Wang Yuan: The beauty and sorrow of pure mathematics

Wang Yuan: The beauty and sorrow of pure mathematics

Reporter/Song Chundan

Published in China News Weekly on May 31, 2021, No. 997

On May 14, Wang Yuan, an academician of the Chinese Academy of Sciences and former director of the Institute of Mathematics of the Chinese Academy of Sciences, died of illness in Beijing at the age of 91.

In the Institute of Mathematics of the Chinese Academy of Sciences, people call Wang Yuan "Elder". One is because of his name, and the other is because he joined the Chinese Academy of Sciences when the Institute of Mathematics was first established, and he is a pioneer in the Chinese mathematical community, especially in the direction of number theory.

Wang Yuan once said that good mathematics is the same as good art, and aesthetics is the first criterion. In his view, the essence of mathematical beauty lies in simplicity, such as the ancient Chinese paper: the rational is simple, the quality is simple, and the god is far away and the hidden is not complete.

Fang Kaitai, a former researcher at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences and who has worked with Wang Yuan for 20 years, told China News Weekly that Wang Yuan is good at describing complex problems in simple language, that is, "avenue to simplicity".

(In his later years, Wang Yuan.) Photo/Courtesy of respondents)

Fang Kaitai said that Hua Luogeng, Wang Yuan, Pan Chengdong, and Chen Jingrun are an echelon of Chinese number theory research, and the Goldbach conjecture research has reached the best level in the world at present. The peculiarity of number theory research is that it may not be fruitful for decades. Fang Kaitai's own field of statistics has big problems and small problems, and can publish papers, but the level of the magazine is different, and the field of number theory is either a major breakthrough or zero. Engaging in number theory does not make money, and it is usually "useless", but once it is useful, it is of great use.

Wang Yuan once quoted the British mathematical master Hardy (Hua Luogeng studied under Hardy when he was studying at Cambridge University): Mathematics without application is good, fortunately it is not applied, otherwise it will become a vassal of other disciplines, and there is no need for independent existence.

"Goldbach conjecture" celestial group

"Goldbach's conjecture is so beautiful that there is no way to solve it yet."

In 1953, Hua Luogeng said this to students in his own Goldbach conjecture seminar. This kind of seminar is a very common teaching method in foreign countries. Hua Luogeng said that this class is not to make them work on this problem, but because the Goldbach conjecture is related to all the important methods of analytic number theory, which can be used as an entry point to learn.

In the seminar class, students take turns to report the designated papers, and Hua Luogeng keeps asking questions, and sometimes the speaker is asked so much that he can't continue to talk, and can only stand on the podium for a long time to think, which is called "hanging the blackboard". Some of the presentation materials were simplified during the workshops, so the workshops proceeded slowly but the participants gained a lot.

The young Wang Yuan works 16 hours a day, and the office and bedroom are combined into one. He described himself as hard as a newborn calf, but gained nothing, and once fell into inferiority and wavering. It was like a person trapped in a dark room, unable to see a little light, not knowing where the door was.

In 1954, Polish mathematicians visited China and brought some Papers by Polish Mathematicians, and that night Wang Yuan used the Buren method to improve part of the results of one of the papers on the function of number theory. The Polish mathematical community attached great importance to it and asked to publish a paper with him. At that time, the central government put forward the slogan of "marching toward science" to the whole country, and this matter was publicized by the domestic media with great fanfare.

Wang Yuan, who tasted the sweetness, also wanted to publish a few more papers, and Hua Luogeng reminded him: "Engaging in mathematical research is like a race, to have speed, there must also be acceleration." The reminder kept him from stopping for a momentary view on the side of the road.

Persistence pays off. Under the guidance of Hua Luogeng, he combined the screening method of the Western mathematician Selberg with the iterative method of the Soviet mathematician Buchsitab to improve the 1940 proof result of "4+4" of Buchsitab and successfully proved "3+4" in 1955. He continued to work hard and proved "2+3" in the spring of 1957. This was the best proof in the world at the time. At this time, Wang Yuan was only 26 years old.

