent.
I don’t 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 people—family, friends, colleagues, professors, and students.
This is the story of my odyssey—between China, Hong Kong, and the United States. I have traveled the world in my pursuit of geometry—a 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 I’ve 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.
Nonetheless, chance encounters with peers can also send us in unexpectedly fruitful trajectories that may last years or decades. In the final analysis, we are the products of our times and of our milieus, of whom we come from and where we come from. It now seems as if I come from many places—a fact that has made my life both richer and more complicated. In the account that follows, I hope to convey a sense of my upbringing, growth, and personal journey to any readers who might take an interest.
I take this opportunity to thank some of the many people who—if not contributing to this book directly—helped make the narrative arguably worth telling. For starters, I owe an incalculable debt to my parents, who supported my siblings and me as best they could, through hard times, while always trying to teach us good values. The main purpose of life, I learned, is not about making money—a lesson that enabled me to pursue a career in mathematics rather than in, say, business or banking. I was close to all of my siblings but am especially grateful to my older sister, Shing-Yue, who, up to the moment of her death, sacrificed so much—foregoing a professional career of her own—in order to help me and her other brothers and sisters.
I was also lucky to have fallen in love with, and eventually married, a woman who shared my view that there is more to life than seeking personal wealth, material possessions, and luxuries—that greater rewards can come from scholarly endeavors. I’m proud to see that our sons have also ventured far along academic paths.
I’m lucky to have lifelong friends, like Shiu-Yuen Cheng, Siu-Tat Chiu, and Bun Wong, whom I’ve known since my school days in Hong Kong. One grade school teacher, Miss Poon, stands out for the kindness she bestowed upon me when I was young and vulnerable. I got an early taste of mathematics from the lecturer H. L. Chow during my freshman year at Chung Chi College. And I was extraordinarily fortunate to have crossed paths during college with Stephen Salaff, who guided me to Berkeley with the help of Chern, Shoshichi Kobayashi, and Donald Sarason.
I’m grateful to the American educational system for providing, since the moment of my arrival, a wonderful environment for pursuing mathematical research. A great feature of this system is that it recognizes and fosters a person’s talent, regardless of his or her race, background, or accent. I should single out Harvard in this regard, which has served as a convivial home for me over the past thirty-plus years. I’ve had many terrific colleagues in the Harvard Mathematics Department—too many in that time, unfortunately, to list here.
My career has been aided immeasurably by somewhat older and more established mathematicians who’ve gone out of their ways to help me. First and foremost is my former advisor and mentor S. S. Chern. But many others have been of tremendous help, including Armand Borel, Raoul Bott, Eugenio Calabi, Heisuke Hironaka, Friedrich Hirzebruch, Barry Mazur, John Milnor, Charles Morrey, Jürgen Moser, David Mumford, Louis Nirenberg, Robert Osserman, Jim Simons, Isadore Singer, and Shlomo Sternberg.
Some mathematicians prefer to work alone, but I do best in the company of friends and colleagues. I am pleased to have had some great ones over the years, among them S. Y. Cheng, John Coates, Robert Greene, Dick Gross, Richard Hamilton, Bill Helton, Blaine Lawson, Peter Li, Bill Meeks, Duong Phong, Wilfried Schmid, Rick Schoen, Leon Simon, Cliff Taubes, Karen Uhlenbeck, Hung-Hsi Wu, Horng-Tzer Yau, and my brother Stephen Yau. I’ve collaborated closely, in particular, with Rick Schoen for about forty-five years and have done some of my best work with him. Although he started out as my student, I’m sure I’ve learned as much from him as he has from me. I truly value his friendship.
I continue to collaborate with other former students and postdocs—such as Huai-Dong Cao, Conan Leung, Jun Li, Bong Lian, Kefeng Liu, Melissa Liu, and Mu-Tao Wang. I’ve got some outstanding math colleagues in China and Hong Kong: Yang Lo, Zhouping Xin, and many others. I’ve also had close ties with physicists for most of my career, enjoying my interactions with people like Philip Candelas, Brian Greene, David Gross, Stephen Hawking, Gary Horowitz, Andy Strominger, Henry Tye, Cumrun Vafa, and Edward Witten. My work in mathematics has definitely profited from these associations, and I’d like to think that some benefits have trickled down to physics as well.
All told, it’s been an exciting journey so far, and I hope (and expect) there will be a few pleasant surprises on the road ahead.
