In the exploration of understanding the objective world, people are increasingly convinced that the rationality of the world can be described by mathematics. Mathematics not only studies the quantitative relationship and spatial form of the objective world, but also studies itself. One paradox after another in the history of mathematics records the crises that mathematics experienced again and again in the process of studying itself. The crisis seems to have shaken the foundation of mathematics, which has consolidated its foundation and made it more solid and reliable in the process of constantly examining itself strictly and constantly overcoming its own contradictions.

People have different understandings of beauty, but in short, beauty is related to perfection, perfection, harmony and order. And mathematics itself embodies the beauty of simplicity and harmony. The existence value of mathematical culture in the upcoming high school mathematics curriculum standards, mathematical culture is a separate plate, which has received special attention. Sun Xiaoli, a professor in Peking University, was the earliest scholar in China who paid attention to mathematical culture. The book Mathematics and Culture, co-edited by her and Deng Donghao, collected the relevant expositions of some famous mathematicians and recorded the thinking on mathematical culture from the perspective of dialectics of nature. Mathematics and Culture, published later by Qi, mainly expounds the cultural value of mathematics from the history of non-Euclidean geometry, especially points out the cultural significance of mathematical thinking.

The motivation, process, methods and results of artistic practice and mathematical activities are all promoting their own values and constantly realizing the powerful description of the world schema. This kind of value is to master the world aesthetically on the basis of a comprehensive and complete understanding of the real world. Art and mathematics are universal idealized world languages. In the process of describing the world schema, art and mathematics have also developed and perfected their own expressions. The most basic carrier of this expression is the unique language system of art and mathematics. Their common characteristics are: cross-culture. Art and mathematics express a common desire of human beings, so they can transcend time and geographical boundaries and realize extensive exchanges between different cultural groups.

The fact that art and mathematics have these three values at the same time endows the spiritual value of art and mathematics with universality. To sum up, the similarities are: (1) self-discipline. The self-discipline of mathematical value is related to the objectivity of mathematical value; The value of art cannot be measured by democratic elections and personal likes and dislikes. The value of art and mathematics is basically recognized, appreciated and evaluated within its own framework. (2) Transcendence. They can transcend time and space and show eternity. In the process of surpassing the value of art and mathematics, reality is expanded and extended. People are remolded and endowed with ideals. The transcendence of art and mathematics is also manifested in the advanced value. (3) Non-utilitarian. The non-utility of art and mathematics is one of the remarkable characteristics that distinguish their value judgments from other cultures and sciences. (4) Diversification, materialization and generalization. Under the impact of modern science and technology and commercialization, the values of art and mathematics have also evolved, and their respective values have been dispersed, infiltrated, applied and crossed in many fields. ?

Through the study of mathematical culture, we can cultivate college students' abstract thinking, image thinking and logical thinking ability, especially their innovative ability, and improve their cultural quality to meet the needs of society. Anyone who has studied mathematics or has never studied mathematics can read this book and get help as long as he has a certain mathematical foundation.