1, elementary mathematics and ancient mathematics: this refers to1mathematics before the 7th century. Mainly Euclidean geometry established by ancient Greece, arithmetic established by ancient China, ancient Indian and ancient Babylon, algebraic equations developed during the European Renaissance, etc.

2. Variable mathematics: refers to mathematics established and developed at the beginning of 17- 19 century. The period of variable mathematics from the first half of17th century can be divided into two stages: the establishment stage of17th century (heroic age) and the development stage of18th century (creative age).

3. Modern mathematics: refers to19th century mathematics. The19th century of modern mathematics is the stage of comprehensive development and maturity of mathematics, and the face of mathematics has undergone profound changes. Most branches of mathematics were formed in this period, and the whole mathematics showed a comprehensive prosperity.

4. Modern mathematics: refers to mathematics in the 20th century. 1900, the famous German mathematician D. Hilbert delivered a famous speech at the World Congress of Mathematicians, and put forward 23 mathematical problems (see below) to predict and understand the future development of mathematics, which opened the prelude of modern mathematics in the 20th century.

From the horizontal division:

1, Basic Mathematics (English: Pure Mathematics). Also known as pure mathematics or pure mathematics, it is the core part of mathematics, including algebra, geometry and analysis, which study numbers, shapes and the relationship between numbers and shapes respectively.

2. Applied mathematics. Simply put, it is the application of mathematics.

3. Computational mathematics. Learn calculation methods (numerical analysis), mathematical logic, symbolic mathematics, computational complexity, programming and other issues. This subject is closely related to computers.

4. Probability statistics. Divided into probability theory and mathematical statistics.

5. Operational research and cybernetics. Operational research is a subject that solves the operation, organization and management problems of complex systems such as manpower, material resources and financial resources by mathematical methods on the basis of establishing models. Development history of world mathematics

Chip, a counting tool used by the Inca Empire. 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. Mathematical Greek μ α θ η μ α κ? 0? 2? 0? 9 (Mathematickó s) means "the basis of learning" and comes from μ? 0? 4θξμα(máthema) (Science, Knowledge and Learning).

The evolution of mathematics can be regarded as the continuous development of abstraction and 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) will naturally occur. Ancient stone tablets also confirmed the knowledge of geometry at that time.

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 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, had been basically completed. 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, which are produced for studying the basis of mathematics, have also begun to develop slowly.

Mathematics has been continuously extended since ancient times, and has rich interaction with science, and both of them have benefited a lot. There are many discoveries in mathematics in history, and they are still being discovered today. According to Mikhail B. Sevryuk's record in the Bulletin of the American Mathematical Society of June 5438+ 10, 2006: "Since 1940 (the first year of mathematical review), the number of papers and books in the database of mathematical reviews has exceeded1900,000, with an annual increase of more than 750,000. Most of this learning sea is a new mathematical theorem and its proof. "