MY FATHER’S DEATH hit me hard, throwing me into an unfamiliar state in which I felt a weird mixture of things, all unpleasant, all at the same time. A powerful sadness welled up in me from a deep place I’d never accessed before. I felt a dull ache that I couldn’t localize, as well as an all-embracing numbness.
That was on the physiological level. But I also felt as if I’d lost my moral compass, because my father was a righteous man who was always pointing us in the right direction, always teaching us about the importance of hard work and positive values—lessons that were often inspired by the writings of Confucius. With my father gone, it seemed as if the center of gravity, the organizing principle in our lives, was gone too.
Our circumstances were so pressing, however, that there was no time to wallow in grief, nor was there any real opportunity for denial to take hold. I realized that not only had everything about my family’s situation changed but that I, personally, would have to change too. Right away I felt pressure to start earning some money to support the family. But it was more than that. Without my father to lean on, I knew I had to grow up fast and start making decisions for myself—decisions that would affect the rest of my clan as well.
His death was therefore a turning point for me. I was forced to abandon the Chinese notion, long drummed into our heads, that we could always count on a strong family leader—someone who’d always be ready and waiting to take care of us. The moment had arrived for me to stand up for my own future. While I was doing that, moving on as best I could, I still had a gnawing desire to make my father proud, even though he was not around to see it. His confidence in me had been unwavering throughout our fourteen years together, but I did not always measure up to his expectations.
To my surprise, I started, quite spontaneously, to recite some of the Chinese poems he had introduced me to years earlier—as a way to feel more connected to him. I used to look at those poems in a half-hearted manner, only when asked, but I now took them more seriously and memorized them, just as Father had instructed us to do. Reciting those poems became not only a hobby for me, but also provided some relief for my sorrow, as well as helping me get through other tough times yet to come.
In addition, I began to read some of the philosophical books in my father’s collection, which were by no means easy to comprehend. Furthering my education was not my primary motivation, although that happened as a matter of course. Instead, I was aiming to get a better grasp of what my father liked to think about. In these texts, I found traces of him—threads that triggered memories that in turn had a calming effect on me. I came to these exercises naturally, almost subconsciously. They helped strengthen my ties to my father, even after he had left us.
I had a new attitude toward school too, resolving to try harder and become more focused than I had been in my previously carefree existence. The stakes were higher now, and I did not want to let him or my mother, or even myself, down. Achieving excellence in schoolwork, as far as I could see, offered me the only conceivable pathway to success. I’d have one chance to distinguish myself, and if I failed, there would be nothing to fall back on.
Between the loss of my father’s income and the medical expenses that had accrued over the several months before his death, our savings had been exhausted. There are no social security payments, retirement benefits, or pensions in China. All you have is your salary, and when a job ends—or worse, when an employee dies—usually not much is left. In our case, nothing was left, and we owed half a year’s rent, along with a stack of unpaid bills.
But our first order of business was the funeral. Showing respect for the deceased is a big deal in China. The ceremony we were preparing was intended not only to honor my father in the best way possible, but also to preserve the dignity of our family. My brothers and sisters and I had missed school for several weeks before and after my father’s death. My sister Shing-Yue and students of my father took care of the funeral arrangements, while the rest of us helped out as best we could. First, we needed to find some land on which to bury him. That cost money, of course, and we had to pay the funeral home too. Luckily, my father’s friends, who were reasonably well off, defrayed some of these expenses. That enabled us to purchase a small burial plot in the New Territories region north of Kowloon.
My siblings and I didn’t know much about funerals and basically did what we were told. One of the things we were told to do was to spend the night before the ceremony in the funeral home, which, according to tradition, is supposed to protect the good spirits, or maybe fend off the bad spirits. We were obedient, even though we didn’t know what we were trying to accomplish with regard to the spirits, good, bad, or otherwise. I read all of the poems displayed in the funeral home that my father’s students had written. These poems assumed a particular form called a “pairlet,” consisting of two sentences that are related to each other. I enjoyed reading them because I learned things about my father, and about how other people viewed him, that I hadn’t known before.
