SYNERGISM OCCURS when the interaction of two or more agents yields a combined output that’s greater than the sum of the inputs, or it may lead to an outcome that the individual agents simply could not have achieved on their own. Synergistic phenomena are ubiquitous in the natural world. Two hydrogen atoms, for instance, can combine with one oxygen atom to create H2O, or water, which covers 71 percent of the surface of our planet, possessing seemingly magical properties—including the ability to sustain life itself—that the separate ingredients lack. Working together, colonies of bees and ants can accomplish tasks that single members of the species could not even attempt. An individual neuron cannot do much at all, but one hundred billion neurons, linked through one hundred trillion synaptic connections, collectively form the human brain, which is capable of feats that technological devices made by humans cannot mimic nor even approach.
Synergistic effects often arise in human interactions too—such as the bucket brigades of the mid-1600s that formed to douse fires in New Amsterdam, the colonial city subsequently renamed New York. Some 350 years later, I was hoping that the combined brainpower we were assembling at Princeton for our program in geometric analysis could tackle problems of a more intellectually demanding nature, though perhaps of lesser life-and-death urgency.
History shows that the greatest breakthroughs in mathematics have been made by solo practitioners and small groups of people; important problems are rarely, if ever, solved by committees in which duties are parceled out piecemeal, like homework assignments. Nevertheless, I still believe in the value of bringing together smart people, who work in different though overlapping branches of mathematics, to facilitate the exchange of ideas, while also giving those same folks the space and resources to pursue their interests without competing demands on their time. My work has always benefited from being in such an environment, and I felt there was a good chance that the eight months from September 1979 through April 1980 could prove to be exciting and eventful. I was doing everything I could to ensure that the “special” year on geometric analysis at IAS would live up to the boastful adjective associated with it.
I invited a number of outstanding researchers, and almost all of them came for some or part of the program. Among the core people who attended were Eugenio Calabi, S. Y. Cheng, Rick Schoen, Leon Simon, and Karen Uhlenbeck, along with Jean-Pierre Aubin, Jean-Pierre Bourguignon, Robert Bryant, Doris Fischer-Colbrie, and Peter Li. Several of my graduate students came, including Andrejs Treibergs. Enrico Bombieri, a Fields Medal winner on the IAS faculty, participated as well. And we had shorter-term visitors, too, such as Jeff Cheeger, Stefan Hildebrandt, Blaine Lawson, Louis Nirenberg, Roger Penrose, Malcolm Perry, and Yum-Tong Siu.
This was, according to Armand Borel, the biggest special program in mathematics that IAS had ever hosted. Although he was the IAS faculty member overseeing the workshop, he mostly let me do as I pleased. I decided to hold three seminars a week—one on differential geometry, one on minimal surfaces, and one on general topics, with an emphasis on general relativity (led by people like Penrose and Perry, a former student of Stephen Hawking) and other areas of mathematical physics. Borel said that the level of “cooperation between mathematicians and physicists [was] probably a first here since the early days” of the Institute.
I invited almost all of the speakers, many of whom were already attending the special year. Just as I’d hoped, we established an atmosphere during the program in which ideas flowed freely and unimpeded. People were motivated to work hard because they were passionate about the subject, not because they were under any pressure to do so. I was pleased at all the research that got done that year, much of which was presented at the program seminars. I provided an overview of geometric analysis to start things off. Calabi talked about some of his recent work on Kähler manifolds—the kind of spaces that lie at the heart of the conjecture named after him. Bourguignon and Lawson explored some geometric aspects of Yang-Mills theory. And Penrose discussed some unsolved problems in classical general relativity that were of particular interest and relevance to geometers. Schoen and I, meanwhile, proved a variant of the original Poincaré conjecture—this one involving noncompact surfaces (or manifolds) in which the Ricci curvature was positive.
Math was, of course, the main priority of everyone there, but we also set aside time for fun, creating what would be called today a work-life balance that contributed to good spirits and, I would wager, overall productivity. We went out to eat frequently and met every Saturday morning to play volleyball. We also played ping-pong. Bombieri was a much better player than I was, but he was not good enough to beat Simon. Each time Bombieri lost, he came up with a new excuse, attributing the setback to a sore arm, a stiff wrist, or some other ailment.
Qi-Keng Lu—the deputy director (under Loo-Keng Hua) of the Institute of Mathematics at the Chinese Academy of Sciences—came to IAS for several weeks during the special year. Lu had made some noteworthy contributions in the field of several complex variables. As one of Hua’s leading students, Lu had also done his share, unfortunately, to perpetuate the fight between Hua and Chern. But Lu had played a big role in organizing my “homecoming” trip to China in 1979, and I wanted to return the favor by showing him New York City. Cheng and Siu, who were more up on things to do “on the town,” took the lead during that tour.
We walked around 42nd Street, taking Lu to see the stage performance of Oh! Calcutta!, which featured many scenes involving nude women and men and the things they might do together when unfettered by clothing. Public displays of that sort were unheard of in mainland China (and caused a certain level of controversy at the time also in the States), and I was worried that Lu would be offended by the show. But I was relieved, and surprised, to discover that he was very much entertained by that long-running Broadway hit.
Back in the math quadrant of the normally staid IAS, some big parties were thrown, with lots of drinking and dancing, and I was told that the best of these affairs, coincidentally or not, were held in my two-bedroom apartment when I was out of town. After all, people tend to cut loose when the so-called boss is away.
One of the trips I took in the fall of 1979 was to Cornell, where I’d been asked to give a talk. I was also eager to visit Richard Hamilton, a Cornell mathematician who did not participate in the IAS special year but had embarked on a very intriguing, and exceedingly ambitious, project related to the notion of “Ricci flow.” Flow, in geometry, involves changing the shape of a space or surface through small, continuous steps. One could, for instance, use a pump to slowly transform a deflated basketball into an almost perfect sphere. Or one could do something similar via mathematics, driving the shape-changing process through differential equations instead—equations that are, at their essence, about incremental (as in infinitesimally small) changes. The technique pioneered by Hamilton, Ricci flow, offers a way of smoothing out large-scale or “global” irregularities in complicated spaces and surfaces so that their overall geometry becomes more uniform. The process can, however, create small-scale or “local” irregularities, and the key challenge of the Ricci flow approach is to understand those irregularities when they crop up and figure out how to handle them or prevent them from forming in the first place.
It was a fascinating idea, but the relevant differential equations, which came to be known as the Hamilton equations, were very difficult to work with. I wasn’t sure at first how to overcome those difficulties in order to make this method truly useful, but Hamilton was undaunted, sticking to his agenda for the next several decades, and he soon made impressive strides. I kept close tabs on this work over the years, touching base with him when I could and regularly arranging for my graduate students and postdocs to work with him.
