The golden generation of mathematics

  "China News Weekly" reporter / Li Mingzi Huo Siyi

  Issued in 2021.4.12, Issue 991 of "China News Weekly"

  On the evening of December 3, 2017, celebrities from the Ames Research Center in Silicon Valley, California, USA gathered. Nearly half of the attendees were founders and investors of well-known technology companies, and the other half were Hollywood movie stars and popular singers. They were all vegetarians. The award ceremony of the Scientific Breakthrough Award, known as the "Scientific Oscar", came.

  Spotlights flickered on the red carpet outside the venue, and many Chinese media were also waiting here.

That night, two mathematicians from China, Yun Zhiwei and Zhang Wei, won the New Vision Mathematics Award of the Science Breakthrough Award.

The Scientific Breakthrough Award was jointly initiated by entrepreneurs from Russia and the United States in 2012. In addition to the three major fields of life sciences, basic physics and mathematics with a single award of up to 3 million U.S. dollars, it also established a New Vision Award for young scientists. The prize is 100,000 US dollars.

  Yun Zhiwei and Zhang Wei are both "post-80s" and are 2000 undergraduate students from the School of Mathematical Sciences, Peking University.

When they were awarded, they were professors at Yale University and Massachusetts Institute of Technology.

At the awards ceremony, the two chose a white shirt with a black suit. Zhang Wei wore a black bow tie, and Yun Zhiwei wore a blue tie with white polka dots. Yun Zhiwei joked with reporters at that time: "Mathematicians usually don’t Chances are to dress so handsome."

  The reason why Yun Zhiwei and Zhang Wei won the award was because they discovered that they proved the high-order Gan-Gross-Prasad conjecture in the function domain.

The "equation" they verified connects the two quantities of geometry and number theory. The "Quantum Magazine" wrote that the collaborative research between Yun and Zhang was "one of the most exciting breakthroughs in the important field of number theory in the past three decades." .

"The most glorious time" is here

  The starting point of their collaborative research can be traced back to the winter of 2014, also in California on the West Coast of the United States.

In an interview with China News Weekly, Yun Zhiwei recalled that the "basic lemma of arithmetic" raised by Zhang Wei in the first half of 2009 was the key to their subsequent cooperation. "It triggered all subsequent developments." Yun Zhiwei said .

In response to Zhang Wei's "Basic Lemma of Arithmetic", Yun Zhiwei proposed some geometric solutions, which have been partially verified, but he is not sure if this is generalized to number theory.

He asked Zhang Wei this question in 2010, but the other party was unable to answer it. Until 2014, Zhang Wei accidentally came into contact with several subjects in his research and suddenly realized that Yun Zhiwei's ideas could be realized in number theory.

  In the winter of 2014, Yun Zhiwei went to Berkeley, California to participate in an academic event on geometric methods and number theory at the Institute of Mathematical Sciences (MSRI), while Zhang Wei went to the 60th birthday meeting of mathematician Michael Harris. Yun Zhiwei and Zhang Wei’s undergraduate classmates Yuan Xinyi has been teaching at the University of California, Berkeley since 2012 and has served as the host of this meeting.

After graduation, the three got together again.

  As soon as Zhang Wei and Yun Zhiwei met, they said that he knew "what to prove".

That night, Yun Zhiwei used geometry to test some simplified situations and thought it was feasible.

During the four or five days of the meeting, the two quickly "fast-forward" to "how to prove". Yuan Xinyi found a blackboard in Berkeley for them to keep calculating.

The gathering in the winter of 2014 started the formal cooperation between Yun Zhiwei and Zhang Wei a few months later, and they cleared customs along the way, opening up the connection between the two quantities of number theory and geometry.

  Also in 2014, on the other side of the U.S. mainland, 28-year-old Chinese mathematician Sun Song was working as a teaching assistant at the State University of New York at Stony Brook. He and his fellow professor and tutor Sun Xiuxion, and the highest international award in the field of mathematics—Philippines The winner of the Erz Prize and British mathematician Simon Donaldson also made a major breakthrough.

  Their research should start with physics.

String theory in theoretical physics believes that the universe is a ten-dimensional space-time, but these complex high-dimensional spaces must be "Keller-Einstein metric".

To this end, the Italian mathematician Calabi proposed the "Calabi Conjecture", that is, the complex high-dimensional space is "sticked" together by multiple simple multi-dimensional spaces, which means that the high-dimensional space can be passed through some simple geometric models. Get assembled.

In 1975, Qiu Chengtong and others conquered the "Karabi Conjecture" in which the Chen class was negative and zero, but only when the problem of the first Chen class being positive could the "Kaller-Einstein metric" be confirmed.

