What is the earliest history of China's number theory research? In China, as early as 1930s, Hua began to study the problem of number theory. His teacher Yang Wuzhi studies the problem of number theory. Hua is the leader of China School, a research team of number theory. In addition to his important contributions in triangle sum estimation and heap prime theory, Hua has also made important arrangements for the research direction and specific problems of number theory in China and the cultivation of reserve talents for long-term research. At the same time, he organized a group of young mathematicians to tackle the world problem "Goldbach conjecture" and made important progress. The study of modern number theory in China was started by Yang Wuzhi. 1928 received his Ph.D. from the University of Chicago and studied under L.E. Dickson. He once proved that "every positive integer is the sum of nine non-negative integers in the form of (x- 1)x(x+ 1)/6", which is the earliest achievement of modern number theory in China.
1929 Yang Wuzhi was employed as a teacher in the Department of Mathematics of Tsinghua University. 193 1 year, Hua came to the mathematics department of Tsinghua University, first as a librarian, then as an assistant, studying while working. Hua and Ke Zhao in the department are very interested in number theory, so they are instructed to learn number theory. 1936, Hua and Ke Zhao went to England, entered Cambridge University and Manchester University respectively, and studied number theory under G.H. Hardy and L.J. Modal. Before going to England, Hua had already begun to study the mainstream number theory at that time, namely Hardy-Te Li Wood-Ramanujin Circle Method and D- Noguera Dover Index and Estimation Method, which enabled him to master the number theory. His work on number theory has a lasting influence on analytic number theory and is respected by international colleagues. In addition, Hua also recruited students and wrote introductory books such as Introduction to Number Theory, which played a leading role in the development of number theory in China. After liberation, the combination of Hua and Min laid the foundation for this study. Hua Yu 1936 went to the World Number Theory Research Center of Cambridge University for further study. On the recommendation of the famous mathematician Weiner, Hua went to Cambridge University in England as a visiting scholar. There are famous analytic number theory experts such as Hardy. He listened to many classes at Cambridge University, participated in discussion classes, and was guided by the famous scientist Hardy and others. Hua's efforts and published articles have also been praised and recognized by everyone. He himself did a lot of outstanding work in number theory in the United States in the 1940s. He finally stepped onto the world stage of mathematical research. Mr. Hua attached great importance to the necessity of "housekeeping" in his study when he offered the course of elementary number theory in Yunnan United University. The so-called housekeeping refers to the most basic and useful skills that are indispensable in scientific research. According to his students' memories, Hua made six notes while reading Landau's "A Course in Number Theory" when he was young, which shows his deep research. And this "number theory course" gave him an analytical basis for mathematical research. According to Chinese students, Hua Yu 1940 opened a course on elementary number theory in Yunnan General Assembly, and he took this course. Teacher Hua's lecture posture is very flexible, and she likes to walk around in front of the blackboard and talk while walking. He didn't write much on the blackboard, only the most needed formulas, but he paid great attention to the ins and outs of the problem and the way of argument, sometimes interspersed with short stories. So I think it's a pleasure to listen to his lecture. 194 1 Hua Zai 194 1 Completed the masterpiece of number theory "On Prime Numbers of Heaps". China sent the manuscript to vinogradov of the Soviet Union, and vinogradov immediately replied by telegram: "We have received your excellent monograph and will print it immediately after the war." Therefore, this book was first published in 1947 with No.22 monograph of Institute of Mathematics, Soviet Academy of Sciences. China's mathematicians spoke highly of China's monographs. At that time, few people in the Ministry of Education could comment on this book. He Lu, an older mathematician, braved the scorching sun and sweated in a small building in Chongqing. When reading the manuscript from time to time, I was amazed and repeatedly said to people: "This genius is also!" He couldn't put it down. He actually copied the book "The Theory of Heap Prime Numbers" himself. He's manuscript was kept in the library of the Institute of Mathematics of China Academy of Sciences, but it was lost in the disaster of the Cultural Revolution. Hua's theory of pushing prime numbers won the first prize of the Ministry of Education. According to the newspaper, Hua once taught his theory of prime numbers at National Southwest Associated University. At first, the students who came here crowded the classroom. Later, it was reduced to four every day. A week later, only Min Sihe and Zhong Kailai were left, who later became famous mathematicians. There are only three teachers and students left in the classroom. Because there are air raids in Kunming every day, Hua simply moved the classroom to Huajia, rented a house and lived there to give lectures. Fahrenheit's books are too profound. From 6: 438 to 9: 46, China accepted the invitation to visit the Soviet Union. In these few months, he and D. Noguera conducted research together and achieved great results. Their development of trigonometric sum method changed the central theme of analytic number theory. 