Several things happened in the spring of 1979, apart from the program under way at IAS, which helped make it a “special” year for me. I was named the California Scientist of the Year—the first mathematician, and the youngest person, to receive this honor in the award’s twenty-plus years of existence. My friend Michael Steele, with whom I’d spent a lot of time when he was a Stanford graduate student, urged me to buy a tuxedo for the awards ceremony rather than renting one. This, he said, would be the first in a series of important prizes given to me. I took his advice and bought a tuxedo, which I used a couple of times. But I soon gained weight and could not fit into it anymore.
At first, I was not particularly enthusiastic about the Scientist of the Year award, as I’d never heard of it before. I even told Steele that the decision of a small selection committee has no real bearing on the value of a person’s work. History, I said (perhaps somewhat pompously), is the only true judge. On the other hand, my mother, who attended the awards ceremony with her California-based cousins, was extremely happy about the prize. And that made me happy too, in light of the fact that she had worked so hard, for so many years, to raise me—and bring me to a position where I might achieve some prominence.
Another thing of note that happened late in 1979 was that Borel popped unexpectedly into my office to tell me that Harvard would soon offer me a job (which turned out to be true), but I should wait before accepting because IAS would offer me a job too (which turned out to be true as well). I also heard from friends in Hong Kong that I would be receiving an honorary degree from CUHK in the following year, which was welcome news, considering I never got a bachelor’s degree from that university, my alma mater.
However, other news coming from Hong Kong was not good at all. My older brother Shing-Yuk, who’d been battling brain cancer for about a decade, had taken a turn for the worse. He’d been working in a grocery store but had to be hospitalized when his condition began to deteriorate. X-ray scans revealed a tumor deep within a central part of his brain, and surgeons didn’t know how to treat it. I spent two weeks in Hong Kong in December visiting him, which gave me a chance to see the kind of care he was getting (and not getting).
Neither of us was satisfied with the doctor assigned to his case. After his physician refused to share the medical records with a surgeon whom we liked, I resolved to take my brother to the United States for treatment, which was easier said than done. Shing-Yuk’s first visa application was turned down. I sought help from IAS officials, who asked a New Jersey congressman to intervene on our behalf, but that didn’t go anywhere either.
I then appealed to Andrew Tod Roy, the vice president of Chung Chi College, whose son, J. Stapleton Roy, was a senior diplomat who later became the U.S. ambassador to China. Andrew Roy wrote an impassioned letter on our behalf, but the embassy decided against issuing a visa to my brother.
Fortunately, my friend Isadore Singer was a presidential science advisor at the time. He played tennis with a very high-level official in the U.S. State Department, and with the help of Singer’s friend, I was able to secure a visa for my brother.
Around this time, IAS offered me a permanent position, just as Borel had predicted. I faced a difficult decision because I loved Stanford and was also extremely impressed by Harvard. When I met with Raoul Bott, Heisuke Hironaka, David Mumford, and others there, I felt that I’d rarely been in the presence of so many intelligent people at the same time. IAS, of course, had a storied history too, as well as its own high-powered faculty. It had long been considered among the best places, if not the best place, for mathematicians to call home, owing to the priority given to research at the Institute and the volume of impressive work that had been carried out there.
One of the reasons I decided to stay at IAS was that many eminent members of the mathematics faculty—including Borel, Harish-Chandra, John Milnor, and Atle Selberg—made me feel quite at home there. Additional motivation stemmed from the fact that the Institute’s director, Harry Woolf, had previously been provost of the Johns Hopkins Medical School, and I was assured that he could help my brother go to the Johns Hopkins Hospital in Baltimore. What’s more, Johns Hopkins’s celebrated director of neurosurgery, Dr. Donlin Long, was willing to treat my brother, in part because my brother’s case was interesting to him and fit into his research program. Shing-Yuk’s treatment, moreover, would come at virtually no cost. This was too great an opportunity to pass up, and I’m still thankful that Dr. Long was willing to waive his normal fees. I arranged for my brother to come to the United States as soon as his visa permitted him to travel, which turned out to be late in the summer of 1980.
Before that happened, the special year on geometric analysis was wrapping up in April, and several participants in the program encouraged me to present a list of open problems in the field. A decade earlier, after I had finished my first year of graduate school, Chern had gone to the 1970 International Congress of Mathematicians in Nice, France, where he discussed a number of unsolved problems with the potential to crack open new areas of mathematics. I vividly recall Chern telling me at the time that doing this sort of thing was one of the best ways of making a contribution to other researchers in the field. I also remember the quotation from the American inventor Charles Kettering, who said, “A problem well stated is a problem half solved.”
With those words in mind, I ended up posing 120 problems, many of which I discussed at length during a series of lectures at IAS. I came up with most of these open problems myself, although some were contributed by other people or taken from the literature. But all of the problems were soon widely circulated, becoming known to practically everyone who did anything related to geometric analysis. About thirty of the problems have been at least partially solved, and the others have given people plenty to think about. I am not deluded enough to imagine that these problems, confined to a rather narrow sector of geometry, have been anywhere near as influential as the twenty-three mathematical problems that David Hilbert famously posed in 1900. But my problems did pique interest and activity in geometric analysis, and for that reason I believe that unveiling them at the conclusion of the IAS program was a fitting way to cap off the year.
That summer, after the IAS program had finished, I spent a couple of carefree months with my wife in San Diego. The two of us then went to China in August 1980, as I had agreed to attend a conference Chern was running in Beijing. Yu-Yun and I would also see some relatives and do some touring. Afterwards, I would continue on to Hong Kong to take my ailing brother to the United States.
The symposium Chern had organized on differential equations and differential geometry was held at the Friendship Hotel in Beijing. A number of important people—such as Bott, Lars Gårding, and Lars Hörmander—were there, as well as Chern, of course. It was an expensive affair for China to host, given how poor the country was at the time, but Chern hoped it would introduce Chinese students and researchers to some exciting ideas in geometry. He also recognized China’s urgent need to send its students and scholars abroad, and for that reason connections with potential foreign hosts—such as Murray Protter, the head of Berkeley’s Center for Pure and Applied Mathematics, who was invited to the symposium—was crucial.
In keeping with the lofty status of this event, the van that took my wife and me and other attendees from the airport to the hotel drove down the middle of the road to show that we were more important than the average vehicle and that others better get out of our way. Fortunately, not many cars were on the road back in those days, though a large number of bicyclists did have to clear a path, encouraged by the continuous beeping of the car’s horn.
I lectured on the open problems I had raised a few months earlier at IAS, hoping to spark some interest among Chinese mathematicians, which eventually did happen. Chern had arranged some nice sightseeing trips in and around Beijing. My visit was marred, however, by another unpleasant encounter with Wenjun Wu’s protégé, who again urged me, in an extremely combative manner, to endorse him for a major government award. When I refused to do so, our disagreement escalated into a heated altercation that aggravated my blood pressure condition, almost causing me to faint. After that stressful episode, the elder Chinese mathematicians who served as local hosts for the event tried to make sure I was not again disturbed by unexpected and uninvited guests.
