Yan was born in Yanjiafan Village, Huangshigang, Macheng County, Hubei Province,1April, 969 1929. His grandfather was a scholar in the Qing Dynasty and liked mathematics. He has a good understanding of the ancient books on elementary mathematics such as Eight Lines Preparation (Trigonometry) and collected a number of arithmetic problems.
1930, Yan moved to Wuhan with her mother and two sisters to live with her father who was a middle school teacher. He went to school at the age of 4 and lost his mother at the age of 7. 1937 When War of Resistance against Japanese Aggression broke out, the whole family returned to their hometown and studied in a private school for two years. 1940 only entered Huangtugang Primary School to attend high school. A high school student who didn't want to be conquered did it. Under the difficult conditions of lack of information and printing equipment, he collected all kinds of arithmetic application problems (including "a set of arithmetic problems" left by Grandpa Yan) for the students to do, which aroused great interest of the students. Some of them can still be recited lang lang. For example, "Today, some people take wine for a spring outing, and when it comes to fog, they double the wine and spend three buckets and four liters. It's foggy today, and the wine is empty. " Another example is "a hundred heads and a hundred monks". At that time, he became interested in mathematics.
1942 In the spring, Yan went to Huanggang County Junior High School, which is far away from home. The school is located in a group of ancestral halls near Lipodun Town, Huanggang County. It is surrounded by mountains, with little money and bad environment, but a group of teachers are unwilling to teach in enemy-occupied areas. Most students work hard and their studies are very active.
One thing impressed him deeply. At that time, they studied experimental geometry for a semester (that is, using some intuitive explanations, simple models or experiments to let students understand and remember some properties of geometric figures), and then learned plane geometry. When learning the logical proof of geometric theorems, students always use intuitive imagination instead of logical proof. Mr. Wang, the geometry teacher, gave a question in the mid-term exam: "It is known that the two base angles of an isosceles triangle are equal. Prove that the three internal angles of an equilateral triangle are equal. " Then he left the classroom. The students took the opportunity to discuss loudly. At first, they couldn't understand it clearly. After discussion, they basically understood. Finally, the teacher came back and said it again, and finally knew what geometric proof was.
There are three places in high school. 1945 entered the Second Senior Middle School of Hubei Province in the autumn of Huanggang Sanjieyuan (near Sanlifan), 1946 transferred to Xiabahe, Xishui County, Hubei Province, 1947 transferred to Wuchang Senior Middle School in Hubei Province until graduation. There is no connection between the courses, and trigonometry has been studied three times. It was reorganized after War of Resistance against Japanese Aggression. At that time, Mr. Chen Huazhen, who taught Yan Sanjiao and algebra, attached great importance to mathematical proof, especially in algebra class, and corrected the wrong concept that "algebra is a calculus problem and only geometry can prove it". Teacher Chen's edification laid a solid foundation for him to engage in mathematics work.
During the winter solstice of 1947 and the last half year of summer high school of 1948, he suffered from lung disease and missed some classes. However, Wu Gao's teacher thinks that his study is actually one of the best, especially in science. The academic director of the school gave him one of the only two walks in Hubei Province and recommended it to Beiping Normal University (now the predecessor of Beijing Normal University). Soon, the People's Liberation Army surrounded the city .40100.00000000005 Gunshots are often heard. Zhao Cigeng, who taught him calculus at that time, was advised not to attend classes. Zhao was unmoved. In class, the students listen carefully. Not only did he not neglect his studies, but he also learned how to cherish learning opportunities. In the first year of college, he also studied Lonnie's coordinate geometry in combination with the review class of elementary mathematics. Drayson's Analytic Geometry and A.A. Albert's College Algebra, written from a modern point of view, initially exercised the ability of self-learning English professional books.
In the second grade, their class moved from Shihuma Street Branch to the headquarters outside Heping Gate. There is a wider academic world. Fu, then head of the department, was entrusted by the Ministry of Education to hold a one-year training course for key middle school teachers. Fu attached great importance to the improvement of academic level, and invited mathematicians from Peking University, Tsinghua and Beijing to give lectures almost every time, no less than 20 times. Yan attended every lecture. The topic he got from Zhang was "Geometric drawing can't be done". From Cheng Minde's speech, I know that real numbers still need to be constructed. Chen Jinmin's speech made him understand the existence of non-Euclidean geometry; Su talked about differential geometry and used tensors from the beginning. Although he doesn't understand, he knows that there are tensors besides vectors, which are very useful for differential geometry ... Various lectures have broadened his horizons, and he knows that mathematical knowledge is like a vast ocean with endless things to learn, which has aroused his enthusiasm for learning. Shortly after Hua returned to China, he gave a semi-homomorphic speech with several young teachers at Peking University Institute of Science (now Higher Education Press).
