Hua has made outstanding achievements in solving the problem of estimating the sum of Gaussian complete triangles, improving the problem of Willing sum, proving the basic theorem of one-dimensional projective geometry, and applying modern number theory methods? .
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".
Hua initiated the China School of Mathematics and brought it to the world level.
Hua's international mathematical research achievements include Fahrenheit Theorem, Huai-Hua Inequality, Fahrenheit Inequality, Laugar Theorem, Fahrenheit Operator, Hua-Wang Method and so on.
In the 1940 s, Hua solved the historical problem of Gaussian complete triangular sum estimation and obtained the best error order estimation. 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, Hua proved the basic theorem of one-dimensional projective geometry left over from history for a long time; 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 professors, Hua has made important achievements in the application research of modern number theory methods, which is called "Hua-Wang method"? .