The next day, in keeping with tradition, we all dressed in white and kneeled around a picture of my father that was surrounded by flowers. Whenever somebody came to pay their respects, he or she would bow three times and we would bow too. This went on all day. It was a draining experience but also very moving. Although I was filled with sorrow, for some reason I did not, or could not, cry.
Afterwards, there was much to do. We had to face our many problems, including the rent, which was many months overdue. Fortunately, our landlord was compassionate, and knowing that we were destitute, told us we wouldn’t have to pay back the money if we left soon. Our mother found a cheaper place in Shatin for us to live, which was nothing like the nice house, with ocean views, that we had occupied for several years. In fact, it was a two-room shack located next to a pig pen. It’s no surprise that living next to a pigsty can be smelly, but it can also be quite noisy. Our next-door “neighbors” got started early in the day, before 6:00 every morning, eager to begin the grunting, snorting, wallowing, and general cavorting that pigs are famous for.
Needless to say, this was not the most serene spot in which to live, but the price was right—or at least close to being affordable. Seven of us—down from ten following the deaths of my father and Shing-Hu and the departure of my oldest sister, Shing-Shan, to England, where she was training to become a nurse—were crammed into this tiny shack. The accommodations were about as crude as you could get, and other kids in the neighborhood looked down on us for being so poor and living in such a miserable excuse for a house.
Of course, that was nothing new; we were used to derision of that sort and the attitudes that go with it. But there was no denying that we were at a low point, surely the lowest we’d ever been. We all hoped that we had “bottomed out” and that things would soon begin an upward turn.
That’s when my uncle jumped in, offering us a way out of our predicament: He would get a farm somewhere near Hong Kong, he said. We could then quit school and work for him, taking part in the proud tradition of duck husbandry. While some might consider this a generous offer, it sounded like a nightmare to me. Fortunately, my mother agreed and would have none of it. Even in our precarious position, she knew that accepting such an offer was beneath our dignity. Instead, she wanted us to live according to our father’s wishes, which was for us to continue our education and become scholars, or at least to go as far along that road as we could. She felt, as had my father, that gaining knowledge and cultivating the mind was more important than pursuing money. There had to be more to life, Father had told us, than simply attending to one’s material needs.
It was a struggle, given our lack of resources, but my mother somehow found the energy to pay the necessary fees so that we could stay in school. This surprised many people, even some of our teachers, who had expected us to drop out at any moment. Mother was malnourished and anemic at the time, as she had been for years, yet she did everything possible to keep us from suffering from dietary deficiencies. Sometimes, when we studied late at night and our energy was waning, she would serve us flavorful broths of beef liver or pig brain, which never failed to give us a boost and temporarily raise our spirits.
Looking back on all that my mother did, I’m amazed at the strength and determination she displayed under such duress. Some people have said that I can be incredibly persistent and stubborn—traits I have applied, for instance, toward solving difficult math problems—and I believe I inherited some of that resolve from my mother. Her encouragement, even while she was suffering such hardships, motivated me to pour myself into my studies. And when I eventually became known in the academic world, she was grateful that her efforts had been rewarded.
I was grateful too, as a fourteen-year-old, when she declined her brother’s attempt to recruit us into the duck trade, which would have consigned us to a life of drudgery. Her decision conformed not only to my father’s wishes, but to mine as well, because I was already committed—to the extent one can be at the age of fourteen—to making my mark in academia.
My first order of business on that front was to take all the exams I had missed during my weeks-long absence and prepare for the big final exam coming up near the end of the third year. I did well in the math portion of that exam, as usual, and in most subjects except for physical education, as usual, too.
The journey to school from our current dwelling, the “Pig House,” was longer than before, because I had to walk nearly an hour to reach the train station. That made for a lengthy round trip, leaving little time for my schoolwork or for sleep. A former student of my father’s, K. Y. Lee, offered to help. An elementary school had just been started on the top floor of a new seven-story building the government had erected in the wake of a typhoon that had killed scores of people and destroyed many buildings. The new school was located closer to Pui Ching, and Lee told me I could stay in the classroom at night in order to shorten my commute.
