There are two main achievements in mathematics in the astronomical work Zhou Bi suan Jing compiled at the end of the Western Han Dynasty (the first century BC): (1) put forward the special case and universal form of Pythagorean theorem; (2) Chen Zi's method of measuring the height and distance of the sun was a pioneer of gravity difference. In addition, there are more complicated root-finding problems and fractional operations.
Nine Chapters Arithmetic is an ancient mathematical classic that has been compiled and revised by several generations. It was written in the early years of the Eastern Han Dynasty (1st century A.D.). This book is written in the form of problem sets, collecting 246 questions and their answers, which belong to nine chapters: Tian Fang, Su Mi, Decline, Shao Guang, Shanggong, Equal Loss, Profit and Loss, Equation and Pythagoras. The main contents include four fractional and proportional algorithms, the calculation of various areas and volumes, and the calculation of pythagorean measurement. In algebra, the concept of negative number and the law of addition and subtraction of positive and negative numbers introduced in the chapter of equation are the earliest records in the history of mathematics in the world. The solution of linear equations in the book is basically the same as that taught in middle schools now. As far as the characteristics of Nine Chapters Arithmetic are concerned, it pays attention to the application and integration of theory with practice, and forms a mathematical system centered on calculation, which has had a far-reaching impact on the ancient calculation in China. Some of its achievements, such as decimal value system, modern skills and surplus skills, have also spread to India and Arabia, and through these countries to Europe, which has promoted the development of world mathematics.
The Tang Dynasty made great progress in mathematics education. In 656, imperial academy established a Mathematics Museum with doctors and teaching assistants in mathematics. Taishi ordered Li and others to compile and annotate ten calculation books (including Zhou Pi Ai Shu, Jiu Zhang Shu Shu, Dao Shu, Sun Zi Shu, Zhang Qiu Shu, Xiahou Yang Shu, Ji Gu Shu and Sun Zi Shu). It has played an important role in preserving ancient mathematical classics.
In addition, due to the need of calendar in Sui and Tang Dynasties, the quadratic interpolation method was established, which laid the foundation for the higher-order interpolation method in Song and Yuan Dynasties. In the late Tang Dynasty, computing technology was further improved and popularized, and many practical arithmetic books appeared, trying to simplify the multiplication and division algorithm.