Characters' Life in Yang Zhongdao's Works

1946 graduated from the Mathematics Department of Zhejiang University. 65438-0948 Assistant in Institute of Mathematics, Academia Sinica. From 65438 to 0949, he studied at Durham University in the United States, and obtained a doctorate in mathematics from 65438 to 0954. In the same year, he went to the University of Illinois to pursue postdoctoral studies, and he was a visiting researcher at Princeton Institute for Advanced Studies from 65438 to 0954. Since 1956, he has been a professor of mathematics at the University of Pennsylvania for a long time. Graduate department, director of the Department of Mathematics for 4 years, head of the Department of Mathematics for 5 years, and published more than 20 papers. 1962, participated in the international mathematics seminar held in the United States. 1963 American citizenship. 1968 was elected as an academician of academia sinica (Taiwan Province province). Yang Zhongdao specializes in algebraic topology and topological transformation groups.

1923 in may, he was born in Pingyang county (now Cangnan county), Zhejiang province.

1942, graduated from Zhejiang No.10 Middle School (now Wenzhou Middle School) High School.

1946, Bachelor of Science, National Zhejiang University.

1946- 1948, teaching assistant, Department of Mathematics, Zhejiang University.

1948- 1949, assistant to the Institute of Mathematics, Academia Sinica.

1949- 1950, assistant researcher at the Institute of Mathematics, Academia Sinica, and lecturer at the Department of Mathematics, Taiwan Province Provincial University.

1952, Ph.D. in Mathematics, tulane university, USA.

1952- 1954, postdoctoral research, University of Illinois, USA.

1954- 1956, Institute for Advanced Studies, Princeton, USA.

1956- 1958, Assistant Professor, Department of Mathematics, University of Pennsylvania, USA.

1958- 196 1 year, associate professor, Department of Mathematics, University of Pennsylvania, USA.

1968, academician of academia sinica, Taiwan

1961-1year, Professor of Mathematics Department of the University of Pennsylvania, USA, 1978- 1983, concurrently the head of the Department of Mathematics of the University of Pennsylvania.

He grew up in a rural area in Pingyang County, Zhejiang Province, and belongs to Pingxiang Township, Cangnan County, Zhejiang Province. Pingyang county was very backward at that time. There are no junior high schools and few primary schools in this county. Yang Zhongdao studied in a local private primary school until the fourth grade. In the fifth grade, the school was five miles away from home. When she was in high school, Yang Zhongdao began to live on campus and went home on weekends.

In the fourth grade, Mr. Huang Zhongdi, a math teacher, discussed the problem of chickens and rabbits in the same cage with logical methods, which aroused his interest in mathematics.

Because of his poor family, Yang Zhongdao did not take the senior high school entrance examination after graduating from junior high school, but taught the second grade in the local junior high school and went to high school with the money he earned. Because he misses school, Yang Zhongdao has become more mature, and he can feel the value of learning opportunities. So he has been the top three in his class for three years in high school, so he completed his high school studies at public expense. In high school, he was good at math and physics, and math was considered the best by teachers and classmates.

Under difficult living conditions, my father encouraged Yang Zhongdao to study engineering. At that time, Yang Zhongdao liked mathematics very much and was a good student of mathematics and physics, so he went to consult Mr. Chen Zhongwu, a math teacher. He said without hesitation, "Of course you study mathematics. If you don't study math, who else will study math? " In the words of Mr. Zhong Wu, Yang Zhongdao started his own way of mathematics.

At that time, although the education in Pingyang County was very backward, there were two mathematicians. The first is Professor Jiang Lifu, who received his Ph.D. in Mathematics from Harvard University in the United States in 19 19, and was the first director of the Institute of Mathematics of Academia Sinica. The second is Professor Su, 193 1 who received a doctorate in mathematics from Northeastern University and was the first dean of the School of Science of Taiwan Province Provincial University. Both of them are the first academicians of Academia Sinica. Yang Zhongdao had heard their names since childhood, but he didn't know them until he was in his forties.

Yang Zhongdao's senior high school entrance examination results can guarantee that he will go to a national university. But he decided to enter Zhejiang University and learn modern mathematics from Mr. Su.