This "Qiu Chengtong Conjecture" that has plagued the international academic community for decades was finally broken by Chen Xiuxiong, Donaldson and Sun Song in 2014.

Five years later, the three jointly won the Veblen Geometry Award, the highest honor in the field of geometry and topology.

  Sun Song's brother Wang Bing was teaching at the University of Wisconsin-Madison.

It just so happens that in 2014, after five years of research between Wang Bing and his tutor Chen Xiuxiong, they proved the two core conjectures of "Hamilton-Tian" and "Zero-Order Estimation", which have been unresolved in the international mathematics circle for more than 20 years. Their results are predicted After the printed copy was posted on the academic website, it caused shocks in the industry.

After a series of twists and turns, the article was published in the top international mathematics journal "Journal of Differential Geometry" in 2020. Donaldson praised this research as "a major breakthrough in the field of geometry in recent years."

  At that time, Sun Song’s undergraduate brother Chen Gaogang came to the United States for two years and was also studying for a Ph.D. under the guidance of Chen Xiuxiong. At that time, he was studying the "Gravitational Instanton" problem raised by Hawking in 1977. This is Hawking's unification of the physics world The mathematical problems raised by the model are of great significance in the mathematics community.

Chen Xiuxiong and Chen Gao solved this problem in 2015, and Chen Gao, who was only 21 years old at the time, was recognized by the international mathematics community.

  At the beginning of this year, Chen Gao returned to the Center for Geometry and Physics of the Chinese University of Science and Technology and was hired as a special-appointed professor.

In March, Chen Gao published an article announcing that he had solved the J equation independently proposed by Chen Xiuxiong and Donaldson, and the deformation of the supercritical Hermit-Yang Zhenning-Mills equation proposed by Qiu Chengtong and others. Chen Xiuxione commented that his research work is "excellent" Imagination".

In an interview with the media, Chen Gao, who was thin and wore a blue and white plaid shirt, casually explained that these two equations describe physical phenomena as large as the cosmic scale and as small as the quantum scale. There is a communication bridge between the physical equations, and my own research results are equivalent to providing a new communication path.

  In 2018, at the International Conference of Mathematicians in Rio de Janeiro, Brazil, 12 Chinese mathematicians were invited to give a 45-minute report. Among them were 5 mainland scholars and 7 mathematicians from mainland China who went overseas, Yun Zhiwei, Zhang Wei, and Sun Songjun. Be among the invited.

The 1-hour conference report (Plenary) and 45-minute report (Session) invited by the conference are generally considered to represent the most significant achievements and progress in recent mathematical sciences. Therefore, this is undoubtedly a high degree of affirmation of their work by the international mathematics community.

  Ten years ago, Zhang Shouwu, a Chinese mathematician and current professor of mathematics at Princeton University in the United States, said in an interview, “I know about 10 people, they are very smart, and they are the same generation... We are almost the same! They are the future of Chinese mathematics, and in their era, it should be the most glorious time of Chinese mathematics."

  At that time, Zhang Shouwu listed several names like a few treasures, including Yuan Xinyi, Yun Zhiwei, and Zhu Xinwen who graduated from Peking University. These young mathematicians have now almost won all the international mathematics that young mathematicians can obtain except the Fields Medal. Awards.

Nowadays, there are more than a dozen new Chinese mathematics stars shining in the mathematics sky. Wang Bing, Sun Song, Chen Gao and others who graduated from the University of Science and Technology of China have also emerged in the international mathematics circle.

"The most glorious time of Chinese mathematics" in Zhang Shouwu's mouth is approaching.

Talent "is nothing more than the result of a lot of time accumulation"

  After the meeting in the winter of 2014, Yun Zhiwei and Zhang Wei formally started working together in February of the following year. The two intensively discussed each step of the proof and their respective tasks.

Yun Zhiwei cuts in from the perspective of algebraic geometry. Zhang Wei is in charge of number theory. In the dark, the two walked along two originally unrelated paths. Suddenly one day, they met each other.

There are many phenomena in the function domain, which do not actually exist in the number domain. However, Yun Zhiwei and Zhang Wei found that the higher-order derivatives of the L function have geometric meaning, which is a unique phenomenon in the function domain.

  The so-called L function, in 1967, mathematician Robert Langlands proposed: "Three relatively independent branches of mathematics: number theory, algebraic geometry, and group representation theory are actually closely related, and the links between these branches of mathematics Links are some special functions, called L functions." This idea of ​​trying to unify the major branches of mathematics is also called the "Langlands Program."