1946, Hua visited the United States, first engaged in research and taught number theory at Princeton Institute for Advanced Studies, and then transferred to the University of Illinois in 1948, and also simplified, improved and applied the D- nogueira mean formula. 1952 organized a discussion class on quadratic theory and Goldbach conjecture. 1953 After the establishment of the Mathematical Institute of Chinese Academy of Sciences in winter, Hua personally organized and led two discussion classes, one was an introduction to number theory and the other was Goldbach conjecture, which lasted once a week until 6544. Although there was no library when the Institute of Mathematics was founded, Hua brought back a large number of books, magazines and printed books from the United States. People in the Institute of Mathematics can borrow it for free, as long as they sign their names in the notebook in his office. This is even cheaper for people in the number theory group. Because most of Hua's works are directly or indirectly related to number theory. In particular, he has an unpublished manuscript of analytic number theory, including the latest achievements of Selberg method and elementary proof of prime number theorem. I was able to understand these things at that time, which was relatively early in the world. According to Hua's plan and arrangement, Goldbach's conjecture discussion class is divided into four units: 1, Shnirman's secret rate, Mann's theorem and Selberg's method. 2. Brunswick method and Buchwey stepping method. 3. Linnik's large sieve method and Rennie's theorem. 4. Estimation method of triangular sum of prime variables, Siegel theorem and D- Noguera theorem of three prime numbers. Hua plans to write a comprehensive paper on these four aspects after the seminar and publish it in advances in mathematics Institute of Mathematics. At that time, only some of the number theory works in the world included the achievements of these four aspects, so this was indeed an attractive plan. The lecture was given by one person, and Hua and others kept asking questions to make sure everything was clear. Hua often asks what will happen next, which makes the speaker unable to speak and think on the podium for a long time. This is called "hanging the blackboard". Some presentation materials are often simplified in the discussion class, so the discussion class goes slowly, but the participants benefit a lot. This is a good form of training talents. It can not only brainstorm, but also enliven the academic atmosphere. At that time, he often attended discussion classes, constantly asking questions and questions, and pushing everyone's thoughts to a more active realm. Goldbach guessed that the plan of the seminar was not completed, and only one, two or four units were carried out, which was interrupted by the arrival of the "anti-rightist struggle". Hua's choice of "Goldbach conjecture" as the theme of number theory group discussion class is very insightful. 10 years later, when Hua recalled his decision, he still showed satisfaction. He said: "I don't want you to make achievements on this issue. My point is that Goldbach conjecture is related to all the important methods in analytic number theory. Learning with the theme of Goldbach conjecture will enable you to learn all the important methods in analytic number theory. " He said, "Goldbach's conjecture is too beautiful to be solved." He also pointed out: "If you know analytic number theory and learn a little algebraic number theory, you can extend the results of analytic number theory to algebraic number field. Regarding algebraic number theory, in addition to the sixteenth chapter of the introduction to number theory, we can learn two theorems, Dirichlet theorem and Dai Dejin theorem, and we can work while learning. " Professor Hua's research on Goldbach's conjecture has a long-term strategic vision, and at the same time, it also promotes the research of analytic number theory, which not only promotes the development of mathematics, but also trains Chinese number theory researchers at home. After that, all three members of this seminar made important contributions to the study of number theory and made important progress in the study of Goldbach conjecture. Since 1954, Min Sihe has opened a "number theory major" in Peking University, with four students. He set up the course number theory, guiding them to do their graduation thesis and engage in the research of analytic number theory. Min Sihe encourages his students to communicate with the number theory group of the Institute of Mathematics and learn from China. Young people in the mathematical number theory group often ask Mr. Min Sihe for advice, which is closely related to each other. Yin Wenlin and Shao, who majored in number theory in Peking University, also came to the Institute of Mathematics to attend the Goldbach conjecture discussion class. 