Hua Luogeng, Chen Jingrun, Wang Yuan... Touch the interesting souls of great mathematicians

The 14th International Congress on Mathematics Education, known as the "Olympics" of the international mathematics education community, was recently held in Shanghai, which is the first time that the International Mathematics Education Conference has been held in China since its inception.

Mathematics is the oldest and most active science of mankind, the fulcrum and cornerstone of all science. Today, mathematics has been widely used in various fields of human activities, and has become the leading and driving force of a new round of scientific and technological revolution and industrial change. In the course of the development of mathematics in China, Hua Luogeng, Chen Jingrun, Wang Yuan and others have made outstanding contributions.

Shan Yuan, former director of the Department of Mathematics of Nanjing Normal University, is one of the first 18 doctors in New China, and also the first batch of doctoral supervisors in mathematics education in China and the leader of the discipline of mathematics and problem solving in the competition, and led Chinese middle school students to win the first place in the overall score of the International Mathematical Olympiad (IMO) for the first time. The newly published Anthology of Mathematics and Education in Monohills contains his representative articles on mathematics, mathematics competitions, mathematics education, and the popularization of mathematics. The following is an excerpt from the chapter "Mathematician Friends" in the book, and readers can touch the hard work and interesting souls of great mathematicians from the memories of Shan Yuan.

AnThology of Mathematics and Education by Shan Ji by East China Normal University Press

Hua Luogeng: Going deep and simple is real kung fu

Mr. Hua Luogeng is the Himalayan mountain in the mathematical community of our country.

Mr. Hua's formal education was junior high school, and he relied entirely on self-study, not only reading Hall and Knight's "Big Algebra", which was considered difficult at the time, but also studying university courses such as analytic geometry, calculus, and algebraic equations. In 1929, when Hua Luogeng was 19 years old, he published a paper entitled "A Study of Sturm's Theorem", and the following year published an article entitled "The Reason why the solution of the fifth equation of Su Jiaju's algebra cannot be established", which not only showed that he was familiar with Abel's theory that the fifth equation could not have an algebraic solution, but also directly pointed out that a 12th-order determinant in Su Wen was wrong. It was this article that attracted the attention of Xiong Qinglai, head of the Department of Arithmetic at Tsinghua University, the highest university at that time, and invited him to Tsinghua as an assistant.

After Mr. Hua arrived at Tsinghua University, his horizons were wide open, and he bid farewell to the "research" of the past primary level, and eagerly studied advanced mathematics, especially with Professor Yang Wuzhi. He finished his college courses and started writing in two years. His research took to a higher level, publishing 21 papers in three consecutive years, most of which were published in first-class foreign journals, including Japan's Tohoku Journal of Mathematics and germany's most important mathematical magazine at that time, the German Mathematical Yearbook (Mr. Hua was the second Chinese to publish articles in this journal).

During his time at Tsinghua, he also came into contact with Adama and Wiener, world-class mathematicians who came to China to teach, and learned about the latest trends in mathematics from them. Wiener enthusiastically wrote a letter recommending Hua Luogeng to hardy, a famous mathematician at the University of Cambridge in the United Kingdom.

In order to play a greater role in mathematics and achieve higher achievements, Hua Luogeng gave up the opportunity to be promoted to lecturer at Tsinghua University and went to Cambridge, England to study.

At that time, cambridge university was one of the world's mathematical centers, and analytical number theory was particularly strong, and there and nearby a group of energetic and talented young mathematicians were concentrated, such as Davenpott, Heilbrunn, Esteman, Wright, Titchmarsh and so on. Hua Luogeng said humorously: "Some people go to England, first learn English, then listen to a course, write an essay, and then get a degree." I listened to seven or eight courses, took a thick set of notes, and rearranged them after returning home, carefully digesting them. While at Cambridge, I wrote more than a dozen articles. He also said: "I only have two years of research time, naturally I have to learn more things, write more interesting articles, and it is inevitable that there will be some red tape when I study for a doctorate, which is too wasteful of time." I don't want to go for a PhD, I just ask to be a visiting scholar. I came to Cambridge to seek learning, not for a degree. ”

At Cambridge University, Hua Luogeng made the world's first-class work (such as estimation of complete trigonometric sums, Hua Luogeng inequality), attracted international attention, and reached the first creative peak of his life. Compared with the work at Tsinghua, it has jumped to a higher level.

