Mathematical culture and mathematical beauty are closely linked with mathematics. You have me and I have you. Mathematics is like a person, its professional knowledge is like a human skeleton, its culture is like a human muscle, and its beauty is better than human blood. A person should not only have a skeleton, but also have muscles and blood to become a person, a fresh person and an aura person. Therefore, mathematics culture and mathematics beauty are indispensable contents in mathematics teaching. Following the footsteps of mathematicians' growth, we can understand the hard-working style, inspiring academic experience and lofty ideology and morality of our predecessors. They are extremely vivid ideological nourishment to stimulate learning interest, enthusiasm, scientific methods and national spirit in mathematics teaching. It can inspire students to climb the peak of science, cultivate the habit of respecting the law of scientific development and rational thinking such as seeking truth, reasoning, criticizing and questioning, and the scientific spirit of persevering in the pursuit of truth. Showing the background of mathematical knowledge, the formation and development process of mathematical concepts and the process of putting forward mathematical theorems can guide students to understand the interaction between mathematical science and the development of human society, which can trace back to the source, broaden their horizons, help them to understand mathematical knowledge comprehensively and deeply, appreciate the value of mathematics, and improve their scientific literacy and cultural literacy. This paper introduces the modern application of mathematical knowledge and mathematical thinking methods, shows the connection between mathematics and other natural sciences and interdisciplinary sciences, makes students feel the application value and social needs of mathematics, and realizes that "there is mathematics everywhere in life", thus correcting their misconceptions that the main function of mathematics is calculation, and the ultimate goal of mathematics learning is to stimulate students' creative desire for exams, so as to change passive learning into active learning. Appreciating the beauty in mathematics, the beauty of unity, simplicity, symmetry and strangeness in mathematics can greatly change the boring situation of mathematics class at present, make students learn with great interest, improve their aesthetic ability in mathematics while enjoying beauty, enlighten their thinking, cultivate their quality, and promote the comprehensive and harmonious development of their personality and emotional experience. Analysis of the present situation and problems of infiltrating mathematical culture and beauty into middle school mathematics teaching: Mathematical culture has gradually entered middle school mathematics classroom, but we can see that the current teaching practice still only overemphasizes the instrumental role of mathematics, weakens its cultural value and ignores its influence on other disciplines, making mathematics an intangible culture for a long time. At present, the way of infiltrating mathematics culture in schools is generally only to introduce the history of mathematics. The teacher introduces a certain stage of mathematics development in one or two sentences, without excavating any connection between them or combining it with the contents of textbooks. Simple form, boring, lack of interest, systematicness and practicality are the present situation of infiltrating mathematics culture into middle school mathematics teaching. How can such teaching achieve the purpose of infiltrating mathematical culture, inheriting mathematical culture and stimulating students' mathematical learning? The main reasons are as follows: First, the utilitarian teaching goal. Under the command of the senior high school entrance examination, the teaching goal of school mathematics is still to implement "double basics of mathematics" [1], and the main task is to improve the enrollment rate. Therefore, the teaching method is generally used in mathematics classroom teaching, and teachers pay more attention to the cultivation of students' problem-solving ability, and strive to instill more mathematical conclusions and do more application problems in a limited time. Nature ignores the infiltration of mathematical culture. In fact, middle school mathematics teaching should aim at cultivating people with mathematical literacy, not a tool for mechanical calculation! In this way, the role of infiltrating mathematical culture can not be ignored. Secondly, a single evaluation system. Examination is the only evaluation system of middle school teaching at present, and written examination can only examine students' mastery and application of knowledge to a certain extent, but can not comprehensively examine students' learning process and mathematics literacy, nor can it fully reflect a teacher's teaching level. Therefore, the evaluation system of mathematics teaching should be diversified, focusing on both the results and the process, and paying more attention to various factors affecting the teaching process and results. The correct evaluation system should include four aspects: the evaluation of course materials, the evaluation of teaching process, the evaluation of students' academic performance (mainly referring to students' mathematical thinking) and the evaluation of students' social adaptability. Furthermore, isolated discipline construction. Every course in middle school is taught in relative isolation, and each course often only pays attention to the formation of knowledge system within disciplines and ignores the knowledge connection between disciplines, such as vectors. When learning vector, it is difficult for students to understand the concept of vector, and many teachers often can't explain its connection with physical mechanics in teaching. If we can understand from the aspect of physical mechanics and establish the connection between physics and mathematics, it will be much easier to understand the concept of vector. Infiltrating mathematics culture and beauty in middle school mathematics teaching is like flesh and blood. We should not only study the theoretical knowledge of infiltrating mathematical culture and beauty into middle school mathematics teaching, but also put it into practice to make it really useful mathematics. This is a very important issue in the teaching reform, and it is hoped that it will receive universal attention and strong support from the society.