  The Cray Institute of Mathematics in the United States put forward the "seven major mathematics problems in the world" at the dawn of the millennium, offering a reward of one million dollars for each problem. Two problems are related to the L function, and the BSD conjecture is one of them.

And Yun Zhiwei's research is directly related to the BSD conjecture.

  The core of the BSD conjecture is to solve the cubic indeterminate equation (elliptic curve). Mathematicians only care about the first non-zero coefficient of the L function, but Yun Zhiwei and Zhang Wei found that not only the first non-zero coefficient, but also every subsequent expansion The term coefficients are meaningful.

"It was equivalent to a formula to prove, but now there are n formulas to prove, making the entire field richer, discovering more phenomena, and doing more problems." Yun Zhiwei said.

  They searched for a deep path that no one had ever walked in the vast mathematics garden. As for where it led, no one knew.

Looking back, Yun Zhiwei feels that breaking the inherent thinking mode is a very difficult process. Sometimes it takes long enough to settle and accumulate until the inspiration breaks through.

In May 2015, the big difficulty was basically solved, but Yun Zhiwei was still stuck in the last step.

In the end, he "understood" the result a month later, thanks not only to a mathematical intuition, but also partly to his early training in mathematics competitions.

  "Olympics is like fighting, training is the ability to meet short-handedly. This ability not only lies in the expansion of the tool library, but more importantly, it can train a kind of'death' spirit." Yun Zhiwei explained, because no matter what method is used, This problem must be solved. If a solution does not work for half an hour, you must break through from a different direction. You cannot always follow the known system in the past. You must constantly generate new ideas and find the literal title. There is no method shown in the above, which to a large extent requires imagination, or in other words, the ability to quickly grasp the nature of the mathematics behind the problem, which can also test a person's mathematical ability.

  Yun Zhiwei, born in 1982 in the famous Yun family in Changzhou, Jiangsu, discovered that he was good at mathematics when he was in the third grade of elementary school.

At that time, the math teacher would leave a difficult math problem on the blackboard every day. Most of the time, he was the only one in the class who could do it.

The feeling of "solving problems that others cannot solve" made him addicted. Moreover, compared with Chinese, the certainty contained in mathematics also fascinated him. The answer to mathematics is only right or wrong, yes or not, clear structure, and orderly. distinct.

  Therefore, Yun Zhiwei began to participate in Mathematical Olympiad in the fourth grade of elementary school. In junior high school, almost all of his spare time was immersed in Olympiad questions. By the third year of junior high school, Yun Zhiwei participated in the Senior Math Olympiad League in advance, and was selected into the National Middle School Math Winter Camp for the next semester, but stopped In the training team.

In the second year of high school, he tried again, entered the national team, and won the gold medal in the 41st International Mathematical Olympiad, becoming the only player in the Chinese team to get a perfect score that year.

In September 2000, Yun Zhiwei, who was not in the third year of high school, was directly sent to the Peking University Academy.

  In Wenzhou, Zhejiang, another "post-90s" genius teenager also came to the fore through a math competition.

Wenzhou is the "hometown of mathematicians", which has nurtured many academicians such as Su Buqing, Gu Chaohao, Jiang Boju, and Li Banghe. According to statistics, in the past 100 years, there have been at least 200 Wenzhou professors in the field of mathematics.

Born in such a soil, Chen Gao also showed an interest in mathematics when he was a child. At the age of four, he realized the law of multiplication of "head and tail together".

Chen Gao's father, Chen Qianlin, was elected as one of the top ten education news figures of the year in Wenzhou, and is a well-known local primary and secondary school principal.

As a teacher, Chen Qianlin cared for and guided Chen Gao's interest in mathematics, allowing him to indulge in the game of "placing matches" and "placing chopsticks", without forcing the children to learn other specialties.

  In 2006, 12-year-old Chen Gao entered the high school of Rui'an Middle School in Zhejiang Province with the first prize of the provincial mathematics competition. Two years later, he entered the junior class of the Chinese University of Science and Technology with a score of 84 points or more and was accepted. Early admission.

  Although the Mathematical Olympiad has developed abnormally in China, many famous mathematicians at home and abroad have grown to become famous in the cradle of Mathematical Olympiad.-Australian-born Chinese mathematician and Fields Medal winner Tao Zhexuan was 10, 11, and 12 years old. Participated in three International Mathematical Olympiads, winning bronze, silver, and gold medals respectively; Russian mathematician Gregory Perelman, who has solved the Poincaré conjecture but refused to receive the 2006 Fields Medal, was the number one in the 1982 Olympiad. Name; 2010 Fields Medal winner, Vietnamese mathematician Wu Baozhu, was the gold medalist of the Olympiad in 1988 and 1989.

