The landlord is studying mathematics, right? Can I get to know him and ask you for advice in the future? The following is the copy. Where did the history of China's number theory study begin at the earliest? In China, as early as 1930s, Hua began to study the problem of number theory. His teacher Yang Wuzhi studied the problem of number theory. Hua is the leader of the China School in the research team of number theory. In addition to his important contributions in trigonometry, 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 of Goldbach conjecture and made important progress. The study of modern number theory in China was started by Yang Wuzhi. 1928 received a doctorate from the University of Chicago. I studied under L.E. Dixon. 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 Department of Mathematics of Tsinghua University, where he worked as a librarian and later as an assistant while studying. Hua and Ke Zhao in the department were interested in number theory, so they instructed them to learn number theory. 16.00000060606 He 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 learn the mainstream number theory at that time, namely Hardy-Te Li Wood-Raman Nugget Circle Method and so on. 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 went to the World Number Theory Research Center of Cambridge University to study and study 0000000005 Hua went to Cambridge University as a visiting scholar on the recommendation of the famous mathematician Weiner. Hardy, a famous expert in analytic number theory, and other experts in number theory are here. He attended many courses and seminars at Cambridge University. He was guided by the famous scientist Hardy and others, and Hua's hard work and published articles were praised and recognized by everyone. In the 1940s, he himself did a lot of outstanding work in American number theory. He finally stepped onto the world stage of mathematical research. Mr. Hua attaches great importance to the need of "housekeeping" in his studies. The so-called housekeeping refers to the most basic and useful skills necessary for scientific research. According to his students' memories, Hua said that when he was young, he read E. Landau's "A Course in Number Theory" in three volumes and made six notes, which shows that he made great efforts. And this "number theory course" gave him an analytical basis for engaging in mathematical research. According to Chinese students, Hua Yu 1940 held a "conference" in Yunnan. I like walking around in front of the blackboard, talking 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. In +094 1 year, Hua completed his masterpiece on number theory, On Prime Numbers in Heaps 1. Hua once sent the manuscript to vinogradov of the Soviet Union, and vinogradov immediately sent a telegram to reply: "We have received your excellent monograph, which will be printed immediately after the war. "Therefore, this book was first published in 1947 with No.22 monograph of" Skilov Institute of Mathematics "of the Soviet Academy of Sciences. China's mathematics circles gave a high evaluation of China's monographs, and almost no one in the Ministry of Education at that time could evaluate this book. The old mathematician Helu. He couldn't put it down enough to copy the theory of piling up 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 Stacking Prime Numbers won the first prize of the Ministry of Education. It is reported that Hua taught his theory of heaped prime numbers in The National SouthWest Associated University, and students who began to admire it began to fill the classroom. That is, Min Sihe and Zhong Kailai, who later became famous mathematicians, left only three teachers and students in the classroom. Due to the constant air raids in Kunming every day, Hua simply moved the classroom to Huajia and rented a room to give lectures. The book of Fahrenheit is too profound. Hua Yu 1948+0946 accepted the invitation to visit the Soviet Union. During these months, he conducted research with D. Noguera. And made great achievements. Their development of trigonometry and methods 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 on 1948. He also simplified, improved and applied the average formula of D- nogueira's flowers. 1952 organized a seminar on quadratic theory and Goldbach conjecture. 1953 after the establishment of the number theory group of the Institute of Mathematics of the Chinese Academy of Sciences, Hua personally organized and led two seminars, one was an introduction to number theory and the other was Goldbach conjecture. These two seminars lasted until 1956. Although there was no library when the Institute of Mathematics was founded, Hua brought back books, magazines and printed books from the United States, and people in the Institute of Mathematics could borrow them freely. Just sign his name on the notebook in his office, which is cheaper for the people in the number theory group, because most of Hua's books are directly or indirectly related to number theory. In particular, some of his manuscripts of analytic number theory have not been published, including the latest achievements of Selberg method and elementary proof of prime number theorem. At that time, it was quite early to see these things in the world. According to Hua's plan and arrangement, Goldbach conjecture discussion class is divided into four units: 1, Nearman density, Mann theorem and Selberg method. 2. Brunswick Act and Buchwitz Act. 3. Linnik large sieve method, Rennie theorem. 4. Estimation method of triangular sum of prime variables, Siegel theorem and three prime theorems of Noguera. Hua plans to put this into practice after the discussion class. Published in advances in mathematics of the Institute of Mathematics. At that time, only some number theory works in the world contained the results of these four aspects, so it was really an attractive plan. The lecture was given by one person, while Hua and others have been asking questions, so every point must be made clear. Hua's method of asking one question after another often 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 cultivating talents, which can brainstorm and 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 for the discussion class was not completed. Only after the first, second and fourth troops, it 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. More than ten 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. If you study with Goldbach conjecture as the theme, you will learn all the important methods in analytic number theory. " He said, "Goldbach's conjecture is really beautiful, and there is no way to solve it now." 