When Yan Zhida was 7 years old (1924), she entered a rural primary school in her hometown. At that time, education in China was very underdeveloped. There are only four-year primary schools in rural areas and only senior primary schools in county towns. The county seat is twenty or thirty miles away from home. Yan Zhida will go to high school after graduating from primary school, which is too far from home. His mother is very uneasy about children who are only eleven or twelve years old. As it happens, the county education bureau plans to set up one in a town near Yan Jia. In addition, the county education bureau entrusted Yan to be responsible for the preparation. Due to strict efforts, this high school was successfully completed soon. The principals and teachers employed were very serious and responsible, and the books and equipment were quite good. So Yan Zhida was able to enter the school nearby. He usually lives in school and goes home on weekends and holidays.
Yan Zhida's childhood education comes not only from school, but also from family and self-study. Yan Zhida not only accepted the new ideological trend and new education, but also was influenced by China's excellent traditional culture. His father has many books, most of which are a subset of all kinds of inscriptions, classics, notes and novels, calligraphy and painting, but there are also a few scientific books, such as geometry and physics. Yan Zhida liked these books very much when he was a child. I also gradually understand the contents of some books. The wonderful and fantastic Strange Tales from a Lonely Studio and the vivid Historical Records made young Yan Zhida deeply moved and fell in love with literature and art, and the thoughts and feelings of the authors of these books also had a great influence on his later life. Today, Yan Zhida's love for literature and art has not diminished, and he still often reads classical literature and history books, which is quite insightful.
1930, Yan Zhida entered the junior middle school class of Tongzhou Normal School in Jiangsu Province. In junior high school, he became interested in mathematics. One of his cousins gave him a junior high school mixed mathematics in the summer vacation of senior one. This is a * * * 6 junior high school textbook with mixed contents, which breaks the boundaries of arithmetic, algebra, geometry and triangle. After the appropriate content, it is accompanied by biographies and portraits or photos of important mathematicians. Can stimulate teenagers' interest in learning. Yan Zhida read the book in one breath during the summer vacation. From this, he knows that there is much more interesting and challenging knowledge besides his father's library. In junior high school, apart from normal study, Yan Zhida had to do an extra-curricular problem every day. For example, the title in "Geometry Proof Method" written by Yan Jici before studying abroad (Commercial Press, 1923).
Yan Zhida studied in Nantong Middle School, a very good school. During middle school, he was interested in mathematics, physics and chemistry, but what he learned most after class was mathematics. Besides, he is interested in physics and chemistry because he thinks they are the most wonderful applications of mathematics.
Yan Zhida, a middle school student, had a passionate love for mathematics and was determined to enter the door of mathematics. 1936, Yan Zhida was admitted to a public student in the Physics Department of Tsinghua University, which is a scholarship to reward students who have good grades and need financial aid. In this way, Yan Zhida, whose family economy is not rich, was able to enter the university smoothly.
1On July 7, 937, the Lugouqiao Incident occurred. Japanese imperialism launched a full-scale war of aggression against China. Later, when Peiping and Tientsin fell, Tsinghua and other schools were dissolved and moved south. Yan Zhida broke through the enemy blockade and fled to Nanjing to return home. In that autumn, Peking University, Tsinghua University and Nankai University established a temporary university in Changsha. Yan Zhida heard the news and rushed to Changsha from his hometown to continue his studies. At this time, the Japanese army entered Changsha on a large scale. Wuhan fell. At the beginning of 1938, Temporary University decided to move to Kunming, Yunnan. After arriving in Kunming, it was renamed Southwest United University. 1938 In the spring, Yan Zhida participated in a walking group composed of more than 300 teachers and students of the Temporary University. Zhang Zhizhong appointed a lieutenant colonel, a lieutenant colonel and a major to accompany the delegation. After two months' trekking, the trekking group traveled thousands of miles to The National SouthWest Associated University, Kunming. The National SouthWest Associated University at that time.