Shing-Tung Yau
Cambridge, 2018
I have compiled a fair number of publications over the years, including profiles of many individuals, but I’ve never written a full-length biography before. Frankly, it’s been a fascinating experience to plumb the depths of someone’s personal history as thoroughly and deeply as one can productively go, and I hope some of that fascination rubs off on those perusing these pages. The task is comparable in some ways to both mining and archaeology—unearthing more and more material, the deeper one digs, and then sifting through the bulk to find the rare gems and other pieces worth holding on to. There are many new things to be learned in the course of such a process, even when the subject of your inquiries is someone you have known, worked closely with, and become friends with for well over a decade.
Of course, I could not have completed this effort without the help of numerous people, and I’d like to thank as many of them as I can, apologizing for any names that I have neglected to mention.
Since this book has a lot to do with family (my coauthor’s family, though not mine), I start off by thanking my parents, my wife Melissa Burns—who provided thoughtful feedback on the first three chapters and endured more talk about this book, and its writing, than almost any other human could tolerate—along with my delightful daughters, Juliet and Pauline. I’m also lucky to have two great siblings, my sister Sue and my brother Fred.
My coauthor and I appreciate the unwavering support of our editor, Joe Calamia, and his colleagues at Yale University Press, including Eva Skewes and Ann-Marie Imbornoni. Joe has been encouraging from the very start, maintaining enthusiasm and general cheeriness throughout the long (and sometimes trying) process. Jessie Dolch provided expert copyediting, deftly curbing our tendencies toward (not “towards”) verbosity, redundancy, and occasional lapses into obscurity. I learned that—regardless of the time, place, or weather—I tend to say “if” when I should say “whether.” And I often say “coming” when, to paraphrase Groucho Marx, I should say “going.”
The following people also helped with various aspects of the book and my work on it:
Sergiu Klainerman |
Barbara Schoeberl |
|
Lydia Bieri |
Joe Kohn |
Rick Schoen |
Jean-Pierre Bourguignon |
Sarah Labauve |
Christina Sormani |
Maury Bramson |
Blaine Lawson |
J. Michael Steele |
Alicia Burns |
Claude LeBrun |
Martha Stewart |
Huai-Dong Cao |
Jun Li |
Andy Strominger |
Lennart Carleson |
Bong Lian |
Lydia Suffiad |
Lily Chan |
Kefeng Liu |
Li-Sheng Tseng |
Raymond Chan |
Yang Lo |
Karen Uhlenbeck |
S. Y. Cheng |
L. Mahadevan |
Emmanuel Ullmo |
Isaac Chiu |
Francisco Martin |
Yifang Wang |
Siu-Tat Chui |
Alex Meadows |
Hung-Hsi Wu |
Robert Connelly |
Bill Meeks |
Hao Xu |
Daniel Ford |
John Milnor |
Hongwei Xu |
Robert Greene |
Irene Minder |
Horng-Tzer Yau |
Xianfeng (David) Gu |
K. F. Ng |
Stephen Yau |
Simon Guest |
Ping-Zen Ong |
Xiaotian (Tim) Yin |
Richard Hamilton |
Dick Palais |
Cosmas Zachos |
Jennifer Hinneburg |
Duong Phong |
Chiyuan Zhang |
Thomas Hou |
Robert Sanders |
Lei Zhang |
Lizhen Ji |
Wilfried Schmid |
Xi-Ping Zhu |
Maureen Armstrong, who works on the Journal of Differential Geometry from within the Harvard Mathematics Department, helped out in many ways—by gathering and preparing the photographs that appear in this book and also by helping to put our manuscript into a presentable form. I am grateful for her efforts and am not sure what we would have done without her. Our deepest gratitude also goes to Lily Chan, who kindly provided many photos along with other assistance. Huai-Dong Cao, Yang Lo, Hao Xu, Hongwei Xu, and Stephen Yau were incredibly helpful. And we heartily thank Xiaotian (Tim) Yin, Xianfeng (David) Gu, and especially Barbara Schoeberl for providing us with some wonderful illustrations. Barbara put all the figures together in only about two weeks—an impressive feat. Andy Hanson also lent some great visualizations of Calabi-Yau manifolds, while offering crucial advice regarding the cover design.
The Berkeley mathematician Hung-Hsi Wu carefully read through each and every chapter draft—going through multiple iterations in some cases. The insights he offered us—about China, the mathematics world, and ways of explaining some complicated mathematical concepts—were invaluable. I am still not sure how he managed to devote so much time to this project, in view of his own appreciable workload, but I’m thankful that he did. And I’m sure that our book is immeasurably better as a result of his sage advice, beneficial prodding, and saintlike patience.
Thank you, Professor Wu, and thanks to everyone else who contributed to this several-year-long undertaking. Sometimes it takes a village, they say. And sometimes it takes even more.
Steve Nadis
Cambridge, 2018