Analytic Number Theory in China

Abstract

F rom 1930 to 1980, China suffered several national disasters, such as the Japanese invasion, the civil war, and the cultural revolution. These catastrophes destroyed not only people’s lives, but also culture and science. However, during that extremely difficult time China produced several famous mathematicians in analytic number theory: Loo-Keng Hua, Jingrun Chen, Yuan Wang, and Chengdong Pan. Their work and their legendary lives made them national heroes in China. Hua’s and Chen’s eventful lives have been documented in popular biographies and TV series. In this report I briefly introduce their mathematical work and tell some of their legendary stories. Before starting the main story, let us review some basic facts about China. Throughout its history, China had made great contributions to world civilization as well as to ancient mathematics. For example, at the beginning of the second century Lun Cai invented a technique for producing paper; in the third century Hui Liu obtained p = 3.14... by approximating a circle by polygons; in the fourth century Chong-Zhi Zu knew the first seven digits of p and how to calculate the volume of a ball; in the middle of the tenth century Sheng Bi invented moveable type. However, modern science, including modern mathematics, came to China rather late. The first university in China, Peking University, was founded in 1898. In the next decades several other universities were founded in Beijing, Shanghai, Tianjin, and other cities. The first mathematics department in China was formally opened at Peking University in 1913 with two professors. At the beginning there were only a few students studying mathematics and the courses were limited to calculus, linear algebra, and linear geometry. Within the next two decades, the number of mathematics students grew rapidly and abstract algebra, differential equations, set theory, differential geometry, and function theory gradually became university courses. By 1930, there were dozens of mathematics professors working in Chinese universities, most of them educated in Europe and America. The Chinese Mathematical Society was founded in 1935 and its first journal, Acta Mathematica Sinica, started publishing papers a year later.