2. From Tang Dynasty to Song Dynasty, especially in the golden age of mathematics, mathematics got further development, geometry and algebra reached a new peak, in which systematic algebra was established and more mathematical methods and concepts were further promoted and developed.
3. In the last century, that is, the Ming and Qing Dynasties, China's arithmetic began to decline. Because China's arithmetic system is not concise enough, China's mathematics has come to a standstill. At the same time, the development of mathematics in western countries has entered a new stage.
4. Since the turning point of the curve is the main research object of calculus, Euler put the function in the center for the first time, and it is based on the differential of the function. It is precisely because of the bold and innovative spirit of these scholars that calculus shows its unique role. With calculus as the adhesive, mathematics and mechanics began to combine, and geometry and algebra began to combine. With calculus as the driving force, probability theory has been further developed and mathematics education has been developed.
5. By the end of18th century, the work of laying the foundation for calculus has been urgently placed in front of mathematicians; On the other hand, the branches of mathematics outside the central discipline of mathematics have accumulated a number of important problems, such as the meaning of complex numbers, the position of parallel postulates in Euclidean geometry, and the possibility of radical solutions of higher algebraic equations. Most of them are put forward from the inside of mathematics;
6./kloc-Since the late 8th century, many new research fields have appeared in natural sciences, such as thermodynamics, fluid mechanics, electricity, magnetism and geodesy, which have injected new impetus into mathematics from the outside. The above factors contributed to the dynamic innovation and development of mathematics in the19th century.
7./kloc-In the 9th century, mathematics broke through the dominant position of analysis, and various branches such as geometry, algebra and analysis sprang up like mushrooms after rain. Only in the first 30 years of the19th century, a group of young mathematicians in their twenties and thirties made pioneering achievements in the fields of number theory, projective geometry, complex variable function, differential geometry, non-Euclidean geometry and group theory.