1, the formation period of mathematics, which is the period when human beings establish the most basic mathematical concepts. Since counting, human beings have gradually established the concept of natural numbers, simple calculation methods, and recognized the most basic and simplest geometric forms. Arithmetic and geometry are not separated.

2. Elementary mathematics, that is, the period when mathematics remains unchanged. The most basic and simple achievements in this period constitute the main content of middle school mathematics. This period began in the 5th century BC, maybe earlier, and lasted for about two thousand years until17th century. This period gradually formed the main branches of elementary mathematics: arithmetic, geometry and algebra.

3. The period of variable mathematics. Variable mathematics came into being in17th century, and has gone through two decisive and significant steps: the first step is the generation of analytic geometry; The second step is calculus, which is the branch of higher mathematics that studies the differential and integral of functions and related concepts and applications. It is the basic subject of mathematics. The content mainly includes limit, differential calculus, integral calculus, equation and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change. It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols. Integral calculus, including the calculation of integral, provides a set of general methods for defining and calculating area and volume.

4. Modern mathematics. The period of modern mathematics began at the beginning of19th century. The beginning of the modern stage of mathematics development is characterized by profound changes in all foundations-algebra, geometry and analysis.