But I was disturbed by something Chern said to the group of ten math “dignitaries” staying at the hotel. He called a meeting, ostensibly for the purpose of soliciting impressions from these experts on the state of mathematics in China, but he had a hidden agenda. He criticized the Institute of Mathematics, which Hua was heading, and urged that it be shut down, even though that was where the major work in the field was being carried out in China. Chern then asked the ten of us to write a letter to the Chinese government recommending that the institute be permanently closed. After his plea was met with dead silence, Chern repeated it.
I finally spoke up, saying that we were guests of the country, and it was neither our place, nor our business, to make such a request. Bott agreed with me, and the others quickly followed suit. They wanted nothing to do with this proposal. But Chern was furious with me, and my forthrightness contributed to further erosion of our relationship. But I don’t regret taking a stand. A letter along the lines that Chern suggested, written by prominent outside scholars, would have been very damaging to Hua and the Chinese Academy of Sciences, as well as a disaster for Chinese mathematics as a whole, which already lagged far behind the West.
I assume that Chern’s motivation stemmed from his long-standing feud with Hua, which, like many of these disputes, seems to have started for no good reason but was sustained by inertia. Although I was a student of Chern—and admired him greatly and was indebted to him in countless ways—I had nothing against Hua. I had learned many things from Hua as well, having reveled in his books as a child, and I was not aware of anything inappropriate that he’d ever done. I wasn’t about to sacrifice Hua, and possibly cause permanent harm to the Chinese math establishment, just to please my former mentor. Nor did I feel the need to choose between Chern and Hua. Both were great mathematicians who had earned their places in the pantheon, and I never saw it as an either-or proposition. Mathematics is not a zero sum game.
Looking back on this incident, I doubt that Chern’s ploy—ostensibly to harm the Chinese Academy of Sciences and Hua, the founding director of its Institute of Mathematics—came out of a vacuum. I believe he was responding to a 1977 report, published by the U.S. National Academy of Sciences (NAS), on the status of Chinese mathematics. It assumed the form of a short book, coedited by University of Chicago mathematician Saunders Mac Lane, who led a delegation of other American mathematicians to China a year earlier. The Pure and Applied Mathematics Delegation, headed by Mac Lane, made special mention of Jingrun Chen’s work on the Goldbach conjecture and the Waring problem, as well as the work on value distribution theory by Yang Lo and Zhang Guanghou—all of whom were based at the Institute of Mathematics. That document had a deep impact on China, where various books, including primary school tracts, instructed people that they needed to learn from wise scholars like Uncle Chen, Uncle Yang, and Uncle Zhang.
Chern, I surmised, was not happy with this rendering of history and hoped to counteract the NAS report with the letter he’d drafted, cosigned by the ten noted mathematicians he had invited to Beijing, which would arrive at an opposite conclusion regarding the merits of the institute and its personnel. But much to Chern’s dismay, this group, of which I was a vocal member, refused to play ball.
My time in Beijing was not taken up solely by mathematics and political maneuverings. Yu-Yun and I met with some relatives who were eager to move to the United States. We weren’t able to help them, though we fielded many requests of this sort during our trip.
Soon after the conference ended, Yu-Yun and I traveled to Shanghai, where we joined thousands of couples who wandered aimlessly along the banks of the Huangpu River, a branch of the Yangtze that runs through the center of the city. It was a curious spectacle. Most of these people had nowhere else to go because they couldn’t afford to eat in a restaurant. And even if they did have the money, one needed a permit or special coupon in those days—immediately after the Cultural Revolution—in order to purchase food at many restaurants. But Yu-Yun and I liked walking, so we were out with the rest of them on the famed waterside known as the Bund, strolling the banks of the scenic Huangpu, watching all the others doing the same.
Our next stop was Hangzhou, about one hundred miles southwest of Shanghai, where we took a boat cruise on the picturesque West Lake and saw some famous temples that had been badly damaged during the Cultural Revolution. Widespread destruction like this was a hallmark of that violent and tumultuous era. A couple of decades later, many of those beautiful, historic buildings were removed and replaced by unsightly, concrete structures.
Yu-Yun was pregnant during our trip and just starting to “show.” As she was also starting to experience morning sickness, she decided to head straight back to San Diego while I made my way to Hong Kong. An official at the American Consulate, where I went to get the visa for Shing-Yuk, told me he was reluctant to let my brother leave Hong Kong. There was, in fact, an inch-thick stack of documents that made the case for why he should not be allowed to go. These arguments were countermanded, however, by an order that came from “high up in the State Department.” I assumed that I had Singer and his well-placed friend to thank for that. And if that was indeed the case, I am grateful that Singer had taken up tennis rather than cricket or croquet.
The plane tickets were expensive because I had to get three seats in a row so Shing-Yuk could lie down. We flew to San Francisco first and then to Chicago. Our mother joined us on a plane from Chicago to Baltimore. Bun Wong, a mathematician I knew from high school who was visiting Johns Hopkins, met us at the airport and drove my brother to the hospital. My mother and I found an apartment somewhat near the hospital, but it was not in a great neighborhood. Even though she didn’t speak any English, my mother somehow figured out how to take the city buses to the hospital each day so that she could be with her son. I had to get back to Princeton almost immediately, as my term at IAS was about to begin.
I returned to Baltimore soon for my brother’s surgery, performed by Dr. Long, which lasted about ten hours. It was a complicated procedure because the tumor was located in the center of his brain. The recovery took a long time, but my brother was eventually able to walk a little, although his balance always remained a bit off. He had to wear a helmet at all times to protect his head, given that part of his skull had been removed.
When Shing-Yuk was finally discharged from the hospital, I brought my mother and him to stay in the home I had purchased on Locust Lane in Princeton—an ordinary suburban street back then, which is now part of a much pricier neighborhood.
My mother spent an inordinate amount of time at home because my brother needed almost round-the-clock care. To help her pass the time, some friends of mine, such as S. Y. Cheng and Bun Wong, occasionally came by to play Mahjong with her. I joined in when I was around. This sounds innocent enough, but years later a series of attacks were launched against me on the World Wide Web in which I was accused of forcing my students to play Mahjong with my mother. Those allegations—which seemed to be correlated with my questioning of the ethical behavior of a former student—were simply untrue. These people came of their own volition, just to be kind, and they were adults, not students. It seems bizarre that I’d even have to defend something like this, involving a board game with 144 tiles that’s played by an estimated one hundred million people worldwide.
