1084, the Secretary Province of the Song Dynasty published and engraved 10 arithmetic classics such as Nine Chapters, which was the first printed mathematical work in the world. Later, mathematicians in the Southern Song Dynasty reprinted these engravings, including Nine Chapters of Arithmetic, Zhou Pian, Sun Zi, Cao Wu, Zhang Qiujian Shu Jing * * *, Shu Shu Ji Ji Jie and so on.

Jia Xian, a mathematician in the Northern Song Dynasty, wrote Nine Chapters of Arithmetic of the Yellow Emperor and Jing Cao Jing, which were important mathematical works at that time. Most of this book is preserved because it copied Yang Hui's "Nine Chapters of Arithmetic Algorithms".

Shen Kuo, a great scientist in the Northern Song Dynasty, made a unique contribution to mathematics. Meng Qian Bi Tan pioneered the gap product technology and the summation of higher-order arithmetic progression. The intersection circle method is also put forward, and the approximate formula for calculating the arc length of bow is put forward for the first time.

The book of arithmetic in nine chapters written by Qin, with a total volume of *** 18. There are 9 kinds of 8 1 topics in Dayan, Shi Tian, Tianjing, Prospecting, Fugong, Qian Gu, Architecture, Military and Stone Art. Their achievements are great, and the problems are more complicated than previous calculations.

Yang Hui * * * has written five mathematical works, namely Detailed Explanation of Arithmetic Algorithms in Nine Chapters, Daily Arithmetic, General Background of Multiplication and Division, Fast Multiplication and Division Based on Field-Mu Ratio, and Seeking Odd Algorithms from the Past. There are four handed down from generation to generation, ranking first among mathematicians before Yuan Dynasty.

The northern center at the turn of the Song and Yuan Dynasties, represented by Ye Li, focused on astrophysics and the solution of higher-order equations. Ye Li's Round Sea Mirror (volume 12) and Yi Gu Yan Duan (volume 3) are the earliest works with celestial technique as the main method.