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Mathematics is a science of research.
What is mathematics? Some people say, "Isn't mathematics the knowledge of numbers?"

That's not true. Because mathematics not only studies "number" but also "shape", triangles and squares, which are familiar to everyone, are also the objects of mathematical research.

Historically, there have been various views on what mathematics is. Some people say that mathematics is correlation; Some people say that mathematics is logic. "Logic is the youth of mathematics, while mathematics is the prime of logic."

So, what is mathematics?

Engels, the great revolutionary tutor, stood at the theoretical height of dialectical materialism, profoundly analyzed the origin and essence of mathematics and made a series of incisive scientific conclusions. Engels pointed out that "mathematics is a quantitative science" and "the object of pure mathematics is the spatial form and quantitative relationship of the real world". According to Engels' point of view, it is more accurate to say: mathematics-a science that studies the quantitative relationship and spatial form of the real world.

Mathematics can be divided into two categories, one is pure mathematics and the other is applied mathematics.

Pure mathematics, also called basic mathematics, specializes in the internal laws of mathematics itself. The knowledge of algebra, geometry, calculus and probability introduced in the textbooks of primary and secondary schools belongs to pure mathematics. A remarkable feature of pure mathematics is to temporarily put aside the specific content and study the quantitative relationship and spatial form of things in pure form. For example, it doesn't matter whether it is the area of trapezoidal rice fields or the area of trapezoidal mechanical parts. What everyone cares about is the quantitative relationship contained in this geometry.

Applied mathematics is a huge system. Some people say that it is the part of all our knowledge that can be expressed in mathematical language. Applied mathematics is limited to explaining natural phenomena and solving practical problems, and it is a bridge between pure mathematics and science and technology. It is often said that now is the information society, and the "information theory" which specializes in information is an important branch of applied mathematics. Mathematics has three most remarkable characteristics.

High abstraction is one of the remarkable characteristics of mathematics. All mathematical theories have a very abstract form, which is formed through a series of stages, so it greatly exceeds the general abstraction in natural science, and not only the concept is abstract, but also the mathematical method itself is abstract. For example, physicists can prove their theories through experiments, while mathematicians can't prove theorems through experiments, but can only use logical reasoning and calculation. Now, even geometry, which used to be regarded as "intuitive" in mathematics, is developing in the abstract direction. According to the axiomatic thought, there is no need to know geometric figures. It doesn't matter whether they are round or square. Even tables, chairs and beer cups can be used instead of dots, lines and noodles. As long as the relationship of combination, order and reduction is satisfied, and it is compatible, independent and complete, a geometry can be formed.

The rigor of the system is another remarkable feature of mathematics. The correctness of mathematical thinking lies in the rigor of logic. As early as more than 2000 years ago, mathematicians started from several basic conclusions and used the method of logical reasoning to organize rich geometric knowledge into a rigorous and systematic theory, just like a beautiful logical chain, with every link connected into a line. Therefore, mathematics has always been regarded as a "model of precise science".

Widely used is also a remarkable feature of mathematics. The size of the universe, the tiny particles, the speed of rockets, the ingenuity of chemical engineering, the change of the earth, the mystery of biology and the complexity of daily life require mathematics everywhere. In the 20th century, with the emergence of a large number of branches of applied mathematics, mathematics has penetrated into almost all scientific departments. Not only physics, chemistry and other disciplines are still enjoying the fruits of mathematics widely, but even biology, linguistics and history, which rarely used mathematics in the past, are combined with mathematics, forming rich marginal disciplines such as biomathematics, mathematical economics, mathematical psychology, mathematical linguistics and mathematical history.

Mathematicization of various sciences is a major trend in the development of modern science.