Back in the real world, where I prefer to reside, Borel was putting some pressure on me to edit the papers from the special year seminars and sort them into two books for Princeton University Press—one devoted to differential geometry and the other to minimal surfaces. As it turned out, I had mostly edited both volumes, and they were almost ready to go. In fact, I had written most of the sixty-page survey paper on geometric analysis in the waiting room of the Johns Hopkins Hospital. The first volume on differential geometry, which I edited, was printed in 1982. I let Bombieri take over the editing of the second volume on minimal surfaces, which came out two years later.
Around that time, I embarked on another big foray into the world of mathematics editing and publishing. In 1980, I agreed to become editor-in-chief of the Journal of Differential Geometry (JDG), taking over from the founding editor, Chuan-Chih Hsiung—a Chinese-born mathematician and friend of Chern’s who was then based at Lehigh University.
JDG, which came into existence in 1967, was the first journal devoted to a subdiscipline within mathematics, as opposed to covering the field as a whole. The journal got off to an auspicious start, featuring papers by Marston Morse, Michael Atiyah, Isadore Singer, John Milnor, and other heavy hitters in the field. In fact, the Milnor paper, “A Note on Curvature and the Fundamental Group,” which had made such a huge impression on me during my first year at Berkeley, was published in 1968 in JDG’s second volume.
The journal wasn’t doing so well, however, when I was approached. Although I was up on the subject of differential geometry, and had been offered the editor’s post for that reason, I had no experience running a mathematics journal. I was therefore hesitant to take on the job and agreed to do so only after Chern, Calabi, and Nirenberg all encouraged me. Hsiung wisely felt that I could use some help in this endeavor, suggesting that Phillip Griffiths and Blaine Lawson also come on board as editors.
I’d always made a point of trying to keep up with major developments in mathematics, and within the realm of differential geometry in particular, and I now had additional motivation for doing so. I was continually on the lookout for papers that might be a good fit for JDG. Because I spent time with Yu-Yun in San Diego each summer, UCSD had given me an office I could use about a quarter of the year, and I got to know Michael Freedman during these visits. Freedman, who was then a young faculty member, was trying to prove the four-dimensional Poincaré conjecture, which we spent a lot of time talking about, sometimes in or alongside the swimming pool in his backyard.
A group of topologists at Princeton University didn’t think much of the method Freedman was pursuing, instead favoring the surgical techniques that John Milnor had introduced. I, however, was intrigued by Freedman’s approach, which involved something called “Bing topology.” When his work was sufficiently mature, I asked him whether we could publish his paper in JDG. Freedman agreed.
The Princeton folks soon realized they were missing the boat. They argued that the paper should appear in the Annals of Mathematics, published out of Princeton, which they considered the best publication under the sun. The Princeton topologist Bill Browder and his colleague Wu-Chung Hsiang called me, saying that it only made sense: The best papers in topology should appear in the best journal, namely the Annals. I was unconvinced, calmly explaining that Freedman and I had talked many times, after which he had decided on JDG. If he chose to withdraw his paper, however, I would let him do so, no questions asked. But I did make one last lobbying pitch, telling Freedman that his paper would be a big deal for JDG; it would give a big boost to the journal and, in so doing, could boost the field of differential geometry as well.
I believe that argument helped win him over, for in the end, Freedman stuck with JDG, and his paper—“The Topology of Four-Dimensional Manifolds,” for which he later won a Fields Medal—was published in 1982. That did not endear me to the Princeton/Annals crowd, even though I, too, was then based in Princeton at IAS, only about a mile from the university.
Even Robion Kirby, a Berkeley topologist who had no direct involvement in this matter, expressed his displeasure with me over the Freedman paper. Many topologists did not like it when problems in topology were solved by nonstandard methods. Kirby was one of those people who were very protective of their turf, trying—or so it seemed to me—to keep their field free of interlopers. I don’t have a high regard for that attitude, which strikes me as small-minded and contrary to the true spirit of mathematics. Nevertheless, I have rubbed up against that mind-set on numerous occasions, and sometimes those exchanges can be bruising. But I refuse to let myself be held back by tradition, especially when traditional methods can’t get the job done.
JDG published another important paper in 1982. This one, by Clifford Taubes, was related to Yang-Mills theory. A year later, the journal secured a big paper by Simon Donaldson, which eventually earned him a Fields Medal. In that same year, 1983, JDG published “Supersymmetry and Morse Theory” by Edward Witten, which turned out to be hugely influential as well, even though some differential geometers initially raised a fuss about it too. The three referees I had lined up to review Witten’s paper also raised a bit of a fuss, as they all voted to reject it. I, as chief editor, decided to override their objections, and I’m glad I did—primarily because of the impact the paper has had on math and physics, as well as for the impact it’s had on JDG itself. The journal I had inherited, which had been close to folding a few years before, had undergone a remarkable turnaround: It was now a major player.
That said, I’d come to IAS to do research, and my new editing responsibilities didn’t get in the way of that. I was starting to acquire a group of talented graduate students, the first of whom was Robert Bartnik, who originally came from Australia. Jürgen Jost, who’d been Stefan Hildebrandt’s PhD student in Bonn, was my first postdoc, and he was quite skillful as well. For the past twenty-plus years, in fact, Jost has been the director of the Max Planck Institute for Mathematics in Leipzig, Germany.
I also began a student seminar at IAS that made some of my older colleagues uncomfortable. They believed that the Institute should hold only advanced seminars on new research, but I took a different view, arguing that an educational component would be worthwhile. Members of the old guard also complained about noise from these spirited offenders, though the high-decibel zones were mainly confined to an area near my office where the students were clustered. I was reminded of how my neighbors in Hong King used to complain when my father held poetry lessons for his children and other kids living nearby. While there are plenty of things to get riled about, I don’t regard an enthusiasm for mathematics or poetry among the younger generation as being legitimate grounds for complaint.
One of my graduate students, an American of Chinese descent, was a talented young man. His father had shopped around for an advisor and picked me, based on a recommendation he had gotten from Atiyah. Wu-Chung Hsiang, who was then Princeton’s math chair, was not happy with this arrangement. “You come from IAS and take the best graduate student away from us!” Hsiang complained. I calmly replied that I hadn’t picked this student and forced him to be my advisee; he had picked me.
That outburst was rather ironic, given that it occurred at a dinner held in the home of Joe Kohn, a Princeton mathematician who strongly supported the idea of my taking graduate students from the university. I discussed the incident with Borel afterwards, who told me he’d had similar experiences, noting that there’s always some competition between IAS and Princeton.
But the student’s admittance to Princeton hit a snag when he failed to pass the oral qualifying exam. I asked a professor on the exam committee what he did wrong and was told that he did not understand the link between symplectic geometry and mechanics. I mentioned this to the algebraic geometer Nick Katz, Princeton’s graduate student advisor, who confessed that he wasn’t familiar with that link either. As a point of historical fact, symplectic geometry (a branch of differential geometry) did have its origins in Newton’s laws of motion, which formed the basis for classical mechanics. This connection arose from observations made in the 1830s by William Rowan Hamilton, who uncovered deep mathematical symmetries between an object’s position and its momentum. Nearly a century and a half later, symplectic geometry had changed dramatically from its roots to the point where many people weren’t aware of its ties to classical mechanics—in the same way that many people forget that Botox was first developed to treat an eye condition and Viagra was introduced to lower blood pressure.