Shortly before liberation, Fu came back from an investigation in England and brought back many new books. At that time, because there were few students, the department reference room was open to students. Yan often browses in the reference room. At first he didn't know what books to read, so he asked young teachers and senior students. Yuan and Liu Shaoxue are his seniors. In order to learn German, Yuan introduced him to read "Fundamentals of Analysis" by E Landau, which he finished in a winter vacation of his second grade. He also translates. In order to lay a solid foundation of mathematical analysis, Liu Shaoxue suggested that he read Pure Mathematics. G.H. Hardy Yuan also told him, "It is good to say that S. paul mcshane's' integration'." He borrowed it, too He also read Te Li Wood's Lecture Notes on Real Variable Functions and K Knoop C C Du Fei's Vector and Matrix and Complex Variable Functions. Most of these books have not been finished, but he has exercised his self-study ability and explored some self-study methods. After learning that "extensive reading is not very rewarding", he carefully read the complex function part of marche's Fund Theory by E.C. Teach and most of Vander Waals's Modern Alcher Bra, and made notes and exercises. If he doesn't understand, he asks, ask anyone you meet. Like Duan Xuefu, Wang Hemin, he has asked many times. Duan Xuefu applied to give lectures on modern algebra to senior three students, Wang gave them lectures on modern algebra, Min Sihe and the theory of real variable function, Tang Zaozhen gave lectures on vector analysis and Fu gave lectures on geometric basis. He listened carefully. He thought that by listening to different teachers talking about the same content, he could learn new content and different ways of thinking.
In the second semester of Grade Two, Yan attended the seminar on environmental theory organized by Zhang Yuan University and read "Tree Rings with Minimum Conditions". Author e. a ding. Zhang asked him to report an important theorem that is not easy to understand. At first he didn't understand it, chewed it repeatedly, and finally understood it. He didn't take the manuscript at the seminar, but made it clear from beginning to end, which won unanimous praise from teachers and classmates.
In the early days of liberation, Yan took an active part in many political activities. He taught the PLA soldiers arithmetic, worked as a food committee member of the Student Union, and was responsible for reading newspapers to kitchen workers. Sometimes he goes early, but before the kitchen workers finish cleaning up, he takes the time to read professional books. When the parade stopped, he also took out his book to read. Some people say that he is backward. The secretary of the Party branch said, "We need talents from all walks of life to build a new China."
At that time, Yan had no other source of income except scholarships and no money to buy books. Fu, the dean of the department, found him a job as a substitute and proofreader. Later, even if he didn't have a job, he was given some pocket money from the manuscript fee earned by the teacher. He used all his money to buy math books. He never buys new clothes. He wore Japanese heel-less socks, and when they were worn out, he asked, "How do you wear them on your ankles?" During 1948, I received cotton-padded clothes from YMCA, which were used as raincoats in summer and cotton-padded clothes in winter until graduation.
Looking back on college life, Yan thinks that although she learned a lot of professional knowledge and lacked systematic guidance, she was able to get in touch with many famous scholars and more professional books, which broadened her horizons and improved her interest. Insisting on self-study, I have experienced self-study exercises from extensive reading to intensive reading, strengthened my self-study confidence and perseverance, gained self-study experience and improved my self-study ability. He felt it was a pity that he learned too little professional knowledge during his college years, and some contents were out of date at that time. In addition, there is almost no training in scientific research, which cannot be said to be some defects. Therefore, he has always hoped to strengthen students' professional training at the university level. This is very important for the growth of outstanding talents. Now, although he is over 60 years old, he still undertakes professional basic courses. 1952 after graduation, Yan mastered the ability of reading Russian professional books by participating in Russian surprise study, and participated in the translation of Soviet mathematics textbooks organized by some teachers of Fu. Some chapters of Algebra and Elementary Functions and Elementary Algebra have been translated successively. 1952 school year, he also tutored mathematical analysis, co-taught the review and research of elementary algebra, and taught high school solid geometry in the No.1 Middle School Attached to Beijing Normal University.