Hua Luogeng was very happy and said: "I really can't imagine that you have made a result in the Goldbach conjecture itself, if you can go further." If you can't, that's all you have for the rest of your life. Unexpectedly, Wang Yuan was unable to go any further in attacking difficult problems.

Li Wenlin, former deputy director of the Institute of Mathematics of the Chinese Academy of Sciences, told China News Weekly that Wang Yuan was the first Chinese mathematician to come to the forefront of the goldbach conjecture. His biggest feature is that he can judge the time and size up the situation, and can choose the right research direction at the right time, which is based on a correct estimate of himself and an accurate judgment of the scientific situation. And this is crucial for a mathematician.

Hua Luogeng originally planned to divide the discussion class into four units, but only completed the first three units, and the "anti-rightist movement" arrived.

In the anti-rightist movement in 1957, Hua Luogeng passed the pass under the protection of Zhang Jinfu and other leaders of the Chinese Academy of Sciences, but since then he has been regarded as a "missed rightist" in the mathematical circles. In the subsequent "raising the white flag and planting the red flag" movement, he became the "great white flag" that mathematics concentrated on criticizing. Chen Jingrun, who he transferred from Xiamen University, became one of the most stubborn "little white flags" and was assigned to the Dalian Institute of Chemical Physics of the Chinese Academy of Sciences to "brush test tubes", and only returned with the support of Hua Luogeng after the climate warmed up in 1962.

Also frequently attending Hua Luogeng's Goldbach seminars was Pan Chengdong, a graduate student in the Department of Mathematical Mechanics at Peking University. When he graduated from graduate school in 1960, Wang Yuan speculated that he might have become a "little white flag" in internal control, so there was no unit in Beijing that wanted him and was assigned to Shandong University.

Wang Yuan said that Hua Luogeng's seminar and the British mathematician Davenport's seminar were at the same level in number theory, and Davenport's seminar produced three Fields Medal winners, but Hua Luogeng's seminar died prematurely. If there were conditions to select talents from all over the country at that time, more talents should have been produced.

The number theory group was abolished, the staff was dispersed, and only a few people privately insisted on the pure mathematical research of "theory divorced from practice", especially Chen Jingrun and Pan Chengdong.

In 1962, Pan Chengdong improved the work of the Hungarian mathematician Renee in an attempt to prove "1+5". He kept writing letters to Wang Yuan to inform him of the progress of his research.

Wang Yuan said that Pan Chengdong is open-minded, indifferent to fame and fortune, does not argue with others, has a good reputation in the mathematical community, and he likes to associate with Pan Chengdong. But he was skeptical of Pan's proof. He said that a mathematician who has done a research work and is hindered often does not easily believe in the progress in this regard, which is a superstition and prejudice against himself, and he has fallen into this "thinking circle" after proving "2+3".

He questioned Pan's proof, and Pan Chengdong explained it, and each other's letters were written at length. During that time, Pan Chengdong only wrote two letters to his fiancée, but wrote more than 60 letters to Wang Yuan, which shows the "fierce struggle".

Finally, indisputable circumstances, Wang Yuan acknowledged pan Chengdong's testimony. In 1963, Pan Chengdong proved "1+4".

Unlike Wang Yuan and Pan Chengdong, Chen Jingrun likes to study alone. Hua Luogeng was familiar with the disposition of his disciples, and once said, "Just let him do it alone." In 1965, Chen Jingrun's work made a breakthrough: he used the sieve method to prove "1 +2".

In 1965 the Soviet mathematician A. A. Vinogradov and the Italian mathematician Pompeini proved "1+3" respectively, not only taking away the record of Chinese, but also widely believed that the use of sieve method to prove "1+3" has come to an end. However, Chen Jingrun was the sieve method of knocking on the bone and sucking the marrow, which proved that 1 + 2. Foreign proofs that "1 + 3" use high-speed computers, while Chen Jingrun is single-handed, completely calculated by hand.