  Ma Zhiming, President of the Chinese Mathematical Society and academician of the Chinese Academy of Sciences, once pointed out that various competitions in China, including Olympiad, are too utilitarian. However, Wu Baozhu, Tao Zexuan and others won gold medals in Olympiad because of their interest in mathematics. .

  In the teenage years of these young mathematicians, the "Olympics" has become an indelible collective memory.

According to Yun Zhiwei's memory, about one-third of the 2000 students from Peking University School of Mathematics came in through the Olympic Winter Camp. Other than that, the others had some experience in competitions.

Several Mathematicians who graduated from Peking University who are familiar with Yun Zhiwei, such as Liu Ruochuan born in 1980, Xu Chenyang, Zhang Wei, Yuan Xinyi and others born in 1981, are also competition students, basically all from the national team, and the lowest is also training. team.

Fortunately, they have shown a talent for mathematics that surpasses their peers since they were young, and their heartfelt love for mathematics is also the original motivation that supports them on the path of mathematics research.

  What is talent?

"It's nothing more than the result of a lot of time accumulation." Chen Qing, a professor in the Department of Mathematics of the Chinese University of Science and Technology, concluded.

In the eyes of many students, they don’t understand the problem for half a day. Talented children like Sun Song and Chen Gao will take a look at it, but what everyone didn’t see was that before the question was raised in class, They have spent a lot of time researching.

"The best way is not to teach,

Is to put them together and grow naturally"

  Sun Song and Chen Gao, who were born in the Junior Class of the University of Science and Technology of China, are regarded as "a genius who will only meet one in three to five years."

Wang Bing said that in the junior class, Sun Song's grades were almost always the first. After arriving at the University of Wisconsin in 2006, Sun Song's graduate courses were basically all full marks.

  "In previous junior classes, such children with mathematics talent are not just Sun Song and Chen Gao, but not all geniuses are suitable for mathematics. In the long-distance mathematics race, in addition to being interested and talented, work hard and persevere. Keeping the rhythm is the most important thing. You must be able to calm down and sit still." Chen Qing recalled that he had served as the director of the juvenile class management committee and the deputy dean of the School of Mathematical Sciences.

Sun Song was admitted to the Junior Class of the University of Science and Technology of China from Huaining Middle School in Anqing, Anhui Province in 2002.

When Sun Song was in his junior year, Chen Qing organized a seminar for students majoring in mathematics to discuss academic papers. At first everyone was very interested, but in the end, only Sun Song persisted.

  Contrary to Yun Zhiwei and Chen Gao, although Wang Bing was also born in the Junior Class of China University of Science and Technology, he considered himself not a "talented" player and even doubted whether he was suitable for basic mathematics research.

When he was studying in the United States, Wang Bing once went to the University of Pennsylvania to participate in an event, and he visited "Master" Calabi.

He asked the other person, "Is it necessary to have a good talent to do math?" Calabi answered him "of course" without hesitation, as if he was saying, "How could you ask such a question?"

After Wang Bing went back, he was depressed for a while, but he soon figured it out again: Mathematics is his best field. He has achieved his personal optimal solution, and there is no point in making too many comparisons.

As long as I can continue to study the math problems I am interested in and train more students, it is also a very meaningful job.

  Wang Bing, who was born in Tongyang Town, Chaohu City, Anhui Province, was from an ordinary family and his parents were not well-educated.

In 1998, 16-year-old Wang Bing was recommended to the Chinese University of Science and Technology Junior Class College with the first place in the college entrance examination score of Chaohu No. 1 Middle School.

The University of Science and Technology of China has always retained the tradition of "emphasizing the foundations of mathematics and science". After enrolling undergraduates, regardless of major, they must study mathematics, physics and chemistry in the first two years.

In order to determine his professional direction, Wang Bing also took popular courses such as computer, software, statistics, etc., but these did not suit his appetite.

In the two directions of physics and mathematics, Wang Bing found that he was not good at doing physical experiments, and finally chose the better mathematics.

  In 2002, after the Russian mathematician Perelman confirmed the Poincaré conjecture, he originally planned to continue to use relevant tools to confirm the "Hamilton-Tian" conjecture, but he retired for personal reasons and did not continue to study.

In 2003, Wang Bing went to the University of Wisconsin-Madison to study for a Ph.D. Instructor Chen Xiuxiong encouraged Wang Bing to continue to explore along Perelman's direction.

Before graduating from his Ph.D., Wang Bing had already proved the "Hamilton-Tian" conjecture in two dimensions under the guidance of Chen Xiuxiong.