I stayed there for more than a year, helping out the young students in my spare time. Like me, these children came from poor families, and most of them were delightful to be around. The accommodations, however, fell something short of spartan. There was no bed, so I usually slept on a table that was about two feet wide and five feet long. Fortunately, I was not very tall in those days, but I did fall off the table from time to time because it was so narrow. There was one bathroom on that floor, and it was barely tolerable from a sanitary and olfactory standpoint. There were also shops and food stands on the first floor where I could get a (very) basic meal of noodles or rice for 1 Hong Kong dollar.
Former students of my father who lived in the building sometimes hung out in the classroom at night, and we’d talk or play chess. But they never stayed very late, which left me alone for many hours to read and get my own coursework done. If I ever overslept, the younger school kids would be sure to wake me up, with not-too-delicate nudges or pokes, when they arrived in the morning. It was a lonely existence, especially compared with the high-density quarters I had been accustomed to. I went home about once every two weeks to visit the family and wash my clothes, but other than that I learned how to survive on my own, and that’s always worth knowing.
Still, I needed to bring some money in, both for my personal expenses and for the others back in Shatin. Shing-Yue had already taken a job as a primary school teacher, giving up her chance to study at a university, in order to generate earnings for the family. My eldest sister, Shing-Shan, began sending money from the United Kingdom once she learned of our father’s death. It was clearly time for me to step up too.
That’s what prompted me in 1964 to start tutoring in mathematics—a small step at the time that nevertheless helped launch me on my current career path. I was about fifteen when I got that going, working with kids who weren’t much younger than me. It was hard to get started in this line of work because I didn’t know how to find pupils, nor did I have a telephone to make it easy for prospective clients to contact me. Fortunately, one of my fellow students at Pui Ching, Ying-Cai Zeng, thought that tutoring sounded like fun. He had a telephone at home and placed an ad in the local newspaper, even though, as things turned out, he never did any tutoring himself.
In this way we lined up the first client, a student at a prominent high school who was just a grade behind me. I earned 25 Hong Kong dollars for a month’s effort, which was almost enough to cover the cost of my meals. That was a start. My mother then found several more pupils through a government agency, which made me happy because I’d have more money to give her. One student was a sixth-grade girl, a few years younger than me, who’d been failing math. She was struggling with simple arithmetic problems like the following: “If you go to the farm and see thirty-six chicken legs, twenty-eight cow legs, and sixteen horse legs, how many animals have you seen?” She was asked to memorize a formula for solving this problem, but I offered her a whole new way of approaching problems like this and other problems as well. Her mother was nervous because I was teaching her methods for solving equations that went well beyond the sixth-grade level. But the strategy quickly paid off. Within a month, she was scoring 100 on her math tests. Her mother was so ecstatic that she wanted me to teach all her daughters English. I declined that offer because my English was pretty shaky back then—and still is a bit rough around the edges, even after all my years in America.
Tutoring kept me busy, especially when combined with my high school workload. I had moved on to the tenth grade and was doing well enough, not only in math but in Chinese literature and history too, which pleased my mother. Although I was forced into tutoring because I needed the money, I got more out of it than I expected: The process of making math more understandable to kids helped clarify my own thinking on the subject. I found that teaching mathematics could be fulfilling, and that discovery helped push me along the route I’ve followed ever since.
I got another push when I came across a book by Loo-Keng Hua, one of the most eminent Chinese mathematicians of the twentieth century. This book, which was on number theory, was my first initiation into higher math. It was a revelation to me, and I read several other books by Hua that were also wonderfully written. I saw that mathematics could be a thing of beauty, something to marvel at. This and other inklings I had received over the years—such as my introduction to Euclidean (plane) geometry—helped persuade me that mathematics would be my calling. And it would not be too much of an overstatement to say that coming across Hua’s books at that time, in the wake of the despair and aimlessness I had felt after my father’s death, gave my life a direction and a sense of purpose that I was suddenly eager to pursue. Of course, I still had a couple of years of high school to get through, and probably some time in college as well, before I could try to put my stamp on the field.
One of the notable aspects of eleventh grade was that I finally started to learn calculus—an elegant set of techniques developed some 350 years earlier by Isaac Newton and Gottfried Leibniz that is still central to much of the current work in mathematics and physics.
