Liu Hui (born around 250 AD) is a very great mathematician in the history of Chinese mathematics, and also occupies a prominent position in the history of world mathematics. His representative works "Nine Arithmetic Notes" and "Calculation on the Island" are the most precious mathematical heritages of China. Jia Xian Jia Xian was an outstanding mathematician in ancient China during the Northern Song Dynasty. The Nine Chapters of Yellow Emperor's Arithmetic Fine Grass (nine volumes) and Arithmetic Ancient Collection (two volumes) have been lost. His main contribution is to create the "Jiaxian Triangle" and the method of multiplication and multiplication, which is the positive root method for finding the higher power. At present, the principle and procedure of mixed division in middle school mathematics are similar, while the multiplication and division method is more neat, simple and programmed than the traditional method, so it shows its superiority, especially when it comes to high power. This method was put forward more than 700 years before the conclusion of European mathematician Horner. Qin Jiushao (about 1202- 126 1) was born in Anyue, Sichuan. He was once an official in Hubei, Anhui, Jiangsu, Zhejiang and other places, and was demoted to Meizhou (now Meixian County, Guangdong Province) around 126 1, and soon died. He, Yang Hui and Zhu Shijie are also called the four great mathematicians in Song and Yuan Dynasties. In his early years in Hangzhou, he visited the Taishi and learned mathematics from a hermit. 1247, he wrote the famous Shu Shu Jiu Zhang. The book "Shu Shu Jiu Zhang" has a total of 18 volumes and 8 1 title, which is divided into nine categories. Its most important achievements in mathematics-"the sum of large calculations" (a solution of congruence group) and "the solution of positive and negative square roots" (a numerical solution of higher-order equations) made this Song Dynasty arithmetic classic occupy a prominent position in the history of medieval mathematics. Ye Li Ye Li (1 192- 1279), formerly known as Li Zhi, was born in Luancheng, Jin Dynasty. He used to be the governor of Zhou Jun (now Yuxian County, Henan Province). Zhou Jun was destroyed by the Mongolian army in 1232, so he lived in seclusion and was studied by Kublai Khan of Yuan Shizu. 1248 was written in "Circular Sea Mirror", the main purpose of which was to explain the method of arranging equations with astronomical elements. "Astrology" is similar to the column equation method in modern algebra. "Let Tianyuan be so-and-so" is equivalent to "Let X be so-and-so", which can be said to be an attempt of symbolic algebra. Another mathematical work by Ye Li, Yi Gu Yan Duan (1259), also explains Heaven. Zhu Shijie (1300 or so), whose real name is Yanshan (near Beijing today), "traveled around the lake and sea with famous mathematicians for more than 20 years" and "gathered scholars by following the door" ("Mo Ruo and Zu Yi: Four Lessons"). Zhu Shijie's representative works in mathematics include "Arithmetic Enlightenment" (1299) and "Meeting with the Source" (1303). "Arithmetic Enlightenment" is a well-known mathematical masterpiece, which spread overseas and influenced the development of mathematics in Korea and Japan. "Meeting with the source of thinking" is another symbol of the peak of China's mathematics in the Song and Yuan Dynasties, among which the most outstanding mathematical creations are "thinking about the source" (formulation and elimination of multivariate higher-order equations), "superposition" (higher-order arithmetic progression summation) and "seeking differences" (higher-order interpolation). Zu Chongzhi (AD 429-500) was born in Hebei Province. He is not only a mathematician, but also familiar with astronomical calendar, machinery manufacturing, music and other fields, and is an astronomer. Zu Chongzhi's main achievement in mathematics is the calculation of pi, which is 3. 14 15926.