Mathematical mechanization refers to the transformation of mathematical reasoning process into a series of mechanized steps, which are expressed intuitively in the form of symbols and graphics, and strictly regulated by logical relations. The characteristics of mathematical mechanization include: fully automatic reasoning process, accurate operation flow and strict normative logic, which can eliminate loopholes and errors in reasoning process and can be applied to numerical calculation and symbolic operation.

This paper discusses the characteristics of axiomatic thinking in mathematics as follows:

Mathematical axiomatization is a rigorous description and understanding of mathematical results through abstract definition, reasoning and theorem proving. Its characteristic is that it provides a clear and concise mathematical language, constructs the structure of mathematical system through axioms and principles, and analyzes and discusses it accurately. The ultimate goal of mathematical axiomatization is to establish a complete and rigorous mathematical system, promote the in-depth exploration of mathematical theory and provide reliability guarantee for practical application.

The significance of discussing mathematical mechanization and axiomatic thinking is as follows:

Mathematical mechanization and axiomatization are of great significance in mathematical research. Mathematical mechanization makes the deduction and operation of mathematical theory more efficient and reliable, and makes mathematical research more deeply and widely used in various fields. Axiomatization of mathematics is a systematic arrangement and combing of the basic knowledge of mathematics, which can improve the rigor and credibility of mathematical research and provide new ideas and methods for promoting the development of mathematics.

In a word, mathematical mechanization and axiomatization are not only important ideas in the development of modern mathematics, but also play an irreplaceable role in promoting the deepening and development of mathematical research.

As follows:

Mathematical mechanization mathematics is a science that studies quantitative relations and physical properties. "Number" and "shape" are everywhere in the real world. Therefore, mathematical science is the foundation of natural science, high technology and even engineering construction, which has been recognized by people. The advantage of mathematical science is that it can turn difficult into easy, turn mystery into common sense, and provide a framework for solving various problems.