(In 2018, Wang Yuanmishou (88 years old).) From left: Yuan Xiangdong, Tian Ye, Ge Liming, Wang Yuan, Zhang Shouwu, Xu Mingwei, Li Wenlin, Sun Binyong. Photo/Courtesy of respondents)

Chen Jingrun asked Wang Yuan and Peking University professor Min Sihe to review the paper.

Wang Yuan immediately understood Chen Jingrun's thoughts, only about Ah Jingrun. The proof of Vinogradov's theorem is not understood at this point (in fact, Vinogradov later revised his own proof), so it is considered necessary to be cautious.

In 1954, Min Sihe opened a specialized number theory class in the Department of Mathematics and Mechanics of Peking University, and Pan Chengdong was a student in this class. Min Sihe often encouraged students to attend Hua Luogeng's number theory seminars, and the young people in the number theory group of the Institute of Mathematics also regarded Min Sihe as a teacher. Min Sihe, who was seriously ill at the time, risked a heart attack at any time, calculated day and night, reviewed the paper that was more than 200 pages long, and solemnly wrote: The proof of the proposition is correct, the paper is too long, and it is recommended to simplify it.

Guan Zhaozhi also supported Chen Jingrun's publication of the certification results. Wang Yuan wrote in "Hua Luogeng" that as a leading cadre of the party to the mathematical community, Guan Zhaozhi's influence was comparable to or only slightly inferior to Hua Luogeng, and they had both cooperation and contradictions, and the contradictions were rumored to be exaggerated. Guan Zhaozhi had previously been unsupportive of the study of classical mathematics, believing that this was the deviant and narrow circle interest of a few mathematicians, and at best a game of intelligence, especially the Goldbach conjecture. But this time it was he who strongly supported the publication of Chen Jingrun's results. Many people feel puzzled, Wang Yuan believes that there may be contradictions in Guan Zhaozhi's views on classical mathematics in his heart, and perhaps he also suspects that someone has suppressed Chen Jingrun, so he feels that he should come out to uphold justice.

Chen Jingrun took the "last train". The Scientific Bulletin, published on May 15, 1966, published his proof (the paper was not published), and this issue was discontinued due to the arrival of the Cultural Revolution.

Ten years after the Cultural Revolution

On August 20, 1966, the Institute of Mathematics held a conference to criticize Hua Luogeng. In advance, the person in charge of the Preparatory Committee of the Revolutionary Committee of the Institute of Mathematics summoned Hua Luogeng's students Yue Minyi, Wan Zhexian, Lu Qiheng, Wu Fang, and Wang Yuan to a meeting, asked them to make a joint speech, and assigned Wan Zhe to draft the speech first, and Wang Yuan to read it.

Some people also asked Chen Jingrun to do work and asked him to talk at the meeting about how he was introduced to the "white road", saying that he was also a victim as a "revisionist seedling", and it is not too late to realize it now. But Chen Jingrun avoided it from afar. He later said that he couldn't tell who was right and who was wrong, and he didn't say anything anyway.

Wang Yuan believes that it is normal for mathematicians not to be strange, and Chen Jingrun's "strangeness" is caused by the political climate at that time. He seems to be "overwhelmed" all day long, but in fact, he uses to pretend to be stupid to protect himself, and always stubbornly insists on research work.

Movement after movement, Wang Yuan has not entered the library for many years, does not read books, and does not read mathematical magazines. It was not until after the "913 incident" that people went from fanaticism to calmness and quietly entered the business. In 1972, some academic journals began to resume publication.

In 1973, Chen Jingrun submitted the full text of his seven-year-old paper to Science in China. The paper was sent to Min Sihe and Wang Yuan for review.

Wang Yuan saw that Chen Jingrun had simplified the original paper quite simply. Of the more than 200 pages of papers, less than 30 pages remain. The proof structure of the paper is easy to understand, but for the sake of prudence, Wang Yuan asked Chen Jingrun to tell him for three days from morning to night. Chen Jingrun spoke in front of the blackboard, and he kept asking questions until every step was clear.

