Mathematics, which originated from the early production activities of human beings, is one of the six great arts in ancient China, and is also regarded as the starting point of philosophy by ancient Greek scholars. (mathematikós) means "the basis of learning", which comes from μ? θξμα(máthema) ("science, knowledge and learning").

The evolution of mathematics can be regarded as the continuous development of abstraction, or the extension of subject matter. The first abstract concept is probably number, and its cognition that two apples and two oranges have something in common is a great breakthrough in human thought. In addition to knowing how to calculate the number of actual substances, prehistoric humans also learned how to calculate the number of abstract substances, such as time-date, season and year. Arithmetic (addition, subtraction, multiplication and division) also came into being naturally.

In addition, writing or other systems that can record numbers are needed, such as Mu Fu or chips used by the Inca Empire to store data. There are many different counting systems in history.

Since the historical era, the main principles in mathematics have been formed, which are used for tax and trade calculation, for understanding the relationship between numbers, for measuring land, and for predicting astronomical events. These needs can be simply summarized as the study of quantity, structure, space and time in mathematics.

By16th century, elementary mathematics such as arithmetic, elementary algebra and trigonometry were basically complete. The appearance of the concept of variables in the17th century made people begin to study the relationship between variables and the mutual transformation between graphs. In the process of studying classical mechanics, the method of calculus was invented. With the further development of natural science and technology, set theory and mathematical logic for studying the basis of mathematics began to develop slowly.

Mathematics has been expanding from ancient times to the present, and it has a rich interaction with science, and both of them have benefited a lot. Mathematics has made many discoveries in history and is still being discovered today. According to Mikhail B.Sevryuk's record in the Journal of the American Mathematical Society from June, 5438 to October, 2006, "Since 1940 (the year when mathematical reviews were first published), the number of existing papers and books in the database of mathematical reviews has now exceeded1900,000. Most of this learning sea is a new mathematical theorem and its proof. "