ZT: The Dinner with the Highest Average IQ in Beijing's History (Note: reposted by Chan)

-- Mathematician Andrew Wiles' Beijing Journey

On August 29, 2005, I had the most intellectually brilliant dinner of my life.

Among the 12 people present were Zhang Jiping, Dean of Peking University's School of Mathematics, Vice Dean Liu Huarong, and Chinese Academy of Sciences academicians Tian Gang, Zhang Gongqing, Jiang Boju, Ding Weiyue, and Wen Lan. The person they were hosting was Andrew Wiles, the man who settled Fermat's Last Theorem -- a foreign member of the US National Academy of Sciences. The previous day, he had set foot on Chinese soil for the first time. This was even his first time in Asia.

I firmly believe this was the dinner with the highest average IQ in Beijing's history.

On the 29th, Professor Zong Chuanming of PKU's School of Mathematics and I accompanied Wiles through the Temple of Heaven, Tiananmen, the Forbidden City, and Beihai Park. Though autumn had arrived, Beijing that day was still unbearably muggy. Every time we reached a shady spot, I noticed a layer of salt crystals on my arms. Wiles remained composed and serene throughout, either smiling warmly or lost in thought. Watching the bustling crowds brush past him, his eyes behind the glasses emitted a kind and shy light. In crowded settings, he mostly listened quietly, and even when speaking, his voice remained constantly below a certain decibel level. Just as everyone who had met him described: gentle and refined. In Dean Zhang Jiping's eyes, this quite distinguished English gentleman was the "Superstar" of mathematicians.

That day, after touring Beijing's landmarks, tasting Beijing roast duck and steamed mandarin fish, and riding Beijing's taxis and buses, we sat by the lake in Beihai, the former imperial garden.

Andrew Wiles was born in England in 1953, graduated from Oxford University in 1974, then earned his doctorate at Cambridge, and joined Princeton University as a professor in 1980. His blond hair was sparse, his complexion somewhat pale, his frame thin and tall, about 1.80 meters. His wisdom-filled head didn't appear particularly remarkable -- in proportion, it even seemed slightly smaller than average. During the warm-up interview, Tian Gang, a Princeton professor and CAS academician, described his colleague: low-key, rarely seen, only appearing at full department meetings, speaking little, conscientious and responsible about his work, carefully reading every student's application materials when admitting students, and respected by colleagues.

After this interview, Dean Zhang Jiping asked me with a smile: "Did you get a taste of how a real mathematician speaks?"

Yes. The most mathematician-like answer appeared here. I asked: "Would you mind telling us how you and your wife met and married?"

"We met at Princeton. We married at Princeton."

"In your research on Fermat's Last Theorem, you relied on paper, pencil, and your mind, without using a computer. Do you now use computers? Will computers play an increasingly important role in mathematicians' work going forward?" I asked. "I now use computers only to find examples, verify them, and collect information in special cases. I never use computers for direct proofs. Different mathematicians have different attitudes toward computers. I myself use computers very rarely, but one of my students used a computer to solve a very important problem. Of course, the characteristics of the problem he solved with a computer were very different from mine. Only very few problems in mathematics can be solved through computers." His answer was almost like describing a theorem.

"Through your proof of Fermat's Last Theorem, the whole world is watching you. Has public attention affected or changed your life?"

"Of course it has changed somewhat. For me personally, the biggest change is that I no longer have to work on Fermat's Last Theorem."

"In the American film 'A Beautiful Mind,' after the protagonist John Nash receives the Nobel Prize, a group of mathematicians in a conference hall each present him with a pen as a sign of respect. Is this a Princeton tradition? Have you received pens?"

"That's fictional, of course." He laughed out loud. "But it's actually a good idea -- they should start doing it from now on."

In this exchange of questions and answers, Wiles' gaze often passed beyond me to somewhere more distant. His conversation was full of pauses and contemplation. What he said was as concise and rigorous as mathematical formulas.

"I have solved Fermat's Last Theorem"

The 17th-century French mathematician Fermat left behind a marginal note in a mathematics book that was discovered after his death, giving birth to a problem that future generations would find enormously difficult: "It is impossible to write a cube as a sum of two cubes; or a fourth power as a sum of two fourth powers; or, in general, any power higher than the second as a sum of two like powers."

This was a puzzle expressed in terms every high school student would understand, yet it stumped the world's most brilliant minds. What was even more tormenting was that Fermat also left a note hinting that he already had a solution, though he didn't write down the proof.

And so, generation after generation of mathematical geniuses charged forward one after another, challenging this conjecture. More than 300 years passed, and the theorem still lacked a complete, rigorous proof. No other problem had ever been so simple and clear to state, yet so long and arduous to solve.

