Hua's early research field was analytic number theory, and his achievements in analytic number theory were particularly famous. The internationally famous "China Analytic Number Theory School" is a school initiated by China, which has made many significant contributions to the distribution of prime numbers and Goldbach conjecture.

Hua is also the founder and pioneer in the research of analytic number theory, matrix geometry, canonical group and automorphism function theory in China.

China's research on the theory of multiple complex variables and canonical group theory is ahead of the western mathematics field 10 years, and it is an internationally famous "canonical group China school".

Establish China School of Mathematics and lead it to the world-class level. Many outstanding young people have been trained, such as Wang Yuan, Chen Jingrun, Wan Zhexian, Lu Qikeng and Gong Sheng.

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.

In the 1940s, the historical problem of Gaussian complete triangular sum estimation was solved, and the best error order estimation was obtained. The research results of G·H· Hardy and J·E· Littlewood on the Welling problem and E Wright on the Tali problem have been greatly improved, and the research results of trigonometry are called "Fahrenheit Theorem" by the international mathematical community.

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.

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".

Hua left ten masterpieces in his life: Theory of Pile Prime Numbers, Evaluation of Exponential Sum and Its Application in Number Theory, Harmonic Analysis of Typical Fields in the Theory of 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 Wan Zhexian) and II. In addition, there are more than 65,438+050 academic papers, among which popular science works, such as Supplement to Comments on Optimal Selection Method and Supplement to Comments on Overall Planning Method, have been compiled as Selected Works of Popular Science by China.