At this time, Mr. Hua Luogeng had formed his own academic views. No matter which mathematics he is engaged in, he always grasps the central problem and strives to innovate in methods. There is an idiom in our country that "Banmen gets an axe", but Mr. Kehua believes that "if you get an axe, you must go to Banmen". He also said: "People can't say that the Heart of the Yellow River is not dead, and I said that the Yellow River is higher." ”

Mr. Hua is not only "specialized" and "refined", but also "comical", and he can transfer from one research field to another. In addition to number theory, he has also made outstanding contributions to algebra, multivariate functions, matrix geometry, and other fields. In particular, Mr. Hua's unique "direct method" is to use as simple and elementary mathematical tools as possible to deal with some important problems in mathematics. This style is highly appreciated by peers at home and abroad.

Mr. Hua Luogeng attaches great importance to the cultivation of talents and the popularization of mathematics. His influence on the mathematical community in our country is so great that I am afraid that no one can compare with it. To some extent, it can be said that without Hua Luogeng, there would be no modern Chinese mathematics.

In 1950, mr. Hua participated in the preparatory work of the Institute of Mathematics shortly after returning to China. In 1952, he became director of the Institute of Mathematics. He collected a wide range of talents (including Mr. Chen Jingrun, who entered the institute in 1956), and led a discussion class on number theory groups and generation arrays to cultivate research talents.

He also taught at Tsinghua University and the University of Science and Technology of China, giving basic courses to college students and writing lecture notes (later published "Introduction to Higher Mathematics").

Mr. Hua is particularly enthusiastic about the popularization of mathematics, often giving popular lectures to middle school teachers and students and mathematics enthusiasts, and writing some popular science books, such as "From Yang Hui's Triangle", "From Zu Chongzhi's Pi", "From Sun Tzu's Wonderful Arithmetic", "Mathematical Induction", "Ping talk of overall planning method", "Ping talk of preferred method" and so on.

Mr. Hua attaches great importance to the popularization work he has done, and in the outline of the report of the University of Tokyo in Japan, he divides his life's work into two parts: "theory" and "popularization", which are on a par with each other.

Mr. Hua also said: "It is really kung fu to go deep and simple. "His report is a good example of what is easy to understand. In 1964, I heard Mr. Hua's report for the first time. Mr. Hua pays special attention to the audience's demands and receptivity. At the beginning of the report, it said: "There are many people coming today, and I must set the 'tone' well, not too high, not too low." The "tone" he set was indeed just right. That day he first gave the example of a teacup and a lid. Round-mouthed teacups, the lid is also round, slightly larger in diameter. No matter how the lid is placed, it will not fall into the cup. But what if the mouth of the cup is square? Even if the lid is a slightly larger square, it will still fall into the cup. This popular question immediately aroused everyone's interest, fully illustrating that there is mathematics everywhere in life, and life is inseparable from mathematics.

In 1966, Hua Lao came to Nanjing to promote the "two laws" and gave a report at the Renmin University Hall. His Mandarin is very standard, not hurried, the language is humorous and vivid, for example, when it comes to factory tasks, the moon is tight, and he uses analogies such as "Heavenly Girl Scattered Flowers", "Night War Horse Chao", "Xiao He Yue Chasing Han Xin" and so on, which caused everyone to laugh.

In the 1980s, Hua Lao was determined to revitalize mathematics in China. In 1981, the 71-year-old Hua Lao led a huge lecture team to hefei University of Science and Technology of China, accompanied by Wang Yuan, Wu Fang, Yang Le, Zhang Guanghou, etc., and invited Xia Daoxing, Gu Chaohao, Hu Hesheng of Fudan University, Zhou Boxun and Ye Yanqian of Nanjing University, and Gong Sheng, Shi Zhongci, and Peng Jiagui of the University of Science and Technology. There are more than 20 universities in the country, and nearly 100 people are sent to listen to the lectures. Hua Lao himself made four reports, including "Matrix Geometry and Special Relativity", "Geometric Theory of Calculus Equations", "Several Personal Experiences of Popularizing Mathematical Methods", and "Mathematical Methods Used in the National Economy". At that time, people flocked to the lecture hall like a tide, and the audience warmly applauded hualao's report, and the response was extremely strong.