Because of his love of mathematics, Yan Zhida transferred from the Department of Physics to the Department of Mathematics (now the Department of Mathematics) when he was at National Southwest United University. Wu was the head of the physics department at that time, and he deeply regretted the departure of those ambitious people.
Kunming is located in the southwest border, with underdeveloped cultural and educational transportation and poor living conditions. However, due to the fall of the Central Plains, a large number of intellectuals took refuge here, making Kunming once the scientific and cultural center of China. The National SouthWest Associated University, in particular, has a group of young professors who have recently returned from abroad. Most of them are excellent talents who have studied in important academic centers abroad. After returning home, they became the backbone of teachers and introduced the most advanced scientific knowledge to China at that time, thus attracting many young students.
At that time, the most famous and creative mathematicians in China gathered in Kunming to teach in The National SouthWest Associated University. Among the young professors are Chen Shengshen, founder of Nankai Institute of Mathematics, honorary director of Nankai Institute of Mathematics, academician of American Academy of Sciences and foreign academician of China Academy of Sciences. ), China (returned from Cambridge University, UK), Jiang Shuomin (returned from G? ttingen, Germany, now a professor at Beijing Normal University), etc. They set up many courses and discussion classes in The National SouthWest Associated University, which were at the forefront of mathematical research at that time and were extremely important branches of mathematics (such as modern algebra, number theory, differential geometry and functional analysis, etc.). ) The seminar on differential geometry hosted by Professor Chen Shengshen systematically introduced the geometric theories of blaschke and E.Cartan, among which Lie group theory is the most important. Blaschke is a professor at the University of Hamburg and an outstanding geometer. His work is very extensive and original. He visited China on 1932. From 10 to 10, Chen Shengshen studied with him and obtained a doctorate. He also suggested that Chen should study Cartwright in Paris, France. There is no doubt that e Cartwright is "one of the greatest mathematicians of this century". His mathematical works can be roughly divided into three categories: group theory, differential equations and differential geometry. But in his works, these contents are often intertwined. Almost everything he does is related to Li's theory. Chen Shengshen studied with him for a year. And then returned to China to teach in The National SouthWest Associated University. The algebra seminar hosted by Hua introduced the representation theory of typical groups. Li Qun Seminar co-founded by Physics Department, Professor Hua and Professor Wang Zhuxi in 1939 is "advanced at home and abroad". According to Chen Shengshen's memory, Yan Zhida was the only student who attended these seminars from beginning to end. In addition, Jiang Shuomin teaches functional analysis courses such as integral equations and variational methods. Jiang Zehan opened the seminar.
The courses of Topology and Quantum Mechanics offered by Wang Zhuxi are both courses that Yan Zhida is very interested in and benefited a lot from.
Yan Zhida's diligent study spirit is not only praised by teachers, but also admired by students. Pontrya, a Soviet mathematician and academician of the Communication Society of the Soviet Academy of Sciences, published the first edition of Continuum Group in 1938 and the English version in 1939. Yan Zhida studied the book carefully. According to Yan's classmates, he even sat down.
Yan Zhida laid a solid foundation in mathematics in National Southwest Associated University, satisfied his desire to enter the mathematics gate in middle school, and embarked on the road of mathematics research here. Because of his intelligence, diligence and the guidance of famous teachers, he showed his creativity in mathematical research when he was in college. He published his first paper in collaboration with Chen Shengshen. The basic formula of integral geometric motion obtained in this paper is called "Chen Yan formula" by MIT Mathematical Encyclopedia. This formula has also been included in the mathematics volume of Encyclopedia of China (version 1988). Later, Chen Shengshen did a lot of in-depth research in this field.
