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 basic theorem of one-dimensional projective geometry left over from history for a long time is proved.

A simple and direct proof of the conclusion that the normal daughter of an object must be contained in its center is given, which is called Cartier-Bourgeois-Hua theorem.

Right, g? h？ Hardy and J. e？ Littlewood's Views on the Waring Problem and E? Wright's conclusion on Tali has been greatly improved.

Hua's book On the Prime Number of Heaps systematically summarizes, develops and perfects Hardy's circle method, vinogradov's triangle sum estimation method and his own method. Its main achievements have remained at the leading level in the world for more than 40 years since its publication, and it has become one of the classic number theory works in the 20th century.

Another mathematical monograph, Harmonic Analysis on Typical Fields of Multiple Complex Variables, combined with group representation theory, gives the complete orthogonal system of typical fields in detail, thus obtaining the expressions of Cauchy and Poisson Kernel, which has far-reaching influence in the world. With its outstanding mathematical achievements, Hua deserves to be one of the great mathematicians in China in the 20th century.