At that time, the Department of Mathematics of Zhejiang University was in Meitan County, Guizhou Province, and the head of the department was Mr. Qing Bu. At that time, there was no staff in the department, and the head of the department was responsible for all the affairs in the department. Mr Qing Bu treats his students like children and takes good care of them. Yang Zhongdao studied calculus and differential equations in grade one, advanced calculus, introduction to series, solid analytic geometry and optional number theory, partial differential equations in grade two, comprehensive geometry, modern algebra and complex variable functions in grade three, differential geometry, real variable functions and mathematical research in grade four. I have never studied functional analysis and topology in Yangzhong Middle School of Zhejiang University, because there is no teacher who can teach these two courses.

In the four years of college, Yang Zhongdao's math score is not less than 90%, and the average score of each semester is higher than 90%. He gave in. What surprised Mr. Qing was not these high scores, but that he got 90 points when he studied theoretical mechanics in Grade Two. Theoretical mechanics is a compulsory course for mathematics majors, but it can be studied in the third and fourth grades. This is a famous and difficult course. It is sometimes difficult for good students in the department of mathematics to study, and even they have to make up exams if they fail, which makes the department of mathematics very dissatisfied. No wonder Mr. Qing Bu saw his high score and smiled and said to him, "The feud of the mathematics department for many years suddenly came out to you." In fact, it is also very difficult for physics majors to learn this course. There are more than a dozen students studying theoretical mechanics with Yang Zhongdao, and only five students have passed.

The third grade comprehensive geometry class is taught by Qing Bu. He encouraged students to read extracurricular reference books, while Yang Zhongdao read the new German version of projective geometry. And was assigned to the Department of Mathematics to manage books and magazines. So, in the fourth grade, Yang Zhongdao found a topic and finished writing a paper. Later, the paper was published in the United States (Duke of Mathematics J, 1947).

After graduating from college, Yang Zhongdao stayed as a teaching assistant. In the past two years, I have done research papers. Besides those published in China, two papers were published in American Mathematics Journal and Argentine Mathematics Journal respectively. Since 1947, the political situation has been quite chaotic. With the consent of Mr. Qing Bu, Yang Zhongdao went to the Institute of Mathematics of China Academy of Sciences in the summer of 1948 to learn algebraic topology from Professor Chen Shengshen, acting director. The purpose is to learn new knowledge and then go back to the mathematics department of Zhejiang University.

Unexpectedly, the situation took a turn for the worse, and the research activities of the Institute of Mathematics stopped completely. The Ministry of Education announced that Bosniak, director of the Institute of History and Linguistics, will succeed President of Taiwan Province Provincial University, so it proposed to move Academia Sinica to Taiwan Province Province. Finally, it was decided to relocate only the Institute of History and Language and the Institute of Mathematics, and only some personnel were allowed to go to Taiwan Province Province, including Yang Zhongdao.

After arriving in Taiwan Province Province, Yang Zhongdao and three other bachelors from the Institute of Mathematics temporarily lived in a warehouse in Yangmei Town. Later, I taught in the Middle School Attached to Teachers College (later the Middle School Attached to Normal University) for one semester. /kloc-in the summer of 0/949, Yang Zhongdao officially became a part-time lecturer in the Department of Mathematics at National Taiwan University. 1949- 1950, teaching calculus in civil engineering and differential equations in mechanical engineering.

1950, Mr. Wang and Mr. Hu helped Yang Zhongdao get a teaching scholarship and went to tulane university (Louisiana) to study for a doctorate. The travel expenses are paid by academia sinica.

When he first arrived in the United States, Yang Zhongdao was ashamed to speak because of his poor English. He is the only non-American among more than a dozen graduate students majoring in mathematics, so everyone takes care of him. In the first semester, Yang Zhongdao took four math courses and a book report. One of the lecturers is Professor A.D. Wallace, who is also the tutor of his doctoral thesis. His teaching method is original by R.L. Moore, which divides the course content into many small propositions and sends them to students in advance. In class, he put the students on stage, which proved that he was sitting under the stage and listening. One student didn't finish, so call the second one up. If he doesn't finish an hour, he will leave it for the next hour. He will never help himself. Although Yang Zhongdao's English is not good, he did well in the class, so I left a good impression on him from the beginning. He is very friendly to students and often goes to the graduate office to talk about math and tell jokes after class. When I see Yang Zhongdao, I always ask big and small math questions to make Yang Zhongdao think more. At the beginning of the second semester, he let Yang read the lecture notes of H. Catan, a French mathematician who taught algebraic topology at Harvard University.

