Narrow sense: mathematical thoughts, spirits, methods, viewpoints and languages, as well as their formation and development.
Broad sense: In addition to the above connotations, it also includes mathematicians, mathematical history, mathematical beauty and mathematical education. Humanistic elements in the development of mathematics, the relationship between mathematics and society, the relationship between mathematics and various cultures, and so on.
In the upcoming high school mathematics curriculum standards, mathematics culture is a separate section, which has received special attention. Many teachers will ask why they do this. An important reason is that there is an isolationist tendency in mathematics at the beginning of the 20th century, which has been affecting China today. The over-formalization of mathematics makes people mistakenly think that mathematics is just a "free creation" imagined by a few geniuses. The development of mathematics does not need the promotion of society, and its truth does not need the test of practice. Of course, the progress of mathematics does not need the edification of human culture. As a result, the "revival of empiricism" appeared in the western mathematics field. White's mathematical culture theory tries to return mathematics to the cultural level. Klein's Ancient and Modern Mathematical Thoughts, Mathematics in Western Culture and Mathematics: The Loss of Determinism were published one after another, trying to create a humanistic mathematical culture.
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. Zheng Yuxin's monograph "Mathematical Culturology" and so on. It is characterized by emphasizing the cultural effect produced by "mathematical isomorphism" with social constructivism philosophy.
The above works and many papers try to liberate mathematics from the circle of pure logical deduction and reasoning, focusing on the analysis of the history of mathematical civilization, fully revealing the cultural connotation of mathematics and affirming the value of mathematics as a cultural existence.
After entering the 2 1 century, the study of mathematical culture has deepened. An important symbol is that mathematics culture has entered the classroom of primary and secondary schools and penetrated into the actual mathematics teaching, so as to make students really be infected by culture in the process of learning mathematics, produce a cultural upsurge, experience the cultural taste of mathematics and observe the interaction between social culture and mathematics culture.