I argued that this student should be given another chance. Joe Kohn and I gave him another oral exam, and this time he performed well. But he was so dismayed by his earlier failure that he went home for six months. Afterwards, he did return to Princeton to earn a PhD, and he has since gone on to a fine career.
Ngaiming Mok, who was born in Hong Kong, came to Princeton in 1980, just after receiving a PhD at Stanford under the tutelage of Y. T. Siu. We talked soon after he arrived at Princeton and began to work on some problems together, following up on some things that Siu and I had joined forces on during the special year. Siu and I looked at noncompact Kähler manifolds, difficult-to-understand spaces that stretch out to infinity. But we found a means of closing up these extended spaces in such a way that we could analyze their structure at infinity. Borel, Mumford, Jean-Pierre Serre, Carl Ludvig Siegel, and others had attacked problems of this sort by algebraic means. I, however, initiated the program to attack such problems by analytic means through the use of differential equations and various geometric techniques. And Siu and I solved the first important case involving spaces whose curvature is strongly negative.
A year or so later, Jia-Qing Zhong, a student of Hua’s in China, arrived at IAS as my postdoc. I suggested some problems in complex geometry that he and Mok could work on, under my guidance, and they did quite well, coming up with some interesting solutions. But Siu, as I mentioned, was quite competitive with me. And once he found out I was helping Mok and Zhong, and sometimes working with them, he became very protective, asking me to no longer collaborate with Mok. That put a stop to my collaborations with Siu and his students that has persisted to this day. I wasn’t happy with that outcome, as Siu is an excellent mathematician. We had done some good work together, and I would have been happy to do more.
Meanwhile, I heard from Siu about another matter, this time concerning Peter Sarnak, who had been a graduate student at Stanford of Paul Cohen, a Fields Medal winner. Sarnak had stayed on at Stanford, and Cohen was hoping to promote him to full professor very quickly, just a couple of years after he’d gotten his PhD, which was quite unusual. Siu, who was then at Stanford, wanted me to ask a Princeton number theorist what he thought of Sarnak’s work. I didn’t want to do this, as I didn’t know Sarnak, nor was I especially knowledgeable about his area of number theory. But Siu called me several times, so I finally felt obliged to talk to the number theorist in question. As Sarnak was barely out of graduate school at that time, it was understandable that the number theorist did not seem to be overwhelmed by Sarnak’s early contributions. I then passed on this offhand impression of Sarnak’s work to Siu.
I subsequently learned that at a Stanford faculty meeting held shortly thereafter, it was somehow communicated that I was against Sarnak’s appointment—although I never said anything of the sort. I had merely relayed another expert’s preliminary impressions after being repeatedly pressed to do so. In the process, I had angered Cohen, with whom I’d been on good terms, and jeopardized my relationship with Sarnak, who had been told that his fate at Stanford rested in my hands. In time, Sarnak and I have come to treat each other professionally and respectfully. But I learned a valuable lesson through this incident—namely, that academic politics can be quite delicate and sometimes even treacherous. I’ve been more careful since then to avoid getting tangled up in situations that don’t concern me, though I’ve been only partially successful at this.
On March 21, 1981, I caught a last-minute flight to San Diego as soon as I heard that Yu-Yun’s and my first child was about to be born, somewhat earlier than expected. Fortunately, I made it to the hospital that night, about eight hours before our son Isaac emerged from the womb. Yu-Yun had gone through an extremely tough labor that lasted more than twenty-four hours. She was in great pain for much of that time but refused to take any drugs because she wanted our son to come out healthy, and he did. When the baby finally emerged, cried, opened his eyes, and looked around, both of us were happy beyond words.
I stayed in San Diego as long as I could before going back to IAS to finish up the last couple of weeks of the term. Fortunately, Yu-Yun’s mother helped her take care of the baby—a rather large, chubby boy—until I was able to return to San Diego for the summer. Raising a child was new to both of us, though I was surprised at how patient I could be. In mathematics, I was always restless, eager to keep pushing forward. Yet I could spend hours doing nothing other than hold Isaac and be completely content (when he wasn’t screaming at the top of his lungs). That feeling of serenity seemed mysterious to me, though perhaps that’s because I went into mathematics rather than biology.
Of course, I still had to return to Princeton in the fall to fulfill my obligations at IAS. It turned out to be a busy and eventful year. The mathematician Karen Uhlenbeck came to IAS for three days, and we spent all of that time working nonstop on the mathematics associated with Hermitian-Yang-Mills equations—central components of the quantum field theories upon which particle physics now rests.
Hamilton also contacted me out of the blue to report on the first major breakthrough stemming from his research on Ricci flow: He had proved a special case of the Poincaré conjecture—one involving compact, three-dimensional manifolds with positive Ricci curvature. I was surprised because I wasn’t sure that his approach would ever pan out. But this latest work was both beautiful and exciting, and his result was far stronger than the one Schoen and I had achieved two years earlier. It was as if he had found a key that unlocked a door that had never been opened before. I quickly realized that the direction Hamilton had been pursuing would be very fruitful.
I invited him to come to IAS to give a series of talks. We spent a lot of time discussing the potential of Ricci flow methods. I told him that these techniques could be used to prove the Poincaré conjecture in three dimensions—a high-profile problem that had been unresolved since the start of the twentieth century. The application of these same techniques, I said, could also solve Bill Thurston’s geometrization conjecture about classifying three-dimensional topological spaces into eight distinct types. Thurston’s conjecture was broad enough to include the three-dimensional statement of the Poincaré conjecture, so that proving Thurston would imply a proof of Poincaré as well. I immediately got three of my graduate students—Shigetoshi Bando (from Japan), Huai-Dong Cao (from China), and Ben Chow—to start working on questions related to Ricci flow.
Hamilton, who had come from Cornell, stayed for a week in an IAS apartment. At the end of his stay, the chief math secretary was livid because Hamilton had made a huge mess of the apartment, and it took a long time to clean up the place. On the other hand, he had given some wonderful talks, and collaborations between Hamilton, my students, and me picked up from that point onward. So, on balance, his visit would have to be called a great success. Hamilton may have posed some challenges to the cleaning and janitorial staff, but he had posed even more consequential challenges to the mathematics community, some of which were taken up by members of my group.