  Whenever the research is not going well or in a bad mood, Wang Bing goes to exercise, and also learns to swim and play badminton.

Because of these movements, Wang Bing got acquainted with his PhD in economics from the same school and his later wife Wang Xiao.

"I didn't fall in love when I first learned to swim, but it really became our common hobby after falling in love." Wang Bing said.

  Originally, Wang Bing planned to work hard to prove this conjecture in a higher-dimensional general situation.

When graduation was approaching, Chen Xiuxiong advised Wang Bing, "You have entered a very dangerous situation", worrying that he would fall into the pit of verification conjecture and affect his career.

Wang Bing followed the advice of his supervisor, postponed his research, published several papers for job hunting, and applied for the post of lecturer in the Department of Mathematics at Princeton University after his doctoral degree.

In the summer of the second year after joining Princeton, Wang Bing picked up the work of proving the "Hamilton-Tian" conjecture he had in mind. In 2012, he returned to the University of Wisconsin-Madison as an assistant professor in the Department of Mathematics, and his research has never stopped.

Until the beginning of 2014, Wang Bing and Chen Xiuxiong lasted five years and finally completed the proof of the "Hamilton-Tian" conjecture and solved the partial zero-order estimation conjecture in the same article.

  Wang Bing, who is now a professor at the Center for Geometry and Physics of the University of Science and Technology of China, recalled the life of the Junior Class and was very grateful to the school’s mechanism and atmosphere that allowed students to fully experiment and freely choose their majors, and he also made a choice that followed his heart. Let yourself go all the way to today.

When Chen Gao recalled the experience of the Junior Class, he also said that the teacher only outlines some key points, mainly relying on students to learn by themselves, and this mode of self-study happens to be what he is best at.

Chen Qing also pointed out that for talented students, the best way is not to teach, but to put them together and grow naturally. For example, in seminars, let the students discuss and learn from each other, and the teacher can point out the key points. .

  The seminar is also the place where Yun Zhiwei gained the most in his four years at Peking University.

During his undergraduate course, Yun Zhiwei focused on self-study, and most of the professional courses had completed all the knowledge points by himself before he took the class.

Peking University School of Mathematics has set up some small seminars for senior undergraduates and graduate students. The number of students is generally less than 10. They focus on a topic or choose a monograph to study. Each student takes turns to give lectures. Teachers and other students can interrupt and discuss at any time. Ask a question.

These seminars are also open to the lower grades, and there are no thresholds, and interested students can choose freely.

Limited by the difficulty of learning content, not many students go to the senior seminars in their freshman and sophomore years, but Yun Zhiwei, Zhang Wei, Zhu Xinwen and others are a few exceptions.

  In the fall of 2002, Tian Gang, director of the Beijing International Mathematics Research Center of Peking University and academician of the Chinese Academy of Sciences, opened a seminar on geometry at Peking University. Most of the participants were juniors, seniors, and graduate students. There were only two sophomores. : Yun Zhiwei and Zhu Xinwen.

He was very impressed by these two people. Nearly 20 years later, Tian Gang recalled to China News Weekly that he organized students to read a postgraduate textbook "Spin Geometry", and at the beginning only Yun and Zhu were in charge of the opposite. The simple chapters were later found to be unnecessary. Their level is very strong compared with that of senior undergraduates, even better than many graduate students.

Tian Gang wrote very few letters of recommendation every year, but when Yun Zhiwei and Zhu Xinwen went abroad, Tian Gang wrote letters of recommendation.

  Yun Zhiwei also organized a discussion group on algebraic geometry with Zhu Xinwen, Xu Chenyang, and Liu Ruochuan, once a week, each lasting at least two hours.

Among the four people, Xu Chenyang and Liu Ruochuan are seniors in 1999, and Yun and Zhu are 2000 students.

At that time, everyone had a "dead" attitude and was bound to read a book.

Looking back now, Yun Zhiwei felt that this form of self-study helped him even more, because the four of them had similar interests and similar backgrounds, so they were much better at running-in.

Yun Zhiwei said that if there are more people in the seminar, the level will be uneven and efficiency will be affected.

  At that time, the four-person seminars were like guerrillas, and empty classrooms were found in the third and fourth buildings of the college.

What impressed Yun Zhiwei most was that once, when Xu Chenyang was talking about a sudden power failure, he proposed to speak blindly, so he continued.

"It seems that there are really very few things needed to do mathematics. You only need to think. It doesn't matter if you don't have electricity." Yun Zhiwei recalled.

  At that time, there was a good run-in with Yun Zhiwei, as well as classmates Zhang Wei and Yuan Xinyi at the same level.

They often eat together, talk about math, listen to lectures, and exchange ideas.