By that time, my family had moved from the Pig House to a somewhat nicer dwelling in Shatin, nestled among pine trees with a stream nearby that rushed down from the mountains. We had built this house cheaply, with the help of friends, relatives, neighbors, and relief agencies in the Hong Kong government. My mother’s wish of having her own house had finally come true. Not surprisingly, the place was tiny—a bedroom and a living room—barely big enough to fit all seven of us at the same time. And it was, in keeping with our recent history, also quite primitive. We relied on kerosene lamps, as we had no electricity, and a wood fireplace for cooking. Once again, there was no running water on the premises. But there were plenty of snakes in the vicinity, some poisonous, and it was my job to take care of them when they ventured inside.
I moved back to Shatin and slept in the attic, which was only accessible via a ladder. The ceiling was so low I had to crawl to get around and could barely sit up. There were also poisonous spiders and scorpions up there, which caused some concern. But despite all that, I enjoyed being with the family after having spent the previous year sleeping, not so comfortably, in a barren, isolated classroom.
The rural setting of our new home, by contrast, was quite pleasant. My mother planted fruit trees in the yard, and we also kept a few dogs, chickens, and geese—all of which helped liven up the surroundings. The geese in particular were a welcome addition, as they scared away snakes that might otherwise have been inclined to make unannounced visits.
In the eleventh grade I took an important test, the Common Exam, which one needed to pass in order to graduate from high school and go on to college. Fortunately, I did all right on that. During twelfth grade, I lived for several months in the house of a former student of my father’s, Pak Win Lee, so that I could tutor his nephew. The house was extremely luxurious, having amenities I’d never been exposed to and in many cases didn’t even know existed. They even had servants to attend to their needs. I’m thankful that in my capacity as a live-in tutor, I was treated respectfully. But as someone who grew up in poverty, I was also glad to see that in this house the servants were treated respectfully too. I would have been extremely uncomfortable had that not been the case. Still, the contrast between my plush quarters there and the attic and tabletop where I had previously slept couldn’t have been sharper, and this brief episode spoiled me a little. I had gotten a glimpse of how “the other half” lived. Although I didn’t need all the frills of the upper-class lifestyle, I saw that life could be better, and easier, if you didn’t have to struggle for every scrap of food.
The biggest thing in twelfth grade was the college placement exam. My best friend, Siu-Tat Chui, who was ranked number one in our high school, failed the Chinese literature section of the exam and was not able get into the Chinese University of Hong Kong (CUHK). Tat, as we called him, was one of the most brilliant people I’d ever met, but he was forced to spend an extra year in high school. However, when he graduated, he won big awards in practically every subject, including math. The president of our high school had even spoken up on Tat’s behalf, but the head of CUHK still denied him admittance. The system had clearly failed him. Tat was so fed up with Hong Kong that he decided to attend college the next year in Montreal. I also thought about studying abroad, but the application fee was expensive enough that it alone would have placed an unwelcome burden on my family.
I somehow managed to talk my way into the General Certificate of Education (GCE) exam run by the British school system—which was similar to what was then called the Scholastic Aptitude Test (SAT) in the United States—even though I was not eligible to take the GCE because I’d been educated in Chinese schools. I did well on the mathematics and English portions but failed the chemistry section, which had a serious laboratory component. Pui Ching didn’t have the facilities for the experiment I was supposed to carry out, so I tried to do it in a friend’s basement, using makeshift equipment, and got predictably poor results. As a result, I could not apply to any British schools, though I did pass the placement exam for CUHK—with some difficulty, like my friend Tat—and that’s where I went.
Chung Chi College, where my father had taught, was part of CUHK, and that’s where I went first so I could stay close to my family. My older brother, Shing-Yuk, was going there too. I didn’t apply to study in another country, as some of my peers did, but I wasn’t giving up on that idea altogether, as I felt that I would need to go to Europe or North America at some point if I wanted to become a first-rate scientist. I never lost sight of that idea, although I was content to start things off at Chung Chi, which I entered in the fall of 1966.