Jürgen Moser, who’d been so nice to me when I visited Courant in 1975, had since moved to the Swiss Federal Institute of Technology (ETH Zurich), inviting me to go there for two weeks in the fall of 1981 to give some lectures before the International Mathematical Union (IMU). My postdoc Jürgen Jost accompanied me on this trip. His presence was helpful, as he was from Germany, and I’ve never been able to get very far with the German language. In addition to the mathematics-related activities, I took some walks in the mountains with Jost, and the Swiss landscapes were sensational, as advertised.
One night, I was invited to dinner at a fancy restaurant in Zurich with Moser and the Indian-born mathematician Komaravolu Chandrasekharan, a founding faculty member of the School of Mathematics at the Zurich institute. Both Moser and Chandrasekharan were high-ranking people at the IMU; Chandrasekharan had served as president during the 1970s, and Moser would become president in the following year. Chandrasekharan urged me to sit at a particular seat in the restaurant, later telling me that several mathematicians who sat there had gone on to win the Fields Medal. I didn’t know how to interpret that remark, though I suspected he was privy to information I was not aware of.
But I didn’t dwell on this matter as I was soon caught up in a wide variety of things. The physicist Gary Horowitz became my postdoc in the fall of 1981, although in IAS parlance he was actually called my “assistant.” Horowitz, who had studied with Robert Geroch at the University of Chicago, was interested in generalizing the positive mass conjecture, which Schoen and I had proved two years earlier. Soon after his arrival at IAS, Horowitz started working on this problem with Malcolm Perry, who was then at Princeton, although I didn’t know about their collaboration initially.
While the concept of mass is straightforward in classical mechanics, it is much more complicated in general relativity—a consequence of the nonlinearity of the governing equations. For the most part, mass in general relativity can be defined only for isolated systems that are very far away, essentially at infinity. Moreover, there is not a single definition of the term “mass.” Different definitions apply to different situations, and in some cases there is no agreed-upon definition. When you’re talking about mass in Einstein’s theory, you are necessarily wading into a murky realm.
The proof by Schoen and me applied to so-called “ADM” mass—named for the authors of this formulation, Richard Arnowitt, Stanley Deser, and Charles Misner—for which there is a rigorous definition that practically everyone accepts. Horowitz and Perry were trying to extend the positive mass theorem to include “Bondi mass,” which is less clearly defined. Many physicists believe that the Bondi mass of a system is equal to its ADM mass minus the energy carried away by gravitational waves—the radiation associated with the force of gravity. Einstein predicted the existence of gravitational radiation in 1916, and this prediction was confirmed one hundred years later based on observations made at the Laser Interferometer Gravitational-Wave Observatory (LIGO).
The positive mass conjecture asserts that the energy of a physical system always remains positive. This means that the ADM mass, which Schoen and I had already shown to be positive, cannot be completely carried away by gravitational radiation. The Bondi mass, therefore, must be positive too, and that’s exactly what Schoen and I were trying to establish.
As I’ve said, I had no idea that Horowitz was collaborating with Perry on this until my graduate student Robert Bartnik casually mentioned that they’d just about finished their proof. I was miffed to find out that my assistant had been doing this without telling me, but I used that news as inspiration for Schoen and me to finish the work we’d already done on the problem.
Schoen was then at the Courant Institute, and I joined him there early the next morning. We worked the entire day without stopping, finishing our calculations at 6:30 p.m. Then I suddenly remembered that I’d been invited to dinner that night as the “guest of honor” at the home of François Trèves, a distinguished French mathematician who was teaching at Rutgers. There was no way I could make it, as the dinner had already begun and I was more than an hour away from New Brunswick, New Jersey. My lapse was particularly embarrassing because Trèves had invited me about two months before and had reminded me of the event several times.
More than thirty-five years later, I still feel bad about that faux pas. But at that point, after offering my apologies by phone, there was nothing I could do but finish the work that Schoen and I had started. Our paper, “Proof That the Bondi Mass Is Positive,” came out in Physical Review Letters a couple of months later, right next to the article by Horowitz and Perry, “Gravitational Energy Cannot Become Negative.” These papers offered further evidence regarding the stability of our universe, as well as reassurance that it is not collapsing.
Does it seem odd that I was motivated in this case to compete with my assistant? I don’t think so. In my experience, it is extremely common in the field of mathematics—and throughout all of science—to be spurred on when another person or group is making advances on a problem to which you’ve already devoted a good deal of effort. As long as you don’t copy someone else’s work, or do anything else that is unethical, competition is healthy in mathematics. Indeed, the field depends on it for a good deal of the progress that has been made.
At around the same time, I met Zhiyong Gao, a former student at Fudan University in China who had since come to Stony Brook, with the help of C. N. Yang, where he pursued a PhD that was supervised by Blaine Lawson. Gao and I worked together to solve an important problem related to manifolds with negative Ricci curvature that had puzzled geometers for a long time. The problem, expressed in elementary terms, concerned whether it was geometrically possible to construct a simply connected manifold (one with no holes coursing through it) that had negative Ricci curvature. Ricci curvature is associated with the “cosmological constant”—a factor added to Einstein’s equations that is thought to account for the accelerated expansion of our universe since the Big Bang. Negative Ricci curvature, which would correspond to a negative cosmological constant, is consistent with an expanding universe, but one whose expansion is decelerating rather than accelerating.
Gao and I drew on some prior work by Thurston to produce an example of a manifold, a three-dimensional sphere, which possessed the desired geometry. I considered this a significant achievement and accordingly wrote Gao a strong letter of recommendation that helped him land a tenured position at Rice University.
To my dismay, it appeared that Gao’s interest in research declined soon after he got tenure. His publications dropped off, from what I could tell, as did his attendance at math conferences. I’ve seen this happen with other Chinese students, who are eager to get a good job but don’t seem to be that fired up about math itself. This may be an unintended consequence of the Chinese educational system, which tends to present subjects in a rote manner that can suck the life out of them.
While that was certainly disappointing, my next brush with China, or at least with a few if its people, had even more negative repercussions. It started innocently enough with a phone call from Chern, who was trying to help his friend, Shisun Ding, the chair of the math department at Peking University. Chern was hoping to expand Ding’s influence in China. The president of Peking University would soon be stepping down, and Chern wanted Ding to take his place. But Ding first needed to beef up his curriculum vitae. He was hosted by Phillip Griffiths at Harvard at the time, which would make for a prestigious entry on his CV, even though Ding didn’t seem to be doing much mathematics there. Chern asked me to get Ding an appointment at IAS.
I told Chern that it was too late, as I had already offered my assistant position to Gary Horowitz. That is the only appointment faculty members can make unless they can persuade their colleagues that someone is such a superb mathematician that IAS simply has to hire him or her. I could not, in good conscience, make such a case for Ding, who had not yet made any outstanding contributions to mathematics that I was aware of. Furthermore, Ding worked in algebra—a field that many people at IAS knew far better than I did—and I didn’t feel comfortable trying to push through an appointment in that area. Nor did I have reason to believe that such an attempt would be successful.
