1930, taught in Tsinghua University.
1936 Visiting study at Cambridge University, UK.
1938 became a professor in The National SouthWest Associated University after returning to China.
From 65438 to 0946, he went to the United States and served as a researcher at Princeton Institute of Mathematics and a professor at Princeton University and the University of Illinois.
After returning to China from 65438 to 0950, he successively served as Professor Tsinghua University, Director and Honorary Director of Institute of Mathematics and Institute of Applied Mathematics of China Academy of Sciences, Chairman and Honorary Director of Chinese Mathematical Society, Director of National Mathematical Competition Committee, Foreign Academician of American National Academy of Sciences, Academician of Third World Academy of Sciences, Academician of Bavarian Academy of Sciences of the Federal Republic of Germany, Deputy Director, Vice Chairman and Presidium Member of Physics, Mathematics and Chemistry Department of China Academy of Sciences, Dean and Vice President of Mathematics Department of China University of Science and Technology.
He was a member of the first to sixth the NPC Standing Committee and vice-chairman of the sixth China People's Political Consultative Conference. He was awarded an honorary doctorate by Nancy University in France, The Chinese University of Hong Kong and the University of Illinois in the United States. Mainly engaged in the research and teaching of analytic number theory, matrix geometry, typical groups, automorphic function theory, multiple complex variable function theory, partial differential equations, high-dimensional numerical integration and other fields, and has made outstanding achievements. In the 1940s, the historical problem of Gaussian complete trigonometric sum estimation was solved, and the best error order estimation was obtained (this result is widely used in number theory). The results of G.H. Hardy and J.E. Littlewood on the Welling problem and E. Wright on the Tully problem have been greatly improved and are still the best records.
Hua's main achievement is the founder and pioneer of China's research in analytic number theory, matrix geometry, canonical group and self-safety function theory. The international achievements in mathematical research include Fahrenheit Theorem, Huai-Hua Inequality, Fahrenheit Inequality, Pu Lawwill-Gardiner Theorem, Fahrenheit Operator, Hua-Wang Method and so on. Comrade Hua left us ten monographs in his life: On the Prime Number, Calculation of Exponential Sum and Its Application in Number Theory, Harmonic Analysis of Typical Fields in the Theory of Functions with Multiple Complex Variables, Introduction to Number Theory, Typical Groups (co-authored with Wan Zhexian), Starting from the Unit Circle, Application of Number Theory in Approximate Analysis (co-authored with) and. "Optimization Theory" and "Mathematical Theory for Optimizing the Scope of Planned Economy" have been translated and published in eight foreign countries, some of which have been included in mathematical classics of this century. In addition, there are more than 200 academic papers such as popular science works "Evaluation and Supplement of Optimization Method" and "Evaluation and Supplement of Overall Planning Method", which are compiled into "Selected Works of Huake Puwen".
In algebra, the basic theorem of one-dimensional projective geometry left over from history for a long time is proved. This paper gives a simple and direct proof that the normal child of an object must be contained in its center, which is Hua theorem. His monograph On Prime Numbers of Heaps systematically summarizes, develops and perfects Hardy and Littlewood's circle method, vinogradov's triangle sum estimation method and his own method. Since its publication more than 40 years ago, its main achievements are still in the leading position in the world, and it has been translated into Russian, Hungarian, Japanese, German and English, becoming one of the classic works of number theory in the 20th century. His monograph "Harmonic Analysis on Typical Fields of Multiple Complex Variables" gives the complete orthogonal system of typical fields with accurate analysis and matrix skills, combined with group representation theory, and thus gives the expressions of Cauchy and Poisson kernel. This work has a wide and deep influence on harmonic analysis, complex analysis and differential equations, and won the first prize of China Natural Science Award. Advocating the development of applied mathematics and computer, he has published many books such as Master Planning Method and Optimization Research, which have been popularized in China. In cooperation with Professor Wang Yuan, he has made important achievements in the application research of modern number theory methods, which is called "Hua Wang Fa". He made great contributions to the development of mathematics education and the popularization of science.