194 1 In September, Yan Zhida graduated from the Department of Mathematics of Tsinghua University and later taught at Yunnan University. 1June, 946, Yan Zhida was admitted as a Sino-French exchange student. After a period of preparation, Yan Zhida embarked on a journey to France in June, 45438+0947. Yan Zhida went to the University of Strasbourg to study for his Ph.D., and studied under Professor C. Ehresmann, a famous topology and differential geometer. There are Lieberman, Wu Wenjun, Tian Fangzeng and Yu Jiarong. He is a student of e. Cartwright. I have a deep understanding of e Cartwright's theory. At that time, he was the main professor at the University of Strasbourg. He is very enthusiastic, cares about his students and is close to his family. Because of his advocacy, the academic activities of the University of Strasbourg are also very active. For example, J.A.Schouten, hopf, G.Derrhum
On 1948, Yan Zhida was employed as an assistant researcher at Centre National Dela Recherche Science, and returned to China on 1952. 1949. Yan Zhida obtained the highest degree in France-Docteuré s Sciences). With excellent results.
During the French period, Yan Zhida made an in-depth study on the topology of Lie groups and the geometry of surface clusters (the geometry of paths-the generalization of the geometry of paths), and obtained many important results.
The determination of Betti number of Lie groups is a basic problem of Lie groups. Mathematicians R. brower and Pontryagin determined the Betty number of a typical Lie group. However, the determination of Betty number of special Lie groups is unparalleled, which "puzzles many leaders in this field" (Chen Shengshen's words). Yan Zhida applied the representation theory of Lie groups to study the topological properties of Lie groups and homogeneous spaces.
1950 In the summer, the World Congress of Mathematicians was held in Harvard University. C.Cheval-ley, one of the founders of Bourbaki School, gave a speech at the meeting. As soon as he came to power, he wrote three Chinese characters "yen chi-ta" (Yan Zhida's French spelling) on the blackboard. A pearl of China's mathematics shines brightly in the global mathematics field. Yan Zhida is indisputably among the mathematicians in the world. Professor Chen Shengshen said: "Zhida has studied the topology of Li Qun. Monument. " When Duncan, a Soviet mathematician, introduced the development of the Soviet Union in Lie Groups in Forty Years of Soviet Mathematics (19 17- 1957), he also specifically mentioned Yan Zhida's achievements in this respect.
During Yan Zhida's stay in France, the research results on the equivalence of quadratic external differential were also remarkable. The work in this field was later popularized by the Polish mathematician Sle-bozinsky. Professor Vranceanu, a mathematician and academician of Romanian Academy of Sciences, wrote this result in 1957' s book Leons de geom trie différentielle or Lectii de Geometrie Differentiala a. In 2002, Yan Zhida resolutely gave up with a strong desire to revitalize China and develop the cause of mathematics in the motherland.
After Yan Zhida returned to China, he conducted research and personnel training in the Lee Group. Lie groups are not only closely related to various branches of mathematics (especially modern differential geometry), but also have essential relations with theoretical physics and chemistry. Therefore, Lie groups not only occupy an important position in mathematics, but also play an increasingly important role in the whole natural science. Lie group is undoubtedly one of the mainstream directions of mathematics. Nowadays, almost all mathematics departments in American universities list Lie Qun and Lie Algebra as postgraduate courses. Although it needs to be popularized by domestic mathematics graduate students and college students, it is also included in the key research projects of mathematics. In 1930s and 1940s, some mathematicians in China, such as Li Qun, Hua, and later Duan Xuefu, all worked on Lie Qun or related fields. But generally speaking, there are few people engaged in this research, and Lie Qun is still a weak field in China. Yan Zhida clearly saw this situation after returning to China and decided not only to inherit China's points here.
Great fine tradition, further carry forward; At the same time, we should cultivate advanced talents in differential geometry, Lie groups and Lie algebra for the new China.