One of the main achievements in Cartan's lecture notes is that "for compact Hausdorff spaces, some two homology theories are equivalent". In Professor Wallace's course, Yang Zhongdao learned the concept of completely normal space. After several weeks of thinking, Yang Zhongdao felt that the achievements in Katan's lecture could be extended to a completely normal space. When he mentioned this discovery to Professor Wallace, Professor Wallace was very surprised, so he took time to discuss his ideas with him. A few weeks later, the professor began to believe that his idea might be correct and could be used as his doctoral thesis.

Tulane university is a good university in the southern United States, and a second-and third-rate school in the United States. Before Yang Zhongdao, there were less than ten doctors in the department of mathematics, so Professor Wallace asked the graduate school to make an exception for him. To get a doctorate, it is customary to complete 20 credits, but Professor Wallace thinks that it is best to give him a doctorate as early as possible for him and the Department of Mathematics, and recommend him to go to places where there are many research activities for further development, so the Department chartered him not to attend classes in the second semester and concentrate on writing doctoral thesis.

Professor Wallace initially wanted to be a lecturer in mathematics department of Princeton University, so that he could learn from Professor N. Steenrod about algebraic topology, but he didn't succeed. 1In the autumn of 952, I worked as a postdoctoral researcher in the Department of Mathematics, University of Illinois, USA, teaching for three hours every week and participating in research activities in the department. At that time, there was a professor of Algebra Topology, D.G. burgin, with five or six doctoral students, who mainly studied (F.J.) Dyson's conjecture. He not only attended Professor burgin's class, but also attended the seminar he presided over. After a year's hard work, he got a proof of Dyson's conjecture. Professor burgin was very surprised when he knew it, because Professor burgin had done almost everything himself. This incident embarrassed Yang Zhongdao, so he went to ask Mr. Chen Shengshen for advice. He was advised that the best solution is that two people write an article and publish it together, but it must be put forward by Professor burgin. If the other party doesn't mention it, Yang Zhongdao should publish it himself, but the article should mention that Professor burgin has an independent certificate. Results Yang's article was published in Mathematical Yearbook 1954, and burgin's article was published in a Swiss mathematical magazine 1955. He stayed at the University of Illinois for two years. When he was there, Mr. Shi Gongxing was studying for a doctorate there. Academician Zhou just left and went to study for a doctorate.

The two articles written by Yang Zhongdao at the University of Illinois are quite interesting, and Professor Wallace continues to make efforts to recommend him to Princeton for research. 1In the autumn of 954, he received a one-year grant from the National Science Council of the United States and went to Princeton Institute for Advanced Studies to do research. The main purpose is to extend Dyson conjecture to include Bolsuke-ulam theorem.

Yang Zhongdao's research plan will be completed within half a year. If we continue along the same route, the future is not optimistic, and he feels it is necessary to find another way. At that time, Professor Montgomery and Professor L. Zippen co-wrote a book Topological Transformation Groups. The first half of this book solves Hilbert's fifth problem, topological transformation group. Because these were recognized as the most important contributions at that time, of course, we should read them well, so he recommended himself to help proofread the book. After reading the whole book, he felt that there were some problems to consider, so he asked Professor Montgomery for advice. Because of this accidental opportunity, Yang Zhongdao co-wrote two articles with them in those two years.

1In the autumn of 956, Yang Zhongdao went to work at the University of Pennsylvania. He worked in the University of Pennsylvania for 35 years, first as an assistant professor, 1958 was promoted to associate professor, and 196 1 was promoted to full professor. During his tenure, he served as the director of graduate department in the Department of Mathematics for four years and the head of the Department of Mathematics for five years. Under his guidance, L.Mann( 1959) completed his doctoral thesis, and later served as the head of the Department of Mathematics at the University of Massachusetts for many years. 196 1 su jingcun 1954 graduated from the department of physics of national Taiwan university, and later switched to the department of mathematics, becoming a professor of mathematics at the university of Massachusetts. The greatest advantage of teaching at the University of Pennsylvania is that you can often visit Professor Montgomery, which has been going on for more than 20 years and has written more than 20 articles.

1968 Yang Zhongdao was elected as an academician of Academia Sinica, and 1972 was listed in the Who's Who of America.