Andrew Wiles was captivated by Fermat's Last Theorem at age 10, and from then on chose mathematics as his lifelong career. After entering university, "I kept thinking that throughout history, many people had tried every conceivable method and still couldn't solve Fermat's Last Theorem. So I had to learn more advanced mathematics. From the graduate stage, I devoted more energy to broadening my horizons." Recalling those times during the interview, he felt that period was one where "it seemed I had temporarily moved away from the Last Theorem."

In 1986, Andrew Wiles decided to launch his assault on Fermat's Last Theorem. He first spent 18 months gathering the mathematical tools necessary for this battle, and his overall estimate was: what lay ahead was possibly up to 10 years of focused effort.

I asked: "At the time, many mathematicians felt this problem was very hard, or felt the prospects of solving it were dim, and gave up. Yet you persisted for 7 years. When you started, how confident were you? Did you proceed even knowing the odds weren't great?"

"Looking at history, among truly serious mathematicians, not many decided to study Fermat's Last Theorem, because they first had to consider whether, given the historical conditions of their time, mathematical development had provided them with tools sufficient to reach the level needed to solve this problem. By 1986, when I decided to study the Last Theorem, the vast majority believed the tools at hand were still insufficient, but I believed there was hope." He denied possessing any reckless determination to do the impossible. "So I wasn't being romantic -- I had very realistic grounds for confidence."

There is a common narrative that Wiles conducted his research in complete secrecy, not letting anyone know what he was doing, not exchanging ideas with anyone. During those 7 years, only his wife knew what he was working on.

During the interview, Wiles clarified this narrative: "Actually, at the very beginning I did tell some colleagues. But once they knew, every time they saw me they would constantly ask about my progress, which created enormous pressure and distraction. So I felt it was better not to tell people. I realized that solving this problem would take a very, very long time. Being constantly asked during this process creates enormous pressure. It's like a child -- if during the process of growing up, people keep asking how old they are, what problems they're having in their development, it's very awkward."

And so, he gradually entered a state of secret combat. Finally one day, he told his wife: "I have solved Fermat's Last Theorem."

In June 1993, Andrew Wiles gave three academic lectures at the Newton Institute at Cambridge University in England. At the end of the final lecture, he completed the proof of Fermat's Last Theorem. The news quickly made the front pages of major newspapers worldwide. In the mathematics community, people spread the word with joy. The news reached Paris almost immediately, where several mathematicians raised their glasses in celebration, among them that year's Wolf Prize winner Tits, French mathematicians Broue, Puig, and Rouquier, and Zhang Jiping, who was then a visiting professor at the Ecole Normale Superieure in Paris.

While mathematicians around the world were toasting him, the paper Andrew Wiles had submitted to Inventiones Mathematicae was undergoing rigorous review. The reviewers encountered a problem in the third chapter of the paper, which meant Wiles could not guarantee that a certain method would work as originally envisioned. He needed to strengthen his proof.

Two weeks before his birthday, Andrew Wiles' wife told him that the only birthday present she wanted was a correct proof.

Unfortunately, two weeks later, Andrew Wiles had not been able to deliver this birthday gift.

As time passed, people who had just been cheering grew anxious again. In more than 300 years, among the many attempted proofs of Fermat's Last Theorem, no one had ever been able to patch a flaw that appeared. The most recent failure was on March 8, 1988, when the Washington Post and New York Times announced that Yoichi Miyaoka of the University of Tokyo had found a proof of Fermat's Last Theorem, only to retract the claim a month later. Could Wiles not escape this fate? BBC science editor John Lynch said: "It's hard for me to imagine Andrew not being just another tombstone in that mathematical graveyard."

This proof effort was conducted under virtually worldwide scrutiny. It was said that Princeton colleagues at the time talked about only two things: the O.J. Simpson case and Wiles' proof.

Andrew Wiles still remembers that period vividly today: "In the first phase, I was very happy -- I was enjoying the process. In the second phase, it was as if I was in the public eye. At mathematics conferences, many people kept asking me. I didn't like that state."

At his most desperate, he had even prepared to publicly admit his proof had a flaw. His colleague Professor Tian Gang, in my interview, described Andrew Wiles as a "brave man," because during that time he was bearing extraordinarily immense pressure. I asked Wiles: "Do you consider yourself a 'brave man'?"

He answered: "I only know this problem can be solved, and I also hope it can be solved. Even if I had admitted my proof was flawed, hundreds and thousands of people would have seen the hope, seen that we already had good enough tools. They would have gone on to solve the problem. Perhaps they would have taken some time -- 8 years, 10 years -- but the tools were there, the direction was there."