These few people who later became the "Golden Generation" in grade 2000 unconsciously formed a kind of "circle of a few people" like ancient Greek philosophers in their school days. There is a wall between them and the outside world, but inside them, mathematics It's no longer a matter of one person.

  Zhang Shouwu said with emotion: "The success of this group of people is really very strange. So many people suddenly appeared in one session. This kind of phenomenon has not happened before, and it has not happened afterwards. It is amazing because they are not alone , But a group of people. They called their classmates right away if they didn't understand something. The classmates were also masters in another industry and knew what was going on right away. They were not competitors but collaborators. "

  "The geniuses of the Peking University School of Mathematics are not cultivated, but protected." Academician Zhang Pingwen, a professor at the School of Mathematical Sciences of Peking University, once said.

In his opinion, people who are engaged in basic mathematics research must be talented and sentimental.

The important mission of an educator is to find such talents, protect them, and create the most suitable environment for them to grow freely.

"Turn China into a factory for transporting mathematicians"

  At the beginning of modern Chinese mathematics, the channels for receiving Western knowledge were very limited. It mainly relied on individual mathematicians to bring in Western theories after returning to China, so there were obvious characteristics of intergenerational inheritance. For example, Xiong Qinglai studied function theory, and Hua Luogeng was analytic number theory. , Chern is a differential geometry.

Therefore, before the reform and opening up, the domestic mathematics circle studied analysis, geometry and other directions. These are the mainstream mathematics directions in the West that have a history of hundreds of years. However, due to the lack of international exchanges for a long time thereafter, some The frontier field is not understood.

It was not until 1975 that Yang Le learned that a problem raised at the International Conference on Function Theory in London in 1964 was solved in a 1965 article by him and Zhang Guanghou, but "we didn't even know about this meeting at that time." Yang Le Say.

  By the time Yun Zhiwei’s generation was in college, with the popularity of the Internet and China’s increasingly frequent foreign exchanges, cutting-edge knowledge in the fields of algebraic number theory and algebraic geometry began to be introduced to China. For example, Qiu Chengtong held a period at Zhejiang University. The summer course is about self-abiding form and Langlands program.

Yun Zhiwei and others gradually felt the comprehensive things such as number theory, and found them very fresh. This was something that could not be seen in the curriculum system of Peking University at that time, so they had a keen interest.

"So, several of our close students have chosen the same general direction," Yun Zhiwei said. In terms of academic direction, compared with domestic academic predecessors, perhaps it is more appropriate to use the term "transition generation" to describe their past few years.

  "How should Chinese mathematics develop? How can Chinese mathematics have several advantages in the 21st century? The method is very simple. It is to cultivate talents, find capable people to do mathematics, and find outstanding young people to develop in mathematics. "In 1992, Chinese mathematician Chen Xingshen pointed out when looking forward to the development of mathematics in China in the 21st century, because China’s current level of mathematics still lags behind that of foreign countries, if you want to cultivate your own mathematics talents, you must turn China into A factory that transports mathematicians, hopes that those who go out can come back, if they don’t, I suggest that they continue to send them.

China has talents, and it is worth sending some to exert influence in the world.

  Going out is a tradition in the Chinese mathematics world.

In 1969, Yau Chengtong graduated from the Department of Mathematics of the Chinese University of Hong Kong. Before graduation, he was determined to study abroad.

"To become a first-class scientist, you must always go to Europe and North America." He recalled in his autobiography "My Geometric Life". After graduating from his undergraduate degree, he applied to the University of California, Berkeley, where the mathematics department was among the top in the world. , And finally chose to learn from Chern.

In 1976, 27-year-old Qiu Chengtong conquered the world mathematics problem "Karabi Conjecture", and he won the Fields Medal for this.

Chen Xiuxiong, who graduated from the Department of Mathematics of the University of Science and Technology of China in 1987, obtained a doctorate degree from the University of Pennsylvania in the United States seven years later. He is a close disciple of the famous geometer Calabi.

  More than two decades later, a new generation of young mathematicians is still practicing the development path of following the world's best mathematicians.

In 2004, after graduating from undergraduate, Yun Zhiwei went to Princeton, USA to study for a Ph.D. Zhang Wei went to New York to study number theory with Zhang Shouwu, a well-known Chinese mathematician and professor of mathematics at Columbia University.

Yuan Xinyi had graduated a year earlier and also entered Zhang Shouwu's school.

In 2004, Yun Zhiwei went to Princeton with Xu Chenyang, a senior who was one level above him, just in time for the last year of the five-year undergraduate and master degree, and graduated at the same time as Yun.