1in the spring of 953, the Ministry of Education entrusted Zhang to run a "teacher training class", which was tutored by Sun Yongsheng. Towards the end, Sun stayed in the Soviet Union, and Yan did not hesitate to take over the tutoring work. Then in the autumn, he enrolled in the first algebra research class. Yan then tutored Zhang. He tutored the foundations of modern algebra, linear algebra over rings and volume theory. He also tutored Min Sihe's elementary number theory in these two classes. Zhang is very careful in preparing lessons, connecting the preceding with the following, and his concept description is very accurate, which has benefited him a lot. Many students in the first algebra research class graduated early, and the content of their studies was relatively old. It is not easy for them to accept the abstract concepts and strict training of modern algebra at once. In order to make students understand these concepts correctly, we should choose topics in strict accordance with Zhang's requirements, set out in strict accordance with the definition and deduce them step by step. Zhang also invited the students to give lectures one by one. During this period, Zhang's words and deeds had a subtle influence on Yan, and he exercised himself in teaching.
1952, the state sent a group of young people to stay in the Soviet Union. Fu was far-sighted and advocated that all those who could be sent should go. 1952- 1955, six people were sent to study in the Soviet union, which was the first milestone in the development of the mathematics department of Beijing Normal University. Later, it proved that these people came back and played an important role in the development of the department. Yan can't stay in Suzhou because of her family background. Fu introduced him to Min Sihe, a part-time math and theory teacher at Normal University, and told him: "You should learn from the old gentleman first, and then create after learning well. Once Mr. Min doesn't come to part-time math and theory classes, you can take over. " He didn't expect much. In the process of serving as Min's teaching assistant, he devoted himself to researching methods and teaching art. On this basis, he wrote the Lecture Notes on Number Theory. In 1954, Min announced that "Yan can teach the course of number theory". He not only took over Min's class, but also cooperated with Min on the basis of the lecture notes to complete the manuscript of Elementary Number Theory, which was published by People's Education Publishing House. 1982.
1953, Hua held a seminar on "Introduction to Number Theory" at the Institute of Mathematics, and taught it himself. The Central Organization Department agreed to participate strictly, and Fu also said hello to the Chinese side, hoping that he would pay more attention. There are many difficulties in attending the seminar. He has a lot of teaching work, and other members are full-time students. Moreover, the traffic was inconvenient at that time, and it took six hours to go back and forth from the two-hour seminar. Several times, he went to the Institute of Mathematics. The seminar was suspended. China couldn't bear to let him make a trip in vain, so he talked to him alone. He was taught: "Don't learn too much, don't compare the quantity of learning with the people in the Institute of Mathematics, and really understand." Hua has long been a famous mathematician, but he respects the questions raised by young people. In a speech, Yan found that she couldn't take a step, and put it forward on the spot. Hua thought about it and felt that he was right. After re-preparation, he talked about the relevant part. From then on, he paid more attention to him, which further encouraged his habit of asking questions. He learned the attitude of "everyone is equal before science" from the older generation of scientists. When reading the contents of the integer matrix in Introduction to Number Theory in the discussion class, Yan also suggested that besides the method in the book, there is another method to represent the general normal square matrix with generators. Hua attaches great importance to this problem, and further puts forward: since there are two methods, can all irreducible identities of generators be found out and become the definition relations of module groups? Yan worked on this issue for six or seven months. Except after class, he keeps calculating from 8 am to afternoon 1 1 every day. When we meet every week, Hua asks, "How's it going?" Once he thinks he has succeeded. At that time, China was holding a scientific planning meeting. When he knew the news, he immediately called him to the meeting place. After Yan went, he said with great regret that something was wrong. His six or seven months' efforts were completely in vain, and he wanted to back down. Huaan comforted him and said, "Never mind, we'll think of another way. Failure is the mother of success. " Yan continued to think from the matrix. Once again, I thought it was finished. I was going to report in the discussion class in the afternoon, but I found something was wrong at noon. This problem had to be put aside temporarily (later, the completeness of the definition relationship of modules was proved by matrix method in 196 1. He reported this result at the Longwang Temple meeting in 196 1, and Teacher Min praised "you have done this problem cleanly and thoroughly". Unfortunately, it was in 80 years.