Chern, of course, was not happy about my response. He believed that if I had wanted to do something for Ding, I would have, but I chose not to. That, in turn, made Ding angry at me. He became president of Peking University in 1984 and later served as chairman of the China Democratic League, one of the eight recognized political parties in the People’s Republic. In this relatively brief encounter with Ding, which I had not wanted any part of, I had made a powerful enemy. Peking University, a leading Chinese university, soon became less friendly toward me—a fact that did not make my subsequent dealings in China any easier. This, in turn, was part of a broader power struggle between the mathematics group at the Chinese Academy of Sciences, led by Hua, and a faction at Peking University, which was under Chern’s sway. I often found myself in the crosshairs of that bitter fight, which was not a pleasant, or particularly relaxing, place to be.
In April 1982, after finishing my term at IAS, I flew to San Diego to be with Yu-Yun and Isaac, with whom I’d celebrated his first birthday a couple of weeks before. While there, I got a call from my brother Stephen, who had received a letter from the IMU that had been sent to me at IAS, where he had a one-year appointment. This letter informed me that I had been named one of three winners of the 1982 Fields Medal for my work on the Calabi conjecture, on the positive mass conjecture, and on real and complex Monge-Ampère equations—the first person from China ever to receive this award. The other two 1982 winners were Alain Connes of IHES (for his work on operator algebras and other topics) and Bill Thurston of Princeton (for having “revolutionized the study of topology in two and three dimensions”). The prize ceremony was supposed to have been held in Warsaw, Poland, in 1982, as part of the International Congress of Mathematicians, but the IMU decided to postpone its meeting for a year, until August 1983, because martial law had been declared in Poland in late 1981 as part of the government’s attempt to suppress the prodemocracy Solidarity movement. Fortunately, martial law was lifted in July 1983, so the IMU was able to go ahead with the event a month later.
Yu-Yun took a three-month leave of absence from her job so that she and Isaac could be with me during the fall of 1982, though she preferred to live in Philadelphia rather than Princeton. We found an apartment close to Eugenio Calabi’s home, and he was kind enough to loan us a crib and other baby gear, even taking the time to help us set things up. It was an hour’s drive to Princeton. I bought a run-down car for $200 that was in decent working condition but looked terrible. The secretaries at IAS thought it was disgraceful for a faculty member to drive a car like that and, worse yet, have the nerve to park it in the Institute lot.
Borel, who had always been extremely supportive of me, disapproved of my mixing business with pleasure by bringing Isaac—then a beefy toddler about a year and a half old—into the IAS dining hall, so I refrained from doing that again. Princeton was a proper place, and years of living on the casual West Coast had apparently left me unfit for the more rigorous social standards of the dignified East.
In April 1983, I went to Berkeley for three months to participate in a program on geometric analysis that Chern had organized. Schoen and I taught a several week–long course, discussing some new theorems we had proved, based on minimal surface arguments, regarding manifolds of positive scalar curvature. Several Chinese students at Stony Brook told me that a former student of Lawson’s had taken detailed notes during the course. It looked as if those notes may have been passed on to Gromov and Lawson, because a preprint of their subsequent paper, which Schoen saw, seemed to incorporate some of our ideas. Schoen complained about this in a letter addressed to Lawson, which he deposited in a mail slot in Berkeley’s Evans Hall. But the mail slot was blocked, and the letter was returned to Schoen a few months later. By that time, it was too late for him to send the letter, and the matter was dropped, as it probably should have been. Mathematics, after all, is a competitive business.
Our second son, Michael, was born in June 1983, which was, of course, another joyous event. The overpowering sense of bringing a new being into the world never gets old, and the emotional impact of the occasion hit me just as hard the second time around. Two months later, however, Yu-Yun and I had to leave Michael and Isaac in the care of my mother-in-law while we went to Warsaw for the Fields Medal ceremony. Demonstrations against the Communist regime were still going on, and Thurston advised me against saying anything to the reporters who were trying to interview us. That was fine with me, as I had a hard time understanding what the reporters—many of whom did not speak much English—were saying anyway.
After the award ceremony, Yu-Yun and I were invited to join Y. T. Siu, Wu-Chung Hsiang, and others for a drink. And that’s where a topic of conversation that I had not anticipated set the stage for big problems down the road—problems for me in particular.
Siu and Hsiang were strongly opposed to a program Chern was formulating with Phillip Griffiths to bring Chinese students to North America. That plan was modeled after the China-U.S. Physics Examination and Application (CUSPEA), a famous program started a couple of years earlier by the physics Nobel laureate T. D. Lee to help Chinese physics students attend graduate school in the United States and Canada. In the wake of the Cultural Revolution, school transcripts, teacher recommendations, and the like were hard to come by in China, and Lee (who was then at Columbia University) worked with American physicists to design an exam that would help them pick out about one hundred Chinese students each year for placement abroad.
Chern was trying to do something similar for Chinese mathematics students, who greatly outnumbered physics students in those days largely because expensive experimental facilities were not needed in math. There was nothing wrong with the general idea Chern was espousing, and indeed much to recommend it, but Siu, Hsiang, and I were not thrilled about some of the particulars. Under the proposal Chern had worked out with Griffiths, students applying to the program in pure math would be given an exam by Griffiths; students interested in applied math would be given an exam by David Benney of MIT. Griffiths and Benney, acting on behalf of the American Mathematical Society (AMS), would then have a large say over who among these students would go to which school.
I was uncomfortable that this program with China, as it was then constructed, would place so much power into so few hands. Siu, Hsiang, and I all felt that the participating Chinese students should have more say over which schools they wanted to attend than this plan allowed. We preferred an approach that made it easy for these students to apply to American schools directly, thereby giving them more choice and reducing the control granted to the AMS.
I had asked Chern on three occasions whether AMS’s role in the program was his idea, and each time he said no—it had nothing to do with him. In view of those statements, our questioning the AMS piece of the program should in no way have been construed as an attack on Chern, Griffiths, or Benney, as I had nothing against any of them.
Nevertheless, Hsiang, Siu, and I were concerned enough over this issue that someone finally suggested sending a letter to China’s minister of education that would present our ideas on alternative ways of running the program. We never wrote that letter, but several months later I was with S. Y. Cheng, my graduate student Huai-Dong Cao, and Chang-Shou Lin, an IAS visiting mathematician originally from Taiwan, and we got onto the same subject again. This time, we drew up a rough draft of a letter along the lines I had previously discussed with Siu and Hsiang. As we would need the others’ support, I initially sent a copy of the letter—an unfinished, handwritten draft—to Siu to get his reaction. From there, our draft somehow made its way into the hands of Griffiths and, shortly thereafter, into the hands of Chern.