Andrew Wiles' judgment was not wrong. Fourteen months later, he submitted a second paper to the Annals of Mathematics, consisting of two parts: "Modular Elliptic Curves and Fermat's Last Theorem" and "Ring-Theoretic Properties of Certain Hecke Algebras." This time, there was no longer any doubt about the proof.

Mrs. Wiles finally received the birthday gift she wanted. "What was your wife's reaction to this birthday gift, delayed by a year?" I asked.

He smiled: "She was even happier than she would have been receiving it a year earlier."

"No, Fermat could not have solved this problem"

CAS academician and PKU professor Jiang Boju called Andrew Wiles' proof of Fermat's Last Theorem "the most brilliant mathematical achievement of the 20th century."

Honors followed in succession. In 1996, Wiles and Robert Langlands shared the $100,000 Wolf Prize. The Langlands program proposed by Langlands is a conjecture aimed at unifying proofs across different areas of mathematics. Wiles, through his proof of the Taniyama-Shimura conjecture, unified elliptic curves and modular forms. This success breathed life into the Langlands program -- a problem in one domain can be solved through the corresponding problem in a parallel domain. This was a breakthrough that could potentially usher mathematics into another golden age of problem-solving.

In 1998, the International Congress of Mathematicians met in Berlin, and the Fields Medal -- mathematics' "Nobel Prize" -- was awarded to Andrew Wiles as a special prize.

The Fields Medal is named after Canadian mathematician John Fields and is used to reward outstanding achievements by young talents under 40. Andrew had just passed 40 when he successfully proved Fermat's Last Theorem. CAS academician Professor Zhang Gongqing, who witnessed Wiles receiving the award and heard his report in person, commented: "The solution of this 300-year-old problem has milestone significance in the mathematics community. This is also the only special prize in the history of the Fields Medal."

The question lingering in the general public's mind is: the Fermat who posed this problem once wrote "I have discovered a truly marvelous proof of this proposition, which this margin is too narrow to contain." Yet in the era 300 years ago when Fermat lived, he didn't have the tools Andrew Wiles used: elliptic curves, modular forms, the Taniyama-Shimura conjecture, Galois group theory, Iwasawa theory, and the Kolyvagin-Flach method. So how did Fermat himself prove the conjecture he proposed?

Andrew Wiles' first paper submitted to Inventiones Mathematicae was 200 pages; his second submitted to the Annals of Mathematics was 130 pages. Dean Zhang Jiping said this is the only flawless, most rigorous, and most economical proof of Fermat's Last Theorem. Is there a simpler proof?

The professors at PKU's School of Mathematics said there are various rumors in the mathematics community about Fermat's Last Theorem, but to date, all other proofs that have undergone rigorous review have been wrong. "Have you ever thought about what Fermat's proof method was? If he were to write a paper, how many pages would it be?" I asked Andrew Wiles.

"Fermat never wrote a paper," he answered simply.

"Many ordinary readers would have this question: could Fermat himself really prove Fermat's Last Theorem?" I continued.

Professor Zong Chuanming, serving as translator, answered directly: the mathematics community generally believes Fermat's claimed proof could not exist.

Andrew Wiles, after hearing Zong's translation, affirmed: "No, Fermat could not have solved this problem."

"Do you think there could be another proof?"

"Although anything is possible, I still believe there won't be a simpler proof than mine. Perhaps my proof could be simplified somewhat more, but the basic ideas and complexity of the proof of Fermat's Last Theorem will not change."

Ten years have passed since Fermat's Last Theorem was proved, and as a mathematician, Andrew Wiles' life hasn't changed. He still does the same thing as before: gets up in the morning, goes to his office, and works on new mathematical problems. "What do you think is the most interesting problem in today's mathematics community?" I asked.

"The Riemann Hypothesis, of course."

The Riemann Hypothesis is one of seven "millennium problems" known to the mathematics community, proposed by the 19th-century German mathematician Riemann. The brief description I found online states: the distribution frequency of prime numbers is closely related to a carefully constructed so-called Riemann zeta function z(s). The famous Riemann Hypothesis asserts that all meaningful solutions to the equation z(s)=0 lie on a single line.

"Are you currently working on the Riemann Hypothesis?"

"I do think about this problem sometimes, but I spend very little time on it. When I started proving Fermat's Last Theorem in 1986, the methods others had discovered happened to be in my area of expertise, and it was something I could solve. But to date, no one in the world can propose any direction or domain for the Riemann Hypothesis. No one knows whether the Riemann Hypothesis should be proved by a number theorist or a function theorist. If the tools for solving it are in the domain of number theory, I would certainly devote more time to it."