The chairman of the math department, who was named Tse, was a nice guy, as well as a friend of my father, although he was not the most accomplished mathematician. He gave an introductory speech to the ten or so students majoring in the subject, which he hoped would inspire us. “You’ve come here to do mathematics,” he said. “The sad truth is that you may not be good enough to become a pillar of this hall of mathematics. But if that’s the case, you can at least paint the wall.” Those words might have sounded depressing to some, but I found them encouraging: He was telling us that we all could make some contribution—in our own ways, large or small—toward progress in the field as a whole.
I soon found that the standard freshman math courses were too easy for me, so I was given permission to skip the classes and just take the exams to demonstrate my proficiency. That enabled me to use the time to take more demanding courses, including linear algebra and advanced calculus. A lecturer named H. L. Chow, who had a master’s degree from the Courant Institute at New York University and later earned a PhD in England, taught the latter course.
In Chow’s class, I learned about the Dedekind cut, which was invented in the mid-1800s by the German mathematician Richard Dedekind, who was a student of the great Carl Friedrich Gauss and a contemporary of the equally great Bernhard Riemann. Through this technique, Dedekind showed how, starting from integers (consisting of counting numbers like 1, 2, 3; their negative counterparts; and 0), one could construct rational numbers (like 1/2 and 3/4) and irrational numbers (like the square root of 2 or pi, which cannot be expressed as a simple fraction). From there, one could build the real numbers, which encompass all the rational and irrational numbers, thereby covering every single point on a number line, including the integers and everything in between.
I was blown away by the fact that one could take integers, which are familiar to most primary school children, and use them—through a step-by-step procedure—to create something as vast and complicated as the real numbers. It reminded me of the excitement I had felt in eighth grade when I was exposed to plane geometry and saw how far one could go starting from a handful of straightforward axioms. I wrote a letter to my teacher, Chow, expressing my appreciation. “I finally understand why mathematics is so beautiful,” I told him. “I am relieved to discover that the subject I love, mathematics, can do what I thought it could do.” And I soon learned it could do far more.
I’m not sure what Chow thought of my note, as I don’t recall a response, but he probably viewed it favorably. He may have been pleased by my enthusiasm and positive attitude toward the subject he taught, because we soon became friends. He invited me to his house a couple of times, which was very considerate, and his wife was extremely kind. The main problem, for me, was that they had eight cats, and the associated smells pervading their residence were so overwhelming that I almost passed out. It took all of my fortitude to conceal my discomfort and keep from bolting from the premises.
But all in all, I had a good time during my first year at Chung Chi College. In addition to math, I studied Chinese, English, Japanese, physics, and philosophy. In the latter subject we not only learned about the great philosophers but also learned about what a student (or person, in general) is supposed to be and do. It was a small college, so we all got to know each other. Because we were near the ocean, we often swam or played games on the beach. And what’s not to like about that?
That first year was fun, but the second year was more exciting, and things became more serious. CUHK was starting to grow, and Chung Chi College with it. The president, Mr. Lee, who came from the University of California, Berkeley, was intent on building up CUHK. As part of that effort, he added a number of new PhDs to the faculty, including Stephen Salaff, a young mathematician who had come to Chung Chi from Berkeley as well.
Salaff was the first professor I ever had who was really up on modern mathematics. He taught our class on ordinary differential equations in the “American style,” encouraging students to speak up and participate at all times—an approach the Chinese students, myself included, weren’t used to. Instead, we’d been encouraged to quietly absorb knowledge without interrupting the teacher’s train of thought. Because of Salaff’s freewheeling style, our classes with him were less scripted and more spontaneous, though he sometimes got stuck in the middle of a presentation. I helped him out at these junctures whenever I could, and he soon took notice of me. Sometimes he let me teach a portion of the lesson, if he felt I was up to the task. I also went to his home quite often, helping him prepare his lecture notes for the class or suggesting a different way of tackling a math problem.
At some point, Salaff realized that these lecture notes, when put together, could provide the basis for a book, which we started working on together. It was hard to get the book published because the preface made it clear that I was still just a teenager. But we did publish it many years later after I had become an established mathematician. And I learned a lot in the course of writing that book, especially after having read through the literature so extensively.
