Mathematics originated from early human production activities. The ancient Babylonians had accumulated some mathematical knowledge, which could be applied to practical problems. Judging from mathematics itself, their mathematical knowledge is only obtained through observation and experience, and there is no comprehensive conclusion and proof, but we should fully affirm their contribution to mathematics.
Many mathematical objects, such as numbers, functions and geometry, reflect the internal structure of continuous operations or the relationships defined in them. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations. In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.
Therefore, we can learn abstract systems such as groups, rings and domains. These studies (structures defined by algebraic operations) can form the field of abstract algebra. Because abstract algebra has great universality, it can often be applied to some seemingly unrelated problems.
The evolution of extended data mathematics can be regarded as the continuous development of abstraction and the extension of subject matter. Eastern and western cultures have also adopted different angles. European civilization developed geometry, and China developed arithmetic. The first abstract concept is probably number (China's calculation), and its cognition is that two apples and two oranges have something in common, which is a great breakthrough in human thought. Besides knowing how to count physical objects, prehistoric humans also knew how to count them.
In addition, it requires writing or other systems that can record numbers, such as Mu Fu or chips used by the Incas. There are many different counting systems in history.
In ancient times, the main principles of mathematics were the study of astronomy, the rational distribution of land and food crops, taxation and trade. Mathematics is formed to understand the relationship between numbers, measure land and predict astronomical events. These needs can be simply summarized as the study of quantity, structure, space and time in mathematics.
After the Renaissance in Western Europe from ancient Greece to16th century, elementary mathematics, such as elementary algebra and elementary trigonometry, has been basically complete, but the concept of limit has not yet appeared.
/kloc-in the 0/7th century, the concept of variable came into being in Europe, which made people begin to study the mutual transformation relationship between changing quantity and number. In the process of establishing classical mechanics, the method of combining calculus with geometric accuracy was invented. With the further development of natural science and technology, the fields of set theory and mathematical logic, which study the basis of mathematics, began to develop slowly.