Elder Hua also listened carefully to other people's reports. Once, when Mr. Wu Fang's report used a trigonometric inequality, Hua Lao immediately said, "I will prove this inequality." With that, he got up and went up to the podium on crutches and performed calculations on the spot. It can be seen that although Elder Hua is more than old, his thinking is still very agile, and his childlike heart is not lost, and he likes to show his hand to everyone.

Hua Lao attaches great importance to mathematical competitions. As early as 1946, during his visit to the Soviet Union, he specially inspected the mathematical competition activities, and listened to the lectures given by Kolmodov and Alexandrov to some teachers and students participating in the mathematics competition activities (the topics were "logarithm" and "plural" respectively), and buried in his heart the seeds of China's initiation of mathematics competitions.

In 1956, Mr. Hua wrote an article to cheer "We are also going to engage in mathematics competitions" and advocated the holding of mathematics competitions for middle school students in four major cities: Beijing, Shanghai, Tianjin and Wuhan. Later, due to the interference of the "Gang of Four", the math competition was forced to stop. In 1978, Hua Lao served as the director of the competition committee, presided over the unprecedented scale of beijing, Shanghai, Tianjin, Shanxi, Anhui, Liaoning, Sichuan, Guangdong 8 provinces and cities of the middle school mathematics competition, and presided over the publication of the "National Secondary School Mathematics Competition Problem Solving", Hua Lao specially wrote a 7,000-word "Preface".

What can be comforted is that in the year after Hualao's death, China sent an official 6-member team to participate in the International Mathematical Olympiad (IMO) for the first time, and achieved three gold, one silver and one bronze, and the fourth place in the total score. In 1989, he won the first place in the overall score of IMO. In 1990, the 31st IMO was successfully hosted in Beijing and once again won the first place in the overall score.

Hua Lao has high hopes for the younger generation. He wrote many articles about learning methods and passed on his experience to everyone. He encouraged young people to study hard, repeatedly emphasizing that "wisdom lies in learning, and genius is due to accumulation." When writing an inscription for his alma mater, Jintan Middle School, Hua Laoyu wrote 4 words in a serious way: "Later on top".

Mr. Hua also once wrote an inscription: "Hard work does not count years, self-improvement never stops, learning mathematics is a lifelong thing." He practiced this sentence, devoted his life to mathematics, and bowed to the end of his life until he fell to the pulpit.

Chen Jingrun: Come with a heart, don't take half a blade of grass with you

Mr. Chen does not have an amazing appearance, always so simple, so ordinary. Flat-topped head, wearing a pair of very ordinary glasses, the dark eyes appear slightly larger, turn less, always in a contemplative shape, wandering in the mathematical kingdom.

Mr. Chen is very humble. In the summer of 1984, he lived in Guizhou Nationalities College. We went up to the mountain to visit, Mr. Chen must personally make tea, we even said that there is no need to bother, Mr. insisted on brewing, the water bottle was empty, and then raised the kettle, filled with water, lit the fire, and was busy. We say goodbye and must send it. Because it was night and it was a mountain road, everyone repeatedly asked Mr. to stay, and Mr. reluctantly agreed, standing in the moonlight, watching us leave.

We walked along the winding mountain road for more than a quarter of an hour, and when we reached the foot of the mountain, we were about to get on the road, when suddenly a person ran out from behind, pounced on everyone, and laughed: "I have been following behind, and you have not noticed." "It turned out to be Mr. Chen!"

After 1984, Mr. Chen has been in poor health, suffering from Parkinson's syndrome, staying in friendship hospital for a while, still having difficulty walking after discharge, and unfortunately being hit by a car again. In 1988, I returned from Canada and the United States and went to greet them. As soon as Mr. Chen saw it, he reached out and shook my hand, and said something in his mouth that he couldn't hear clearly. The secretary who accompanied the mathematics institute understood the language of the gentleman and immediately "translated" it to me: "Hello professor. Then the gentleman told me: "Because of the inconvenience of walking, I took medicine and walked better, but it affected my speech." Of course, this passage was translated by the secretary.