Salaff decided that if I really wanted to pursue mathematics, I ought to study abroad. He was upset that my scholarship money from CUHK was so low, about half of what other students typically received, because I hadn’t scored well on my college entrance exam, particularly the Chinese literature portion. He made a big fuss, insisting that I was a talented student who should be getting more money. The university was indifferent to his pleas, but that just made him fight harder.
The college’s dean of physical education, a woman called Lu, had also come from Berkeley, and she advised Salaff to abandon this fight, since it was likely to make my situation worse. Knowing that my family was poor, she offered me another way to make money: I could teach tai chi to the school’s professors, most of whom were foreigners and therefore unfamiliar with this form of martial arts. Frankly, I wasn’t great at tai chi, but it was a pleasant enough way of earning money, and I was grateful to Lu for arranging it.
Another nice development during my second year at Chung Chi was that I was able to get together regularly with faculty and students from the other schools in the CUHK system, including United College and New Asia College. United had just hired James Knight, a very good mathematician from the University of Cambridge whom I came to know. I attended his algebra course, which was excellent, and we built up a nice rapport during the year. At the end of the term, Knight gave me the original copy of his PhD dissertation as a gift before he returned to Cambridge to be a lecturer. Unfortunately, he died about ten years later in a motorcycle accident; I was shaken up when I heard the news, even though we’d long been out of touch.
From the various interactions I’d had with mathematicians like Chow, Salaff, and Knight, word had gotten out that I might be a talented student, at least when it came to math. After receiving a request, from a joint math panel representing all three of CUHK’s colleges, that I should graduate early, Mr. Lee (who was now the university’s vice chancellor) decided to find out just how exceptional I was (or wasn’t). The plan was for me to meet with Y. C. Wong, Hong Kong’s most distinguished mathematician. Wong was a differential geometer at Hong Kong University, and he was charged with carrying out the evaluation singlehandedly.
It took me more than an hour and a half to reach Hong Kong University by train, ferry, and bus, followed by a pleasant walk up to the mountains. When I reached his office, it soon became apparent that Wong was not going to test me in any formal way, or in any way at all. He just wanted to talk about his research, which, frankly, didn’t sound all that fascinating to me. Wong was working on the geometry of “Grassmannians,” which basically involve a space of higher-dimensional planes passing through the origin. He was getting hung up at that time on a calculation that didn’t strike me as very difficult. When Wong sensed that I could not appreciate the exciting work he was doing, he reached what was for him the obvious conclusion: I could not possibly be a genius.
I’m not going to dispute his contention, but one might take into consideration the qualifications of the judge. I soon learned that Wong was unable to publish many of his papers on this subject, suggesting that the editors of the math journals in question also failed to appreciate the exciting work he was doing.
But the fact is, I don’t like the term “genius,” and almost never use it, because I don’t really understand what it means. I suspect that some people have a romanticized notion of geniuses as individuals who come up with incredible ideas, or amazing mathematical proofs, virtually out of thin air, as if a vision had suddenly appeared before them. Their intellects are so advanced, according to the folklore, that they can produce these feats without breaking a sweat. In the movie Good Will Hunting, for example, the lead character takes a few minutes away from his janitorial chores at MIT to knock off major problems in mathematics. While things like that might happen, I have never seen it. In my experience, solving hard math problems takes hard work, and there’s no way around it, unless the problem is rather trivial. If, on the other hand, you work really hard for a really long time and eventually succeed in doing something that no one has done before—and perhaps something that no one thought could be done—does that make you a genius? Or just an overachieving drudge? I don’t know, but I also think it’s not worth spending much time on such questions.
The bottom line is that the powers that be at CUHK concluded I was not a genius—and they got no argument from me. I never contested that verdict. But then again, I’ve never let that judgment hold me back either.
Nevertheless, my encounter with Wong did nothing to assuage Salaff, who was hell-bent on my graduating early so that I could continue my education abroad and begin what he hoped would be a brilliant career.
I had completed four years of coursework in three years, but CUHK still required four years of study. Vice Chancellor Lee was unmoved by Salaff’s entreaties and was unwilling to waive the traditional four-year stipulation. Salaff, however, didn’t stop there; he wrote a letter to the newspaper and an article for the Far East Economic Review, criticizing the university’s bureaucratic approach to this issue. He urged CUHK to show greater consideration for its most gifted students.