From 1952 to 1965, Yan Zhida made a thorough and systematic study of symmetric spaces, real semi-simple lie groups and real semi-simple lie algebras. 1959 published the article "Classification and Angular Representation of Real Simple Lie Algebras", which greatly simplified the previous work. Moreover, this achievement has many applications. It is worth mentioning the Soviet Union. In 1960 and 1963, the structural problems of real semi-simple lie groups are solved. Yan Zhida himself used this achievement to study the local classification of noncompact symmetric spaces, and solved a very basic problem raised by French mathematician M. Berger in this study, thus successfully solving the extremely important classification problem of noncompact symmetric spaces raised by a generation of geometric master E. Gardiner. Unfortunately, the western mathematicians at that time knew little about Yan Zhida's work because he had little communication with western mathematicians. It was not until 1965 that Nobuyuki Murakami, a Japanese mathematician, got a similar result about the classification of real semisimple Lie algebras again. Later, Nobuyuki Murakami learned about Yan Zhida's works and admired him very much. When the French mathematician J. Tits gave a speech at 1988+0987, the first academic conference of train groups in China, he boarded the platform and used it.
From 1952 to 1965, Yan Zhida has also made gratifying achievements in the cultivation of advanced mathematics talents and curriculum construction. At first, he offered Lie Groups and Lie Algebra courses in the Department of Mathematics of Nankai University, and organized seminars on Lie Groups and Differential Geometry among graduate students and teachers (especially young teachers). These are rare in China, and he is also very enthusiastic about academic exchanges between domestic universities and research institutes. In 2008, he was also enthusiastic about academic exchanges between universities and research institutes.100000000005 At the request of Fudan University, Yan Zhida gave a report on Lie Groups and Symmetric Riemannian Spaces for more than a month. According to these reports and the research results he just got at that time-the classification and automorphism of real simple Lie algebras (see later results), Yan Zhida wrote a book Lie Groups and Differential Geometry. This book is not only Yan Zhida's first book, but also China's first book on Lie groups and differential geometry (mainly symmetric Riemannian spaces). This has greatly promoted the study of China Lie groups and symmetric Riemannian spaces. In order to better teach Lie Groups and Lie Algebras and further study the representation theory of Lie Groups and Lie Algebras, Yan Zhida wrote the Representation Theory of Semi-Simple Lie Groups, which is the first book in China to discuss the representation theory of Lie Algebras and Compact Lie Groups, based on the specialized lectures of geometry algebra given by Nankai University 196 1 962. This book has been included in the bibliography of Lie Algebra by China Encyclopedia of Mathematics. At the invitation of Institute of Mathematics, China Academy of Sciences, Yan Zhida reported his research results in real semi-simple Lie Algebra .46666.66666666666 His report inspired many young mathematicians and embarked on the road of studying Lie groups. His report was later compiled by Jiang Jiafu (currently the deputy director of the State Ethnic Affairs Commission and a graduate student of Yan Zhida, a member of the Standing Committee of Chinese People's Political Consultative Conference) into the Lecture Notes on Real Lie Algebra. Later, he wrote a book Lie Groups and Lie Algebras on this basis. In this paper, the structure and representation of Lie groups and Lie algebras are discussed in detail, especially Yan Zhida's classification of real semi-simple Lie algebras. This book won the Excellent Textbook Award of the State Education Commission. By the mid-1960s, China had made gratifying progress in the research, curriculum construction, textbook construction and personnel training of the Lee Group.
Because of his work in Lie Groups and Lie Algebras, Yan Zhida was listed as one of the experts who made contributions in this field by J. Dieudonne, an academician of French Academy of Sciences and a famous mathematician, in his masterpiece An Overview of Modern Mathematics (1977). From 1938+0966, due to the influence of political movement, Yan Zhida's work was interrupted. He was treated unfairly like an intellectual. Until 1972, due to the need of mechanical industry, Yan Zhida engaged in the research of gear meshing theory. He applied differential geometry to gear meshing theory, expounded many important concepts in gear meshing theory, and deduced the curvature relationship between tooth surfaces, that is, the induced curvature formula, thus giving the mathematical basis of gear meshing theory. It provides a powerful tool for the research of gear meshing theory in China, promotes the scientific research of bevel gears and plays a certain role in the development of China's machinery industry. Yan Zhida's work in this field was mainly completed between 1972 and 1973, but his research paper was published after 1976. At that time, Nankai University had a research group on gear meshing theory, except Yan Zhida. Professor Wu Daren, Professor Wu Daren and Professor Luo Jiashun wrote in the preface of their co-authored Theory of Gear Meshing (Science Press, 1985): "From 197 1, Nankai University began to study the theory of gear meshing, and later set up a gear meshing group in the Department of Mathematics. Professor Yan Zhida participated in the research group for a long time and founded this book. The relative derivative method, the expressions of two bounded functions and their relations, and the general formula of induced curvature (chapter 4: 1, formula (3)) as expounded and demonstrated in chapters 2 to 4 are all his important contributions, and other achievements cannot be enumerated one by one. " Professor Su also pointed out in the entry "Differential Geometry" written for "China Encyclopedia Mathematics"
The research on gear meshing theory was selected as an important achievement of the 1978 National Science Conference and won the first prize of Tianjin Science Award. Yan Zhida introduced the above work at 1978 Yugoslavia International Gear Conference, which aroused great interest of the participants.
