The first stage: the budding period of mathematics (4000 BC-6th century BC).

With the development of ancient human beings, the application of numbers gradually involved in life, and human beings established the most basic mathematical concepts. Natural numbers appear, simple calculations, and the most basic and simple geometric figures are known.

The outstanding representatives of mathematics development at this stage are ancient Babylonian mathematics, China mathematics and Egyptian mathematics. The mathematics knowledge in this period is roughly equivalent to the content of kindergarten and grade one or two in primary school, and even simpler than this.

The second stage: the period of elementary mathematics and constant mathematics (6th century BC-AD16th century).

With the progress of history, mathematics has also been greatly developed. During this period, Greek mathematicians took a big step forward in mathematics. Taking Euclid's Elements of Geometry as the representative, the axiomatic system and rigorous proof are introduced to make mathematics more complete and change mathematics from simple and concrete measurement to strict and abstract proof.

Pythagoras school completed the strict proof of Pythagoras theorem, and then discovered irrational numbers, which triggered the first mathematical crisis. This also makes mathematics develop from rational number to irrational number.

The third stage: variable mathematics stage (17th century-1middle and late 9th century).

This stage is also called modern mathematics stage, and mathematics develops rapidly. China was in the closed-door Qing Dynasty.

The symbol of this stage is that mathematics has changed from constant to variable, and its development has two milestones.

The first milestone was the birth of analytic geometry. 1637, the French mathematician Descartes invented the coordinate system, founded analytic geometry, introduced variables into mathematics, and combined numbers with shapes, which laid the foundation for the establishment of calculus.

The second milestone is the creation of calculus. Newton, the greatest figure in the history of British science, introduced the concept of infinitesimal from the movement of physics. 1669, he put forward the concept of calculus, which provided the most favorable tool for the development of modern mathematics and opened a new era of mathematics. It also pushes mathematics from the static constant stage to the research stage of dynamic variables.

The fourth stage: the period of modern mathematics (after 1874).

1874, German mathematician Cantor founded set theory, which marked the arrival of modern mathematics and the beginning of pure mathematics. The appearance of Poincare, Klein and Hilbert, the three giants of mathematics, also indicates that mathematics is more abstract and pure. It also led to the rise of four abstract branches: real variable function, functional analysis, topology and abstract algebra.

Although the third mathematical crisis caused by set theory has not been solved, we believe that the arrival of the crisis is still the driving force for the development of mathematics, and the solution of the crisis will definitely make mathematics go up a storey still higher, which has been confirmed by the previous two mathematical crises. Of course, the current mathematical knowledge is far from being understood by ordinary people. Except for specialized mathematics talents, it is estimated that others have never met it, let alone used it directly.