Salaff’s perseverance was not applauded; several people told him it would be wise to back off. Lee countered, meanwhile, by saying I did not need a degree from CUHK because the famed mathematician Loo-Keng Hua had never gotten a college degree either. I could carry on without a college degree, he said, just as Hua had done.
That piqued both my curiosity and Salaff’s on the subject of Hua’s educational background. When I read up on him, I found out that he didn’t even have a high school diploma. Hua grew up poor in what was then the small town of Jintan, due west of Shanghai. He helped his father, who ran a general store apparently without much success. Hua did math problems on the side, working without any supervision, whenever he had time. He later attended a vocational college in Shanghai, where he won a national abacus competition, but he dropped out of school and resumed working in his father’s store when he could no longer afford living expenses at school. Shortly thereafter, Hua published a brief note in a Shanghai scientific journal, pointing out a mistake in a prior article of that journal, which claimed to present a general solution to the “quintic,” a fifth-degree equation. Hua’s note caught the attention of a mathematician at Tsinghua University in Beijing, which invited Hua to join the department. Hua accepted, starting as a library clerk and eventually working his way up to the status of lecturer. A few years later, he was invited to the University of Cambridge, where he worked under the direction of the famous number theorist G. H. Hardy. Hardy assured Hua that he could earn a PhD in two years, but Hua did not enter a degree-granting program because he believed the registration fees alone would be too expensive for him. He returned to China after two productive years at Cambridge. Although he still did not have a PhD, a college degree, or even a high school degree, his reputation had been established and his career launched.
Salaff was inspired to write an essay about Hua, which was eventually published. Much of the source information about him was in Chinese, of course, which Salaff asked me to translate. So I ended up reading more about Hua, and the more I read, the more impressed I became.
The moral of the story, from CUHK’s perspective, was that Hua was able to achieve all that he did in mathematics without the benefit of a college degree—or any other degree, for that matter. The university felt, accordingly, that it did not need to waive its standard rules in order to give me a degree, regardless of how vociferously Salaff objected. For if I was as talented as Salaff claimed, I should be able to overcome a minor impediment like that.
Nevertheless, Chung Chi College did give me a diploma (though not a degree) at the graduation ceremony in June 1969, and practically the whole student body cheered when I received it. It was a small school, as I said, and most people knew about the debate that had ensued regarding my early graduation.
Once Salaff accepted the fact that CUHK would not budge on the college degree issue, he turned his attention instead toward getting me into a PhD program at Berkeley. I asked him whether I should consider other schools, but he thought I should apply just to Berkeley, where he had strong connections to the math department, which was rated among the best in the world.
I saw no reason to disagree. So I took the Graduate Record Examinations (GRE), Test of English as a Foreign Language (TOEFL), and other exams and, fortunately, did well enough. In the meantime, Salaff had written to the mathematician Donald Sarason, a friend of his at Berkeley, touting my promise in mathematics. Sarason sent an application to Salaff, saying that he could probably get me into a graduate program there even though I had not received an undergraduate degree. That gave me some hope. I applied, of course (how could I not?), and heard on April 1, 1969, that I had been admitted. This was among the most important news I had received in my life, and I was elated.
Not only had I gotten into Berkeley, however; Sarason had also lined up the cushiest fellowship available. Funded by IBM, it provided $3,000 per year—a sum that would be very helpful in view of my family’s financial straits. I was truly lucky because this situation may have been unprecedented: No third-year student from Hong Kong, as far as I know, had ever started graduate school at Berkeley with such a generous financial package. I’m pretty sure that the mathematician Shoshichi Kobayashi, who was then head of graduate student admissions, and the famous Chinese geometer S. S. Chern, who was also at Berkeley, played roles in securing this fellowship for me. I’m grateful to all four of them—Salaff, Sarason, Kobayashi, and Chern—but most of all to Salaff. Without him I probably wouldn’t have made it to Berkeley and perhaps might not have had the opportunity, nor acquired the wherewithal, to leave Hong Kong in the first place.
