I. Abstraction
The abstraction of mathematics is manifested in the abstraction of spatial form and quantitative relationship. In the process of abstraction, it abandons the specific characteristics of more things, so it has a very abstract form. It is characterized by high generality and symbolization of specific processes. Of course, abstraction must be based on concreteness. Abstraction can be summarized as the following three points:
1, not only mathematical concepts are abstract, but also mathematical methods are abstract, and abstract symbols are widely used.
2. The abstraction of mathematics is abstracted step by step, and the next abstraction is based on the previous abstract material.
3. A high degree of abstraction must have a high degree of generalization.
Second, rigor.
The rigor of mathematics means that mathematics is logical and accurate. Stiffness is the basic feature of mathematics. It requires that the description of mathematical conclusions must be concise and accurate, while the reasoning and systematic arrangement of conclusions are strict and thorough.
Even some of the most basic and commonly used original concepts that cannot even be defined by logical methods are not satisfied with intuitive descriptions, but require axioms to determine them.
Third, applicability.
The wide application of mathematics shows that all science and technology can solve related problems with the help of mathematical knowledge and thinking methods in principle. Mathematics is closely related to people's life, social development and scientific and technological progress. Mathematics provides conditions and foundations for the establishment and development of other disciplines.
Mathematics is an important part of human culture. The position of mathematics has changed or is changing greatly.
In recent decades, with the rapid development of modern mathematics and the rise and wide application of computer technology, many scientists have not only separated mathematics from natural science, thus establishing its position as the foundation of natural science, but also devoted themselves more and more to the frontier research of applied mathematics, making the application of mathematics a means, a way of thinking and a habit of thinking.