As an important part of calculus, the limit concept of quadrature and the study of infinitesimal method, China was not much behind the west in ancient times, even before the west, and China had already begun to study calculus. In the philosophical thoughts and works of Laozi and Zhuangzi, there has been infinite separability and limit thought; Mo Jing has already had mature definitions about the concepts of infinity (without internal minima), infinity, finiteness, infinitesimal (without internal minima), instantaneity and limit. Liu Hui, a mathematician in Wei, Jin, Southern and Northern Dynasties, calculated the area of a circle according to his secant technique, and calculated pi to four decimal places. But this kind of calculus thought began to appear and develop in western countries at the beginning of17th century. In ancient China, Liu Hui was not the only one who studied limit theory and infinitesimal method. As early as the 5th century, Zu Heng had used limit theory and infinitesimal method to find the volume of the ball. As for the sum of higher-order arithmetic progression, it has been studied in the ancient Northern Song Dynasty in China, and it has been developed and applied more maturely. Among them, Shen Kuo is a representative figure, and his mathematical methods such as gap product, meeting circle and chess number can be reflected in the in-depth study of higher-order arithmetic progression's theory of peace at that time. The publication of Shu Shu Jiu Zhang by Qin in the Southern Song Dynasty is of epoch-making significance, among which the approximate solution of any number (higher order) equation is solved by the methods of increase, multiplication and division, that is, the method of seeking a skill by taking great derivative is world-famous. /kloc-around 0/4th century, it can be said to be a peak in the development of ancient mathematics in China, including cholesky decomposition's radical diagram, combinatorial mathematics, finding big difference, recruiting difference (internal difference method of high-order difference), calculating the total number of big differences (solution of a congruence group), Pythagoras mathematics, four-element method (solution of four high-order equations) and superposition (superposition). Mathematical theories such as multiplication, multiplication methods and the reform of computing technology were very famous in China at that time and even in the century, which also made ancient mathematics play a decisive role in the century. Generally speaking, China's ancient calculus theory was more than 500 years earlier than that of the West. Ancient Chinese mathematicians successfully completed the first two stages of establishing calculus, namely, the concept of limit and the infinitesimal method of quadrature, which is also the most critical stage. However, due to China's Yuan Dynasty system, the theory of the relationship between integral and differential in the last stage was not successfully completed, and the stereotyped writing system in Yuan Dynasty was a big obstacle to academic development. Especially in the study of mathematics, China in ancient times was infinitely close to the completion of the theory of calculus, but this theory was hindered at the critical moment when calculus was founded, which led to the stagnation of the development of calculus and eventually made the research of calculus backward.