Chern came to Hong Kong in July 1969 to receive an honorary degree. I had arranged to talk with him during that visit at Hong Kong University, where he’d been invited to give a lecture. I’d read an article about Chern when I was in high school that had called him the most famous mathematician from China—a scholar who was known and respected throughout the world. That was the first time I realized that someone from China could actually be a mathematician of international renown. I hadn’t recognized that before because China had a big inferiority complex that lasted a long time, although it was alleviated to some extent in 1957 when two Chinese-born physicists, Chen Ning (C. N.) Yang and Tsung-Dao (T. D.) Lee, won the Nobel Prize in Physics. Yang and Lee’s award, coupled with Chern’s growing reputation in mathematics, showed that Chinese people could accomplish something on the world stage. Their success and accompanying distinction gave hope to the whole nation—or at least to those of an academic bent.
Yang, in fact, delivered a lecture in Hong Kong in 1964 when I was a high school student. Although I wasn’t able to attend the event, I still felt Yang’s influence by reading newspaper accounts of his talk. And I now feel lucky to have grown up in an era when prospects for Chinese students were looking brighter than they had just a decade earlier.
It’s fair to say that my own prospects were looking brighter too, now that I was headed to Berkeley. Chern knew that his school had accepted me and asked during our meeting whether I was going to go to Berkeley. “Yes,” I replied, “I am.” That was pretty much the sum total of our conversation at the time, but we would have more to say in the future, for this terse exchange was the start of a long and fruitful—and sometimes difficult—relationship.
Although I was committed to going to Berkeley, just as I’d told Chern, I still had to overcome the usual problem: I didn’t have enough money to get there. Nor did I have a visa or an identity card, and getting a visa for the United States was no easy matter. A travel agent with TWA walked me and other students through the process of how to get a visa with the expectation that I would purchase my plane ticket through him. He was angry when I bought my ticket from Pan Am, which offered a better deal.
My mother was happy about my going to Berkeley, while perhaps at the same time a bit worried about my venturing so far overseas. I felt bad too about leaving her alone to take care of my older brother, Shing-Yuk, who’d gotten sick the year before and was subsequently diagnosed with a brain tumor. He’d already had surgery to relieve the pressure in his head. This was yet another trying time for our family, and it made the parting all the more difficult for me. But I also felt a strong desire to make my way in the world, knowing that a number of elements had lined up just right, including Salaff’s coming to CUHK, all of which resulted in an opportunity for me at Berkeley. An offer like this might not come again, and I needed to jump on it. I assured my mother that I would remain close to the family in spirit, even though I would be nearly seven thousand miles away, and I promised to write faithfully, sending money every month.
I was excited about my future, having a sense that many doors would open up to me once I landed on U.S. shores. I was a bit apprehensive, to be sure, as I’d never been outside of Hong Kong before, except for the months I spent in China as an infant. In many ways, and on many different levels, this was going to be an adventure. But I was up for it, ready to take on new and bigger challenges at twenty years of age.
I set off for San Francisco International Airport in early September 1969, eager to explore the New World using mathematics as my point of entry, guide, and beacon in my evolving search for truth and beauty. I was traveling light, with just one suitcase and less than $100 in my pocket. I’d left all my friends and relatives behind, as well as all the math books I’d collected over the years, not realizing that my personal library would affect the fate of my younger brother, Shing-Toung, who now goes by the name of Stephen Yau. I was about to start graduate school, while he was just starting college at Chung Chi, where his two older brothers had gone before him.
At American colleges, students often have the luxury of taking a couple of years before deciding what to study. But that’s not how it worked in China, or in Hong Kong. Stephen, who was still a teenager, had to decide from the outset what area he’d focus on. My mother weighed in on the subject. “Since your brother left all these math books on our shelves,” she said, “the best thing would be for you to study math.” So that’s what he did, and that shows how things are done in China. Much depends on chance, rather than on a conscious act of will. Fortunately, things have worked out all right, as my brother has done pretty well in mathematics and seems to like it. He’s never expressed any regrets to me about his choice of profession—a choice, I suppose, that was only partly his.
Nevertheless, there are worse things one can do, in my opinion, than learning about mathematics and eventually making a career of it. And my brother is, in fact, returning the “favor” bestowed upon him decades ago by purchasing math books in America and donating them to Chinese libraries.