1957, Hua's Introduction to Number Theory was published, which contained many unpublished results and basic data on trigonometric sums, Diophantine equations, modular transformations and sums. Later, Hua discovered Chen Jingrun and transferred him to the Institute of Mathematics. After years of hard work, Chen Jingrun finally proved 1+2, and achieved the best result in proving Goldbach's conjecture in the world. Wu Wenjun once said: "Comrade Chen Jingrun was originally a nobody, but Comrade Hua learned about some of his work and led him to the Institute of Mathematics. Under the guidance of Mr. Hua, Comrade Chen Jingrun has done a lot of important work in the environment of the Institute of Mathematics. The most prominent one is the proof of the so-called Goldbach conjecture (1+2) that everyone knows. This appears in 1965. I believe that without Comrade Hua bringing Comrade Chen Jingrun to the Institute of Mathematics, his growth miracle would be impossible. 1962, Hua, a student of China University of Science and Technology, set up a major in number theory and algebra to train reserve talents. Recalling 1962, Hua wanted to set up a major in number theory and algebra in our grade. Since I liked number theory from middle school, I signed up, so 15 students including me began to enter this major from the fourth grade, and Hua personally taught the "typical group". When I was in the fifth grade, Wu Fang instructed me to do a paper, the content of which was to make the latest achievements of Chen Jingrun's estimation of the remainder of the integer problem in a circle into an ellipse. This is my first paper. Hua came from 65438 to 0963 as vice president, bringing graduate students from the Institute of Mathematics of Chinese Academy of Sciences. Even Wang Yuan's relationship has been temporarily transferred to HKUST, ready to concentrate on training students to engage in scientific research based on HKUST. The task he gave me was to study algebraic number theory, which was a research field of number theory he taught in the United States in the 1940s. After returning to China, he organized a team to analyze number theory, but for various reasons, the research on algebraic number theory could not be carried out comprehensively. In addition, Hua He is also applying number theory to approximate integral calculation at this time, and they also use algebraic number theory tools, so he hopes that some of the eleven graduate students can learn algebraic number theory at this time. This is the study of number theory by algebraic method, which is very much to my liking. 1973 China's research on number theory has achieved fruitful results. After Chen Jingrun's famous paper on Goldbach conjecture was published, Pan Chengdong began to study analytical mathematics. The representative paper of this period is A New Mean Value Theorem and Its Application. His main contribution is to put forward and prove a new mean value theorem of prime number distribution, and give the important application of this theorem in many famous number theory problems including Goldbach conjecture. 1In July, 979, Pan Chengdong was invited to give an hour-long lecture at the International Conference on Analytic Number Theory held in Durham, England, which was highly praised by Hua and the participants. 1982, Pan Chengdong published a paper "A New Attempt to Study Goldbach's Conjecture", which put forward a completely different method from the existing research and made a beneficial exploration of Goldbach's Conjecture. During the period from 1988 to 1990, Hua and Pan Chengbiao published three papers on the topic of "Estimation of triangular sum of prime variables between communities", and put forward a method of estimating triangular sum of prime variables between communities by pure analysis, which strictly proved the theorem of three prime numbers between communities for the first time, which was his further improvement and improvement of the article "Some new results of prime number theory on piles". The work of Hua and his students in number theory shows the high level and talent of China mathematicians in number theory, and is called "China School headed by China" by the world mathematics community. This is the first time that the research group of mathematicians in China has been affirmed and praised in the development of mathematics in the world. And this result is obtained by mathematicians through decades of efforts. China systematically studied the problem-Goldbach problem. 19 In the 1940s, few people knew the circular method of heap prime number theory and the estimation method of two indexes of D- Noguera doffer. Hua's monograph "On the Prime Number of Dui" contains all the important research results in the field of number theory, and his Chinese proof of the generalized trigonometric sum theorem is very beautiful. This book is not only the latest achievement at that time, but also very easy to understand. All theorems have been proved except the real zero estimation of Siegel's L- function, so this book is self-sufficient and a good book of number theory. As Ha Beistine said in mourning for China: "Several algebraic theorists learned the knowledge of circular method from China's monograph" The Theory of Overlapping Primes ",which is still influential today." In 1958, Hua improved and simplified the estimation of H.Weyl sum by D. Noguera Doff. Hua's research on problems and "Fahrenheit inequality" is a very important achievement in number theory and has been quoted by many people. Chinese students first proved (3+4) in 1956 and (3+3) and (2+3) in 1957. Pan Chengdong proved it in 1962 (1+5), and then Pan Chengdong and Wang Yuan cooperated to prove it (1+4). In 1966, Chen Jingrun used Pombini mean formula, which proved very well (1+2). Mathematicians in China have made great progress in the process of exploring Goldbach's conjecture, but in the end, who can pick this pearl and overcome this world problem, will it be from China? These are still unknown mysteries, waiting for someone to answer them.