He described his situation after becoming world-famous: "Fermat's Last Theorem has brought me into contact with many people outside the mathematics community, letting me experience others' feelings about mathematics. I receive invitations from all over the world -- including this trip to Peking University. I've met very friendly people from around the world and I'm very happy, but I don't take many such opportunities."

It's said that a joke circulates among Princeton professors: suggesting Andrew Wiles go do commercials, including men's underwear. So I asked him: "Have you really received invitations to do commercials?"

His answer surprised me: "There actually was one, but the clothing company was called 'G.A.P' (gap meaning 'defect'), so I declined."

On July 1st of this year, Andrew Wiles assumed the position of Chair of the Mathematics Department at Princeton University. As an internationally top-tier research and teaching institution, Princeton's mathematics department is called "the place that defines what good mathematics is." When I asked if he liked this position, he answered in a calm tone: "Only when I've finished this position will I be able to say whether I liked it."

"It was this problem that chose me"

Professor Chen Dayue of PKU's School of Mathematics had posted the news of Andrew Wiles' upcoming visit to PKU on the campus website early on. Within two days, over 5,000 people viewed the post.

At 1:30 PM on August 30th, Qin Jin, a sophomore at Beijing Institute of Technology's Department of Mathematics, arrived at PKU's Yingjie Exchange Center Sunshine Hall to grab a seat. Students from PKU and nearby Renmin University and Beijing Institute of Technology also arrived in succession. By 3:30 PM, all 300-plus seats were filled.

At exactly 4:00 PM, Andrew Wiles began his public lecture to applause. On stage, he was no longer given to the contemplative pauses of the interview setting, but was as comfortable and at ease as if returning to his own kingdom. His fluent English had a musical rhythm. In one hour, he reviewed the history of Fermat's Last Theorem and more than 300 years of the mathematics community's brilliant efforts to crack it, then raised some unsolved problems in the mathematical domain, ending with the abc conjecture. The final slide displayed a set of enormous numbers, and a knowing smile rippled through the Sunshine Hall.

In the subsequent Q&A, Liu Qi, a 2003 direct PhD student at PKU's School of Mathematics, asked Professor Wiles why he chose this research topic that took seven or eight years. Wiles answered: "I didn't choose this problem -- this problem chose me." The previous day, he had briefly shared his impression of Beijing with colleagues at PKU's School of Mathematics: the Forbidden City, where the emperor lived, was even more magnificent than he had imagined. However, "I wouldn't want to be an emperor. I'd rather be a mathematician."

Yuan Xili, who graduated from PKU's Department of Mathematics in 1995, happened to be visiting his alma mater that day and encountered this lecture. Standing beside his seat, he listened to Andrew Wiles' entire lecture and said with deep feeling: "This kind of mathematician, who doesn't pursue practical applications and devotes himself entirely to theoretical research, is far too rare in our country right now."

Andrew Wiles' scholarly experience left PKU colleagues deeply moved. CAS academician Ding Weiyue, Director of PKU's Mathematical Research Institute, said: "Professor Wiles spent 7 years specifically tackling a world-class problem. Very few people today can endure such solitude. Many people rush for quick results and instant success. Everyone should learn from Andrew Wiles." Vice Dean Liu Huarong of PKU's School of Mathematics was more blunt: "His spirit of dedication to science is worth learning from."

Some mathematicians raised questions about our research system. Jiang Boju said: "In China, even if someone had the wisdom to solve Fermat's Last Theorem, they probably couldn't succeed. Nowadays everyone is busy coping with evaluations, having to produce quick, short-term results. Much energy and wisdom is wasted."

"A 300-year problem, 7 years of effort -- for us, the evaluations alone would eat up all the time," said CAS academician Wen Lan of PKU's School of Mathematics.

"If someone like Andrew Wiles spent 7 years devoted to one problem without producing results or publishing papers, in China he'd have long since lost his stipend and funding," Zhang Gongqing added.

"At the root, it's still a problem of the science and technology system needing reform," Zhang Jiping summed up in one sentence.

On the morning of August 31st, Andrew Wiles would give a specialized academic lecture at PKU's School of Mathematics, then travel via Hong Kong to receive the 2005 Shaw Prize in Mathematical Sciences and its one million dollar award.

Zhang Jiping called Andrew Wiles' China visit "a major event in the history of Chinese mathematical development."

As Andrew Wiles was about to complete his Beijing trip, he wrote a message for readers of China Youth Daily at the hosts' invitation -- I believe China's young people work very hard. I hope they will have the courage to pursue what they truly love, for dedication to and love of one's career will make them invincible on their journey forward.

Andrew Wiles' message to readers of China Youth Daily:

I believe China's young people work very hard. I hope they will have the courage to pursue what they truly love, for dedication to and love of one's career will make them invincible on their journey forward.

Andrew Wiles