The evolution of mathematics can be regarded as the continuous development of abstraction, or the extension of themes. Eastern and Western cultures have also adopted different perspectives. European civilization has developed geometry, while China has developed arithmetic. The first abstracted concept is probably the number (Chinese computing chip). The recognition of something similar between two apples and two oranges is a breakthrough in human thinking. In addition to knowing how to count the number of actual objects, prehistoric humans also know how to count the number of abstract concepts, such as time—days, seasons, and years. Arithmetic (addition, subtraction, multiplication, and division) also arises naturally.
Furthermore, writing or other systems that can record numbers are needed, such as Fumu or the Chip used by the Incas. There have been many different counting systems in history.
In ancient times, the main principles in mathematics were to study astronomy, the rational distribution of land and food crops, taxation and trade related calculations. Mathematics is formed to understand the relationship between numbers, to measure the land, and to predict astronomical events. These needs can be simply summarized as mathematical research on quantity, structure, space and time.
Western Europe went through the Renaissance era from ancient Greece to the 16th century. Elementary algebra, trigonometry and other elementary mathematics have been largely complete, but the concept of limit has not yet appeared.
The emergence of the concept of variables in Europe in the 17th century led people to study the interrelationships between quantities and figures and the mutual transformations between figures. During the establishment of classical mechanics, the method of calculus combined with geometric precision was invented. With the further development of natural science and technology, the fields of set theory and mathematical logic, which are produced to study the foundation of mathematics, have begun to develop slowly.