Griffiths, unsurprisingly, was not enthusiastic about the letter—or I should say this extremely preliminary draft of the letter. Nor was Chern, who was up in arms over my apparent “treachery.” He then complained to all his friends at Berkeley, Courant, Princeton, and elsewhere, tearfully proclaiming, “Yau has betrayed me!” Chern spread that message far and wide, and even people who had been supportive of me, like Moser and Nirenberg, were shaken up by his allegations.
This was another step in the protracted falling out between Chern and me—a period that lasted almost until his death more than twenty years later. I had stood up for what I believed was right, even though I knew my position might displease my mentor, which it ultimately did. But things turned out worse for me than they might have, in part because Hsiang and Siu—who also had big roles in initiating the letter—seemed content to let the blame fall squarely on my shoulders.
Looking back on this incident, it’s kind of ironic that some of the grief that befell me, months and even years later, started with a casual conversation that took place during a time of celebration, just hours after I’d gotten the Fields Medal—widely regarded as the most prestigious award in mathematics.
Winning such a prize would normally be considered a joyous occasion, though in my case it was offset by another, rather grave development. For while I was in Warsaw, being feted and carousing with my wife and friends, my brother Shing-Yuk had gotten sick again. He was taken to the hospital where doctors found a blood clot in his leg, for which he was prescribed blood thinners. Shing-Yuk was kept on blood thinners for a while, too long as it turned out, which caused bleeding in the brain that eventually resulted in a coma. He stayed in a coma for the last six months of his life. It was a tragic end for my brother, who’d fallen ill at a young age and never had the chance to do all that he might have done. Of course, I had no idea things would unfold in this way while I was in Warsaw, but I still thought of him often and was preoccupied with concerns over his frail health.
I learned from this latest flap among colleagues, and many others over the years, that life is never just one thing. You can’t keep going up—even after capturing a great honor like a Fields Medal. Eventually, gravity will overtake you and pull you back down, in some cases crashing down.
I have mixed feelings about mathematical awards, of which I’ve been lucky enough to win more than a few. I have never done any work in the field for the purpose of winning a prize, as I am of the opinion that doing mathematics is its own reward—especially when the work goes well. On the other hand, it is nice to be recognized for the hard work you’ve put in. But recognition—and fame, if you could call it that—does have its trappings. I was no longer an anonymous researcher who could move around unnoticed, focusing on mathematics twenty-four hours a day if I cared to. I was now somewhat of an authority figure, someone whose convictions carried weight. As such, I was asked to express my opinions and sometimes assume a bigger role in policy, administrative, and political matters, which inevitably resulted in my being drawn into skirmishes I had no desire to be involved in.
The news that I was the first person of Chinese descent to win the Fields Medal traveled fast, and I became something of a folk hero in China. But I also heard that some people were not rejoicing, or at least had mixed feelings about my award, if not actually feeling bitter. Perhaps they felt that they deserved a Fields Medal more than I did.
Someone else was angry at me too, though for an entirely different reason. My two-year-old son Isaac became upset every time I left San Diego to return to Princeton. He was starting to protest more violently, sometimes pounding the floor or even banging his head against it. While I could handle the fact that some people in the mathematics world did not love me, and maybe bore some animosity toward me, I could not ignore the feelings of my own son, especially when they were displayed in such an emotionally raw and unfiltered fashion.
I was perhaps too slow in coming to this realization, yet it was now vividly clear to me that the present situation, living on the East Coast while my family was installed on the West, was untenable. I had to do something about it—to find a way of bringing my family together. Given that Yu-Yun did not want to come to Princeton, I needed to go somewhere else.
David Mumford had been coming to IAS regularly for a program in algebraic geometry he was running with Phillip Griffiths, and I told him I might have to leave. Mumford spread the word to Henry Rosovsky, Harvard’s dean of the Faculty of Arts and Sciences, who came to Philadelphia (where I was then living) to try to persuade me to join the Harvard faculty. A charming and erudite man, Rosovsky even managed to weave a famous work of Chinese literature, Romance of the Three Kingdoms, into his argument as to why I should come to Harvard. Although I can’t reconstruct the exact line of reasoning he put forth—and how he had related my employment at his university to the tale of three warlords struggling for dominance near the end of the Han Dynasty, some seventeen hundred years ago—I was still swept up by Rosovsky’s rhetoric and smooth elocution. The bottom line, however, was that Harvard could offer only 75 percent of my current salary. That was a nonstarter, given our current economic situation: Yu-Yun and I now had two children to support, plus her parents and my mother and brother Shing-Yuk, who was still hanging on, though barely, at the time I was making this decision. So I reluctantly had to say no to Harvard for a second time.
I also felt bad leaving Stanford, where I’d been treated extremely well by Robert Osserman, the department chair Hans Samuelson, and many others. I had no complaints about Stanford at all, but the more I thought about it, the more it seemed that UCSD would now be the best choice, given that my wife and sons were already living in a home not far from campus. Isadore Singer, one of the most connected people I knew, put me in touch with his friend Richard Atkinson, the UCSD chancellor, who made a very tempting offer.
I then spoke with Borel, who kindly told me they’d keep my position at IAS open for two years in case I wanted to come back. But UCSD had some advantages that other schools could not match. First and foremost, my family was there, and Yu-Yun had a job in San Diego that she was happy with. Second, the university promised that I could make two additional appointments in the department so that I would have a handpicked team of colleagues to collaborate with—something I valued strongly. Rick Schoen agreed to move from Berkeley to San Diego, and Richard Hamilton agreed to move there from Cornell. With a strong group of us working on geometric analysis together, Hamilton believed that UCSD would provide “the ideal environment” for him to further develop his ideas on Ricci flow. San Diego offered Hamilton the ideal environment for another reason: He was an avid surfer and wind surfer and loved being near the ocean, and the UCSD mathematics building on Gilman Drive is not much more than a mile (as the crow flies) to the beach.
Although IAS had been a convivial home for me, one drawback was that it had been hard for me to get graduate students. I’ve always found that interactions with younger people are not only healthy, but essential. It keeps you current in the field. And with a constant influx of new students, your research is less likely to dry up. Lining up students at a large state university like UCSD would not be a problem.
Furthermore, with Hamilton, Schoen, and me, we had a good core of geometric analysts, and the German differential geometer, Gerhard Huisken, soon came to San Diego as a visiting professor too. I started thinking about bringing in other strong mathematicians and turning San Diego, which already had what was advertised as the world’s greatest weather, into a mathematical paradise as well.
Michael Freedman was still at UCSD, after having gained considerable renown for his work on four-dimensional manifolds. Quite a few other accomplished faculty members were also there. With encouragement from the administration, I would soon get involved in building up the department further—without realizing at the time how much trouble that would prove to be, how much resistance I would face, or how many quarrels that would incite. Looking back, I realize I would have been much smarter to stick to my research. But sometimes you have to learn the hard way. And the hard way, for better or worse, has often been my way.