I really didn't expect that this would be the last time I saw Mr. Chen.

Mr. Chen's life has been too hard.

In 1957, mr. Chen was transferred to the Institute of Mathematics because his research on the problem of the tower was appreciated by Mr. Hua Luogeng. At that time, my husband was still very young. A lot of excellent work was done in 10 years (1957-1966): the Waring problem was solved by g(5); the study of the integer problem within the circle and the estimation of g(4) also set a "world record" and remained for a long time. Of course, the most famous is the creation of the Chen sieve method, which solves the "1 +2". A summary of this result was published in the Scientific Bulletin in 1966.

So many results, all in a 6 square meter hut, nibbling on dry steamed buns.

Later, I was ordered by the university to ask my husband to give a lecture at the University of Science and Technology of China (I was at HKUST at the time). At this time, the husband had moved, but there were only two small rooms, and he was still single. Mr. insisted on leaving me to eat, and personally made the self-proclaimed "cover rice", that is, a bowl of rice, a poached egg and a number of carrots, probably Mr. Li's usual self-serving food has not been so "hearty". The gentleman also repeatedly proposed "don't buy a soft sleeper, hard sleeper or hard seat", and asked me for a ticket: "Give me the ticket, I will change it into a hard sleeper." ”

Mr. is so frugal, paying so much, enjoying so little, really "holding a heart, not taking half a blade of grass to go."

Wang Yuan: If you can't do it, think slowly

Mr. Wang Yuan is my mentor, and everyone respects him as the Elder.

He mainly studies analytic number theory at the Institute of Mathematics of the Chinese Academy of Sciences, and Mr. Hua Luogeng is good at circular law. The sieve method was just getting started in the world, and the elders studied this new method, and at the age of 26, they used this new method to prove the "3+ 4" of the Goldbach problem, and achieved the best results at that time. The elders also used this method to study the number of Latin squares, and also obtained long-term leading results. He himself said he was young and could do anything.

The elder talked about his own experience in studying and governing, and he said that he did not work hard when he went to middle school, and he watched a lot of foreign movies. When I entered the university, I failed to get into the best university and went to in the University of Ince. However, later the faculties were adjusted and merged to form Zhejiang University. There was a complex function exam, the singularity attribute of the test, only he answered correctly, since then he has been favored by the department, and chose to take mathematical research as the lifelong direction.

The Elder once said that now he was not in a hurry to get caught up in a certain problem, and spent most of his time observing the dynamics to see what meaningful problems were worth doing (he told me many times that too small problems were not worth doing), and what problems could be done.

He gave me a topic, but said to me: "It may not be able to make it, it doesn't matter if you can't do it, think about it slowly." ”

But this question, I have not made it (I feel that I can't start, I think about it and put it down). In 1983, I went to Beijing to attend the first batch of doctoral degree conferences. Thinking of going to see the elder, I felt that it was difficult to explain, so I thought about it overnight on the train, and actually came up with it (fortunately, the train had to drive for more than 10 hours at that time). He was also very happy to see the elder and tell him about it. Later, after revision, this article on Goldbach numbers was co-authored and published in the Acta Mathematica Sinica , No. 1, 1985.

When the elder was the director of the Institute of Mathematics of the Chinese Academy of Sciences, he advocated reform and invited some people to visit. I also jumped to the occasion and read some articles during my visit and made some results.

In 1992, I was invited by the chairman of the Hong Kong Mathematical Society, Shum Ka-chiu, to visit, and it happened that the elders were also there to discuss a problem, and Professor Shum wrote an article, which was recommended by the elders to be published in Science in China.

The elder loved to swim, and one year held a number theory conference in Shandong, and Mr. Pan Chengdong of Shandong University served as the host. Elders often went into the water.

In his later years, the elder loved calligraphy, and once gave me a hand scroll, written by Xin Jiaxuan's words "Qinyuan Chun Lingshan Qi'an Endowment When Zhuyan Lake Was Not Completed", the pen was vigorous and neat.

Column Editor-in-Chief: Gu Xuewen Text Editor: Shi Chenlu Title Image Source: Figure Worm Image Editor: Xu Jiamin

Source: Author: Shan Yuan