However, seven or eight months' efforts were not in vain. Yan knows the properties of matrices like the back of his hand, and has mastered the operations of matrices. At that time, Wan Zhexian told him that he had solved the automorphism problem of linear groups on main rings and left ideal subrings. Inspired by this, he further considered the automorphism of linear groups over general commutative rings. First, he extended the linear group on commutative ring to the linear group on quotient body by embedding. The second is to make full use of the generator identity familiar in the previous paragraph to determine the image form of the generator under automorphism. By these two methods, the automorphism problem of special linear groups generated by flat extension is solved. This is the first international research achievement on the automorphism theory of typical groups over general rings. It was nine years earlier than the publication of the related achievements of Milla School. Its abstract was first published in Science Record of 1957 with the title of "commutative linear groups over an integral ring" and Journal of Mathematics of 1965 with the title of "linear groups over a ring". This method was later fully used and highly praised by J. Ponfort and B. R. McDonald in the United States. R), r a local ring "(TAMSVol. 173( 1972), 379-388).
It is said that "O'Meara and Yan respectively studied the automorphism of general linear groups over the whole ring" and "we determined the automorphism according to strict methods". B.R.McDonald commented in the paper "Automorphism of GL(n, r)" and the monograph "Geometric Algebra over Local Rings": "Historically, three main methods or techniques have been developed to describe the automorphism of typical groups: (a) involution, (b) Omera school or residual space method, (c) matrix method or China school (. The effectiveness of this highly computational argument lies in directly dealing with the matrix and its elements, which makes it easier to accommodate the greater fluidity of scalar rings, that is, allowing zero factors. " In addition, the Soviet Union published Selected Works of Typical Groups on the Ring in 1970s, which was included as the representative work of China School.
Then, the homomorphism problem of the generated symplectic groups is solved in the same way strictly, and his paper "Symplectic Groups over Commutative Rings" is completed. After the Cultural Revolution, he sent this achievement to Omira. O 'meara added: "It seems that the automorphism of symplectic groups over rings is done strictly first."
1956 In late August, People's Daily, Guangming Daily and China Youth Daily reported on Yan and a group of young mathematicians. At the same time, due to his outstanding teaching achievements, he was awarded as an activist of Beijing youth socialist construction this year.
When the work of "Linear Groups on Rings" was completed, Yan was already a graduate student in China. He said with great appreciation to the students' achievements: "Nothing grows! You keep trying. If there is no better job, this article is enough for graduate thesis. "
Before and after the first national science plan of 1956 was formulated, Hua Zeng said to Yan: There may be a deep connection among the geometry of numbers, quadratic forms and multiple repeated variable modulus functions, which is a direction worthy of serious study. Yan, a graduate student who entered China, hopes to cooperate with him in this field. Later, Beijing Normal University sent Yan back to school and terminated his postgraduate study, which naturally lost a very valuable learning opportunity for Yan.
Under the situation of 1958 "Great Leap Forward", the Institute of Mathematics has conducted extensive discussions on the research direction of mathematics. At that time, some proposed to put the study of mathematics problems in the important task of national construction to promote the development of mathematics discipline; Some propose to develop mathematics by studying mathematical problems in cutting-edge technology; Some people think that the development of mathematics is mainly to create and accumulate effective methods and tools, so it is effective to ask questions about the object of mathematics from a new angle or to conduct in-depth research on some essential problems only if a group of people concentrate on making systematic achievements in a certain direction. Polish mathematics has such characteristics between the two world wars, and so on. Of course, these views are only Yan's understanding. The discussion atmosphere was very warm. These discussions and various academic activities of the Institute of Mathematics of the Chinese Academy of Sciences also influenced him and formed some opinions. He believes that young mathematicians must do certain scientific research as soon as possible, so as to acquire scientific research ability. However, most of the results they started to do were practical. They must be interested in doing problems that are really useful for the development of mathematics and put forward some new ideas and methods. He thinks that if China's mathematics is to be influential in the world, it is necessary to form some world-class academic groups and have systematic research results. In order to achieve these goals, it is an important measure to learn from the experience of advanced mathematics groups in China and hold seminars continuously. These views profoundly influenced his later academic activities.