  More than ten years later, the offices of Yun Zhiwei, Zhang Wei and Xu Chenyang are in the same corridor. On the fourth floor of Building 2 of the Massachusetts Institute of Technology, Yun Zhiwei only needs to walk through an L-shaped corridor to ring his old classmate Zhang Wei’s The office door, in the meantime, just passed the room of brother Xu Chenyang.

  During his Ph.D. study in Wisconsin, Wang Bing often went to Chen Xiuxiong's home to "cook meals".

Sun Song was 20 years old when he arrived in the United States, and Chen Gao was even younger when he was studying for a Ph.D. He was only 18 years old. Both were taken care of by Chen Xiuxiong and his wife Tao Dongqing.

Tao Dongqing's father, Tao Maoqi, was the first director of the Management Committee of the Chinese University of Science and Technology Junior Class.

Just as Chen Qing expected, Tao Dongqing and Chen Xiuxiong created a more welcoming living environment for these young and undetermined children, minimizing the pressure of survival outside of learning and cultural conflicts, thereby minimizing the pressure on them. Focus more on your own academic research.

  Yun Zhiwei also mentioned the importance of the work environment.

He said that if mathematics researchers want to make great progress, they need three things: a stable teaching position, a moderate standard of living, and a working environment where they can concentrate on thinking for a long time.

  Yun Zhiwei feels that the older generation of mathematicians has a more ethnic complex, and will always have a mood to compare with foreign countries.

Many of them have gone through hardships and are eager to improve China's mathematics strength. However, the younger generation of mathematicians do not have such historical burdens and are generally more international, focusing on academics, hoping to have outstanding results.

  Yun Zhiwei believes that modern mathematics has developed to a crossroads. After the professional subdivision after the 1960s, the trend of connection and unification has inevitably begun. Many major discoveries are "using tools in one field to solve problems in another field." , Both the intuition of geometry, the intuition of number theory and the intuition of representation theory are needed, and cooperation becomes inevitable.

  In May 2015, the collaboration between Yun Zhiwei and Zhang Wei was still stuck in the final step.

One day, Yun Zhiwei was chatting with Stanford Mathematics Professor Vinkates, he suddenly asked how to deal with similar problems in number theory. Vincatesh gave him a number theory technique that he often uses.

"He talked to me for about 5 minutes. I went back to the office and thought about it. After half an hour, I think I can basically get through." Yun Zhiwei said.

  In addition to cooperating with Yun Zhiwei, Zhang Wei also cooperated with Yuan Xinyi and Zhang Shouwu.

Zhang Shouwu, Zhang Wei, and Yuan Xinyi jointly established a simulation of the Valspur's thermal formula under arithmetic and algebraic geometry. The Valspur's thermal formula is also related to the L function.

Zhang Shouwu later called this cooperation "a once in a lifetime."

In the eyes of his teacher, Zhang Wei's thinking is leaping and unconstrained, with a lot of ideas. Yuan Xinyi has a calm personality and solid basic skills. He is used to looking for counterexamples before drawing conclusions.

The two have their own strengths, and they work together to complement each other.

  Yuan Xinyi received the Clay Research Award from the Clay Institute of Mathematics the year he graduated from Columbia University, and was the first Chinese to receive this award.

After that, he moved to Princeton, Harvard and Columbia, and spent eight years at the University of California, Berkeley.

In January 2020, Yuan Xinyi decided to return to his alma mater and is now a professor at the Beijing International Mathematics Research Center of Peking University.

  After graduating from Columbia University, Zhang Wei also went to Harvard for a period of postdoctoral and researcher, and then returned to Columbia University. At the age of 34, he became a tenured professor of mathematics at Columbia University. He joined MIT in 2017.

Before winning the "New Horizons Mathematics Award", he was awarded the Ramanu Gold Award for the most promising young mathematicians at the age of 29, and the "Morning Award for Mathematics" at the age of 35, which was sponsored by the World Congress of Chinese Mathematics (ICMM) The mathematics awards issued every three years are called "Chinese Fields".

After graduating from Peking University, Zhu Xinwen spent most of his time on the West Coast of the United States. He has obtained tenure at the California Institute of Technology and was promoted to full professor in 2016.

"Cultivating mathematicians who lead the development of mathematics around the world"

  Yun Zhiwei does not have WeChat or a smart phone. He is still holding a Nokia candy bar when attending various awards ceremonies.

Initially, he was afraid that his mobile phone would interfere with his thinking. Now he is used to this kind of "quietness."

However, during the epidemic, the two children were at home, and Yun Zhiwei only had a relatively quiet time at night.