Wang Yuan was branded in the movement as one of the members of the "counter-revolutionary clique attacking the proletarian command", Chen Jingrun was a "white expert model", and it was risky to support the publication of the paper, but after repeated consideration, Wang Yuan wrote down the review opinion: "No proof of error was found. ”

He later confessed that if it were not for the political situation, this sentence would not have been enough. At that time, he did not give Chen Jingrun's paper a full evaluation, which has always been a major regret in his heart.

In 1974, the book "Sieve Method", co-authored by the British mathematician Hubstein and the West German mathematician Richter, was published, and before printing it, "Chen's theorem" was added as the final chapter, and wrote: "From any aspect of the sieve method, it is the culmination of brilliance." ”

In February 1978, on the eve of the National Science Congress, the People's Daily reprinted Xu Chi's reportage "Goldbach Conjecture" in full, and Chen Jingrun became a national hero overnight.

In 1982, Wang Yuan, Chen Jingrun and Pan Chengdong shared the first prize of the first National Natural Science Award after the Cultural Revolution for their contributions to the goldbach conjecture to prove the work. This is the heyday of the Chinese school of analytic number theory. Fang Kaitai said that Wang Yuan, Pan Chengdong and Chen Jingrun are like relays in the study of the Goldbach conjecture, and one is better than the other.

It was only Hua Luogeng himself, but he never returned to the field of number theory.

As early as 1965, Wang Yuan found that Hua Luogeng's mind was no longer pure mathematics, and he had no interest in studying the applied mathematics of numerical integration, but was bent on publicizing the "double method" (that is, the "optimal method" based on improving the process and the "overall planning method" for improving organizational management) to the workers, peasants, and soldiers. He didn't consult with anyone beforehand and suddenly decided.

A French mathematician once said: "A mathematical theory should be so clear that you can explain it to the first person you meet on the street." Until then, this mathematical theory could not be considered perfect. "But only Hua Luogeng really tried to do that. His footprints have spread all over the country, promoting the "double law". In order to make it clear to ordinary workers, he simplified these two methods and explained them in the most understandable language. Wang Yuan and other students are not willing to give up their work to follow him, and he also expressed his understanding, and he has been doing it for nearly 20 years without hesitation.

But Hua Luogeng's love for pure mathematics did not really fade. Wang Yuan remembered that when Luo Geng, a Chinese during the Cultural Revolution, was hospitalized once, he had a little idea about the Goldbach conjecture, and he hoped that Wang Yuan and Pan Chengdong would cooperate with him, but neither of them responded, because they both knew what it was like.

After the end of the Cultural Revolution, Hua Luogeng had the idea of transferring students together to engage in pure mathematics, but after thinking about it, he gave up. He said with emotion: "Actually, in the past, it was still possible for me to organize you to engage in popularization and theory at the same time. Now, of course, I won't talk about it. ”

Passed on for Hua Luogeng

In 1982, Hu Yaobang wrote back to Hua Luogeng, suggesting that he should not work too hard, write memoirs, and leave the moving experience of his lifelong struggle for science to future generations. Wang Yuan offered to write this book, believing that only he knew best about his mentor, especially his mathematical work.

In 1985, Hua Luogeng was quite weak. He called Wang Yuan home and handed him a biographical reference outline that he had drafted, which was mainly his mathematical work. Soon after, he died.

Wang Yuan felt that if the biography was written in this way, it might only have some reference value for mathematical workers, and ordinary people would not read it. He decided to write as comprehensively as possible, including the historical background and Hua Luogeng's joys, wanderings and disasters.

In order not to be bound by anything, he did not apply for any funding, did not sign a contract with the publishing house, did not find an assistant, and began to write alone. He could only write in his spare time, planning to write one or two chapters a year.

At that time, there was no internet access, and all the materials he collected little by little in the library. He also took advantage of his visit to Chinese University in Hong Kong to check information. The whole process is like finding a needle in a haystack.

He wrote two drafts of the book, the first of which was about 400,000 words, and after writing it, he threw it all over and started all over again. It was his habit that the first draft was only a clear idea and a framework, and the second edition could only be finalized.