After 1978, Yan Zhida continued to study Lie groups and differential geometry. He discussed the real representation of real semi-simple lie algebras by using Satake graph (another graph describing the classification of real simple lie algebras), and obtained general results in this respect, avoiding some complicated calculations in E. Cartan's paper. He also applied the representation theory of Lie groups to the spectral theory of symmetric Riemannian spaces. A very simple method for calculating the spectrum of symmetric Riemannian space with rank 1 is given. These achievements have also been highly praised and paid attention by colleagues at home and abroad. In order to do a good job in the basic construction of China's mathematics, after studying 1978, it was decided to compile the Encyclopedia of Mathematics in China and set up a mathematics editorial committee headed by China and the Soviet Union. In view of Yan Zhida's extensive knowledge and full understanding of Li Qun, the editorial board.
1978, Yan Zhida was in his sixties. In addition to continuing his scientific research, he pays more attention to the cultivation of talents. Since 1978 resumed postgraduate enrollment, as many as 20 or 30 doctoral and master students have been trained and are being trained, and some young and middle-aged teachers inside and outside the school have been instructed. He always warmly encourages, gives specific guidance and patiently helps them, just like Du Fu's praise of the spring rain, "moistening things silently".
After 1978, Yan Zhida was also very keen on academic exchanges at home and abroad. He pays special attention to the actual effect of international communication. For example, in 1988+0 and 1983 respectively, he invited Nobuyuki Murakami, a Japanese professor, and Kosgur, a French professor (also translated as Koschel, J. Koszul) to Nankai. It is also closely related to the international research trends at that time. Therefore, these lectures are very effective. The contents of these two lectures are wonderful, and the participants benefited a lot. Yan Zhida also visited the United States and France twice to personally understand international trends and guide graduate students and young and middle-aged teachers. 1987, Yan Zhida initiated and presided over the first Li Qun academic conference in China. Since then, mathematicians engaged in the study of Lie groups and Lie algebras in China have met many times to learn from each other.
Due to Yan Zhida's outstanding achievements in academic research and education, many "Who's Who" at home and abroad came to him for a manuscript, and he always declined as much as possible. Indifferent to fame and fortune, modesty and good fortune are also his good qualities.
1993, Nankai University and Chen Shengshen suggested that Yan Zhida apply to become a member of the Department of Mathematics and Physics of China Academy of Sciences. On the recommendation of Duan Xuefu and Wu Wenjun, Yan Zhida was elected as a member of the Department of Mathematics and Physics of China Academy of Sciences (now renamed as an academician) on 1993.
1962 10, Yan Zhida wrote in the preface of "On the Representation of Semi-Simple Lie Groups and Lie Algebras": "It went to press in a hurry, but due to the limitation of the author's level, I had to be satisfied with' not surprising' ..." In fact, this book is a very good one. Today, Yan Zhida is over 70 years old, but he is still working hard.
Xinhua News Agency, Tianjin, May 4th-Professor Yan Zhida, academician and mathematician of China Academy of Sciences, died on April 30th at the age of 82.