Apart from taking care of the children, he spends the rest of his time thinking about mathematics, and an average of eight or nine hours a day is spent on mathematics.

He jokingly said: "We have very low demands on life. If we send the children away, the world will be peaceful."

  Not long ago, Yun Zhiweigang and Zhang Wei completed a new cooperation.

Now, at a fixed time each week, he will have a video conversation with Zhang Wei. Of course, not every time he gains, but they will use their intuition to correct which direction they want to go in the next step.

Perhaps, at the next "crossroads", they will meet again.

  Chen Gao usually works at work and home. He spends most of his time doing mathematics research. Qiu Chengtong and his mentor Chen Xiuxiong have repeatedly told him to "decline interviews" and "concentrate on things."

Every Saturday morning, Chen Gao will communicate new research progress with Chen Xiuxiong online. He is now collaborating with Chen Xiuxiong to study one of the core problems of geometry raised by Calabi in 1954-the constant quantity relation curvature Keller measurement problem .

  After Wang Bing returned to the University of Science and Technology of China, he also opened a seminar. This semester was every Tuesday and Thursday afternoon, with a classroom and a blackboard. Everyone took turns to give lectures.

The students in the seminar are not limited to the University of Science and Technology of China. Some are high school students who have participated in independent enrollment and have completed their own university courses. There are also sophomores and juniors who have completed graduate courses in advance, and some have already applied for graduate studies in the United States. Of graduates, but because of the epidemic, they rented an apartment near the University of Science and Technology of China and come to seminars every week.

  Chen Qing is a 1978 student of the University of Science and Technology of China. He has been teaching since graduation. According to his memories, with the reform and opening up, the demand for talents in the computer and financial fields has increased, and the number of students studying mathematics has visibly decreased.

According to Chen Qing's recollection, in the early 1990s, the University of Science and Technology Department of Mathematics had the least number of students in a year with only 23 students.

  Around the millennium, China's economic development level has been greatly improved compared to the 1980s and 1990s.

Tian Gang pointed out that out of economic considerations, many students from the Mathematics Department of Peking University in the 1980s and 1990s went abroad to study finance or chose banks and other high-paying institutions in China to work.

But by the 99th and 00th grades, many students choose to enter the Mathematics Department of Peking University because of their true love for mathematics.

At this time, Peking University's teaching staff and the completeness of curriculum design have also been greatly improved compared with the previous stage, which can better cultivate students' interest in mathematics.

  According to Yun Zhiwei's recollection, there were more than a dozen people who were still engaged in pure mathematics research from that time to the present. This is a maximum no matter when compared with previous or later sessions.

Tian Gang also said that from the perspective of the curve, it is indeed possible to see "an obvious mountain" during the period from 1999 to 2002. There have been several top talents in the subsequent sessions, but the number is not as large as these sessions. The younger generation is still growing up.

  In January of this year, Li Yu, a doctoral student trained by Wang Bing in the United States, will return to China and join the Center for Geometry and Physics of the Chinese University of Science and Technology.

"Compared with when we were studying, Wang Bing and his generation have a more systematic, scientific, and consistent mathematics education. They generally have working experience in first-class academic institutions overseas, and they have a good mathematical taste and vision." Chen Qing commented. .

In Wang Bing's view, the level of undergraduates at the University of Science and Technology is much higher than when he was studying 20 years ago, and some individuals have even reached the level of graduate students in prestigious foreign universities.

  How to evaluate the performance of young Chinese mathematicians such as Yun Zhiwei, Zhang Wei, and Sun Song?

Qiu Chengtong replied with the rationality of a mathematician: “Achievements in mathematics and science are objective and have scientific evaluation standards. Young people have done important things now, but the final conclusion must be evaluated by time. Five years or ten years, looking back at the importance of these tasks."

  Qiu Chengtong, who has lived overseas for most of his life, now focuses his work at home and focuses on cultivating young people.

At the end of last year, he began to carry out Qiu Chengtong's Leading Talents Training Program in Mathematics at Tsinghua University, recruiting students from all over the world with outstanding mathematics potential and talents at the middle school level, from undergraduate to doctoral level.

Qiu Chengtong said that it will take another ten years to reach the level of keeping pace with American mathematics.

  At the 8th World Congress of Chinese Mathematicians in 2019, Qiu Chengtong once concluded: "In the future, the development of Chinese mathematics will be an important turning point. Whether mathematics is applied or not, pure mathematics is important. We must challenge the world's best-in-class mathematics. Science requires training mathematicians who will lead the development of mathematics around the world."

  China News Weekly, Issue 13, 2021

Statement: The publication of the "China News Weekly" manuscript is authorized in writing