Mathematics has three levels. First, mathematics, as a theoretical thinking, focuses on cultivating and embodying the ability of human rational thinking; Second, as a technical application, the combination of mathematics, mathematical technology and computer makes mathematics a productive force that directly creates wealth; Thirdly, mathematics, as a cultural accomplishment, has become a part of the basic quality of modern people.
Mathematics is a subject that studies concepts such as quantity, structure, change and spatial model with symbolic language. Mathematics, as an expression of human thinking, embodies people's aggressive will, meticulous logical reasoning and pursuit of perfection. Although different traditional schools can emphasize different aspects, it is the interaction of these opposing forces and their comprehensive efforts that constitute the vitality, availability and lofty value of mathematical science.
The knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be found in ancient mathematical documents of ancient Egypt, Mesopotamia and ancient India. Since then, its development has made small progress. Until the Renaissance in16th century, the mathematical innovation generated by the interaction with new scientific discoveries led to the acceleration of knowledge.
Mathematics is used in different fields of the world, including science, engineering, medicine and economics. The application of mathematics in these fields is usually called applied mathematics, and sometimes it will lead to new mathematical discoveries and the development of new disciplines. Mathematicians also study pure mathematics, that is, mathematics itself, without any practical application. Although many studies started from pure mathematics, many applications will be found later.