1. The history of mathematics and human development shows that mathematics has always been the main cultural force of human civilization, and it is closely related to human culture. In different times and cultures, the size of this power is different.

2. Mathematical culture is the basic form of spreading human thoughts; Mathematical culture contains special language forms created by human beings; Mathematical culture is a tool for the interaction between nature and human society; Mathematical culture has relative stability and continuity; Mathematical culture is very permeable.

3. Mathematical language is precise, never vague, organized, rigorous, concise and standardized.

4. The three crises in the history of mathematics were all related to paradox, which had a great influence on mathematics and philosophy. However, the mathematical crisis not only did not destroy mathematics, but also promoted the development of mathematics, which has rich ideological and cultural significance and promoted people's understanding of mathematics.

5. Mathematics also provides a methodological basis and technical means for human culture from the perspective of thinking and technology, thus enriching and promoting the development of culture. Mathematics is the foundation of scientific and cultural development in the information age.