He repeatedly verified the people and things at that time to ensure truthfulness. He also did not shy away from some sensitive issues, including the history of his own participation in the critical draft. He wrote that although this was a trivial matter during the Cultural Revolution, and even Hua Luogeng himself had long forgotten it, he himself felt infinite guilt whenever he thought about it. He said: "As a student, the attack on the teacher, even if it is to save his life, is ultimately shameful. ”

He also discussed the mystery of Hua Luogeng's withdrawal from the academic mainstream in his prime years and the popularization of mathematics for 20 years. In his view, Hua Luogeng's choice was not a temporary stopgap measure. Although Hua Luogeng was also criticized during the "Cultural Revolution", he was protected by Mao Zedong and Zhou Enlai very early on, and he could completely practice pure mathematics at home behind closed doors, but his determination did not waver.

Wang Yuan said that Hua Luogeng knows how difficult it is to do mathematical theoretical research, especially for older mathematicians. "Mathematicians are roughly until they are 35 years old" is a well-known mantra, and Hua Luogeng's teacher Hardy said: "Mathematics is more a young man's game than any other art or science." If an old man loses interest in mathematics and abandons it, the resulting loss will not be serious for mathematics or for him personally. ”

As early as the 1950s, Hua Luogeng lamented how difficult it is for a mathematical achievement to be left in history, and sometimes the entire field of mathematics will be eliminated. In a "review", he wrote: His conservative thinking is inseparable from the decline in scientific research work, and he reads only one or two dozen articles every year, and the level of academic thought stagnated in the 1930s and 1940s.

Wang Yuan felt that these words more or less reflected Hua Luogeng's state of mind. He himself has a good understanding of this. He once told reporters that doing science is extremely cruel, and when people can't do it, they will feel crazy. After proving goldbach's conjecture of "2 + 3", he thought of a way out: this result was enough for him to "use" for five years, and after five years, he could not make new results, so he went to teach at a university, even if it was a third-rate university in a foreign country.

But at that time, he probably never imagined that he would spend nearly 10 years writing a biography for his teacher.

In 1994, the 300,000-word Hua Luogeng was published by Enlightened Publishing House.

"If you stop studying, no matter how big your fame is, it will not be worth anything"

Fang Kaitai recalls that his cooperation with Wang Yuan began in 1975.

That year, the Ministry of Metallurgy entrusted the Beijing Iron and Steel Research Institute to identify the rationality of the national standard of alloy structural steel, because to deal with complex production data, the Iron and Steel Research Institute turned to the Institute of Mathematics of the Chinese Academy of Sciences, and Fang Kaitai participated in the project. The study required the calculation of a large number of quintile integrals, which were almost impossible to achieve at computer speeds at the time with traditional methods.

Fang Kaitai thought of Hua Luogeng's 1965 collaboration with Wang Yuan in "Approximate Calculation of Integrals", a number theory method of high-dimensional product formula that has been internationally named the "Hua-Wang method". He asked Wang Yuan for advice, and Wang Yuan took out a collection of papers from the bookshelf and explained to him in detail the simple algorithm "good grid point method". After Fang Kaitai's test, he admired this efficient method.

In 1978, engineers from the Three Academies of the Seventh Aircraft Department encountered difficulties in the project of three missile commanders. Limited by the speed of computer operations, it takes a day to solve the system of differential equations, which is far from meeting the actual needs. Fang Kaitai thought that the number theory method might be helpful, so he found Wang Yuan, who agreed to develop it together, and agreed to meet once a week to discuss.

Three months later, Wang Yuan and Fang Kaitai calculated the first batch of "uniform design tables", which were published in the internal data "Probability and Statistics Newsletter" and submitted to the "Chinese Journal of Applied Mathematics". When submitting, Wang Yuan insisted on using the name of Fang Kaitai and did not participate in the signature.

As a result of the cooperation between the two, "Theory, Method and Application of Uniform Experimental Design" won the second prize of the National Natural Science Award of China in 2008 (the first prize was vacant), which is considered to have created a new research direction.