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. "In addition to Chapter 16 of Introduction to Number Theory, we can also learn two theorems, Dirichlet Theorem and Dai Dejin Theorem, and we can work while learning." Professor Hua's research on Goldbach's conjecture is very long-term and strategic. It also promotes the research on analytic number theory, which not only promotes the development of mathematics, but also trains China's number theory researchers in China. After that, the three members of this seminar made important contributions to the study of number theory and made important progress in the study of Goldbach conjecture. From 65438 to 0954, Min Sihe opened a special course in number theory at Peking University, with four students. He opened this course of number theory to guide them to do their graduation thesis. Guide them to engage in the research of analytic number theory. Min Sihe encourages his students to communicate with people in the number theory group of the Institute of Mathematics and learn from China. The young people in the group of mathematics numeration often ask Min Sihe for advice, which is closely related to each other. Pan Chengdong, Yin Wenlin and Shao, students majoring in number theory in Peking University, also came to the Institute of Mathematics to attend the Goldbach conjecture seminar. Hua 5438+0957. The book contains many unpublished results and basic materials about trigonometric sum, Diophantine equation, modulus transformation and Waring. 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. Comrade Hua knew some of his work, so he took him to the Institute of Mathematics. Under the guidance of Mr. Hua, Comrade Chen Jingrun has done a lot of important work. The most prominent proof is the so-called Goldbach conjecture (1+2), which appears in 1965. I believe that if Comrade Chen Jingrun had not been taken away by China, his growth miracle would have been impossible. 1962 Professor Feng Keqin, a student of China University of Technology, opened a major in number theory and algebra to train reserve talents. He recalled that 1962 Hua wanted to open a major in number theory and algebra in our grade, because I liked number theory from middle school, so I signed up, so 15 students including me entered the major from the fourth grade. Wang Yuan talked about "number theory guidance", Wan Zhexian and Zeng Jiancheng talked about "abstract algebra", and Wu Fang talked about analytic number theory, which concentrated the most powerful number theory and algebra teacher camp in China at that time. In the fifth year of college, Wu Fang instructed me to write a paper, which was my first paper. Hua 1963. He brought his graduate students from the Institute of Mathematics of the Chinese Academy of Sciences to HKUST, and even the relationship with Wang Yuan was temporarily transferred to HKUST, preparing to focus on training students to engage in scientific research based on HKUST. He gave me the task of studying algebraic number theory, which is a research field. He was an American professor in the 1940s. After returning to China, he organized a team to analyze algebraic number theory, but due to various reasons, the research on algebraic number theory could not be fully carried out. At this time, Hua He is also applying number theory to approximate integral calculation, which also uses algebraic number theory tools, so he hopes that some of the eleven graduate students can learn algebraic number theory at this time. This is a knowledge of learning number theory by algebraic method, which is very to my taste. China's research on number theory has achieved fruitful results. After Chen Jingrun's famous paper on Goldbach's conjecture 1973 was published, Pan Chengdong began to study analytic mathematics again. 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. 1979 In July, Pan Chengdong was invited to give an one-hour 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 Interval Prime Numbers", put forward a method of estimating Triangular Sum of Interval Prime Numbers by pure analysis, and strictly proved the theorem of interval three prime numbers for the first time, which is his further perfection and improvement of the article "Some new results of prime number theory on heap". The work of Hua and his students in number theory shows the high level and talent of China mathematicians in number theory. Known as the "China School headed by China" by the world mathematics community, this is the first time that China mathematicians' research group has been affirmed and praised in the development of world mathematics, and this achievement has been obtained by mathematicians through decades of efforts. China systematically studied the problem-Goldbach problem. 19 in the 1940s, few people knew the cyclic method of heap prime number theory and the estimation method of two exponents by Noguera doffer. The monograph "Heap Prime Number Theory" written by Hua covers all the important research achievements in the field of number theory, and its Chinese proof of 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 Siegel's real zero estimation of L- function. So this book is self-sufficient and a good monograph on number theory. As Beistine said in Mourning for China, "Several algebraic theorists learned the knowledge of circle method from China's monograph On Prime Numbers of Overlapping Basis, which still has influence today." Hua improved and simplified the work of D. Noguera doffer on H.Weyl in 1958. 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, then (3+3) and (2+3) in 1957, and later Pan Chengdong and his cooperation proved (1+4). In 1966, Chen Jingrun used Pombini's mean formula, which proved very well (1+2). Mathematicians in China have made great progress in the process of exploring Goldbach's conjecture, but who can finally pick this pearl and overcome this world problem, will it be China? These are still unknown mysteries, waiting for someone to answer them.