In 1983, Zhang Shouwu was admitted to the Institute of Mathematics of the Chinese Academy of Sciences to pursue a master's degree. At that time, Wang Yuan believed that the classical analytic number theory he studied had no way out, and encouraged Zhang Shouwu to choose the direction freely, and he chose the problem of arithmetic algebraic geometry, which was rarely asked in China at that time. Wang Yuan was not familiar with the field, but he gave Zhang Shouwu enough freedom and encouragement to tell him how to do research.

When Zhang Shouwu defended his master's thesis, Wang Yuan said: "I don't know what you are talking about, and I can't understand a word, but considering that you come to the office very early every day and work very hard, this master's degree will be given to you." ”

Zhang Shouwu, a mathematician who later became a new generation of Chinese leaders, commented that his mentor Wang Yuan was an "extremely enlightened" teacher, measuring and grandiose. Wang Yuan said that in fact, Zhang Shouwu was his teacher later, and he always asked him for advice. Because if you don't pay attention to and learn new things at the forefront, then no matter how big the fame is, it is worthless.

In addition to researchers at the Chinese Academy of Sciences, Wang Yuan has almost no social part-time jobs. In 1984, he served as the director of the Institute of Mathematics of the Chinese Academy of Sciences, and together with Yang Le, deputy director of the Institute, he made the Institute of Mathematics one of the two institutes open to the whole country of the Chinese Academy of Sciences, and widely invited domestic visiting scholars and trainees to work at the Institute. But he insisted on serving only one term and stopped serving as director in 1987. He was one of the first academicians to apply for retirement, and he was also a member of the Chinese People's Political Consultative Conference who offered not to be re-elected.

In the 1980s, Wang Yuan and Pan Chengdong often had the opportunity to meet. Once, more than a dozen analytic number theorists went to Qingdao for academic exchanges. Wang Yuan recalled that every day when he watched the tide rise and fall, when it was calm, the sea and sky were colorful, and the lonely boat was dotted; when the wind rose, the waves crashed on the shore, and the sound was like muffled thunder. Pan Chengdong is highly myopic, and Wang Yuan will help him to go for a walk on the beach. The two often reminisce about the happy times when letters clashed and climbed the peak of Goldbach's conjecture together.

Wang Yuan is a member of the National Committee of the Chinese People's Political Consultative Conference and Pan Chengdong is a deputy to the National People's Congress, and during the two sessions, the two made an appointment to meet on the right side of the entrance and rest hall of the Great Hall of the People. When the academicians meet, they live together and chat together.

In his later years, Wang Yuan underwent several surgeries for heart, prostate and other diseases, and in order to restore his health, he began practicing calligraphy in 1996. He went from Linyan Zhenqing and Liu Gongquan to Wang Xizhi, Wang Xianzhi, Mao Zedong, and also asked the calligrapher Ouyang Zhongshi for advice. He got up at 5 o'clock every morning to practice writing, and did not quit in winter and summer.

On the evening of March 18, 1996, Chen Jingrun was critically ill. Wang Yuan and Yang Le rushed to the Beijing Hospital to see Chen Jingrun, and this was their last side. At noon the next day, Chen Jingrun passed away.

Wang Yuan said in a letter to the Joint Office of the Faculty of Chinese Academy of Sciences: "Brother Jing Run is gone, and he has been together for forty years and often remembers it. He said that the natural sciences are the "territory" of Britain, the United States, and Russia, and they are very arrogant, adopt discriminatory attitudes towards developing countries and even Japan, and it is not easy to mention work other than them in academic papers, it is difficult to mention them in monographs, and if it is mentioned in textbooks, it is impossible unless it is not mentioned. Chen Jingrun's work was mentioned in their college textbooks and written in their monographs, and it will last forever in history.

At the end of 1997, Pan Chengdong also died. Wang Yuan wrote in "Remembering Pan Chengdong": "Chen Jingrun has only been gone for more than a year, and Pan Chengdong has gone again, leaving a blank and desolate. ”

Now, Wang Yuan was finally with them again. They can share the pure and eternal beauty of mathematics without barriers in the temple of the lovers of mathematics and the transcendent.