Reflections on Mathematical Culture after Reading

In the long and splendid ancient culture of China, mathematical culture is a wonderful flower. Mathematics is not only the cornerstone of China's ancient practical science, but also contains mysterious cultural color and profound cultural accumulation. It permeates all fields of China and is an indispensable part of China culture. The following are my thoughts on mathematical culture. Welcome to reading.

Reflections on Mathematical Culture 1 When I first studied the history of mathematics in college, I became interested in the history of mathematics and fell in love with the subject of mathematics. After work, I became a math teacher. I often wonder how interesting it would be to integrate mathematics culture into the classroom. So, I carefully studied the book "Mathematical Culture" and gained a lot.

As we all know, mathematics is an important part of human civilization. At first, babbling created a colorful counting system, and then more and more detailed mathematical branches were established in the rainy season. Today, it has demonstrated its dazzling mathematical achievements in In the Mood for Love. Like other cultures, mathematical science is the crystallization of thousands of years of human wisdom.

After reading Mathematical Culture, I was deeply moved. What kind of feeling is that? It is the heart of an ambitious man with religious devotion to mathematics, and it is also the yearning of a pursuer with endless desire to explore history. Every generation adds a floor to the ancient building of mathematics. It is necessary for us to know the history of this building when adding bricks and tiles to it. Through this book, I have a more comprehensive understanding of the development of mathematics. The book introduces some important events, important figures and important achievements in the development of mathematics through vivid and concrete examples, which gives me a preliminary understanding of the historical process of the emergence and development of mathematics, the role of mathematics in the development of human civilization, and the rigorous academic attitude and persistent exploration spirit of mathematicians.

Mathematics is the process of human creative activities, not just the result of formalization; Looking at mathematics science and mathematics education from the viewpoint of dialectical materialism, in the process of their formation and development, it not only shows the characteristics of contradictory movement, but also has close ties with society, politics, economy and general human culture. Mathematics has a long history. I learned that in the early days of human society, mathematics, language, art and religion together constituted the earliest civilization of mankind. Mathematics is the most abstract science, but the most abstract mathematics can breed the gorgeous flowers of human civilization. This makes mathematics the most basic subject in human culture. Engels pointed out: "The degree of application of mathematics in a science marks the maturity of this science." In modern society, mathematics is providing indispensable theoretical and technical support for the development of science and society.

The history of mathematics is not only a chronological record of mathematical achievements. The development of mathematics is by no means smooth sailing. In the case of following reading, it is full of hesitation, wandering, experiencing difficulties and twists and turns, and even facing difficulties and crises. The discovery of irrational numbers, the creation of calculus and non-Euclidean geometry ... These examples can help people understand the real process of mathematical creation, and they are packaged in the form of theorem to theorem in textbooks. Understanding this creative process can make people learn from exploration and struggle, gain inspiration and enhance confidence.

In the long river of mathematics, the huge waves caused by three mathematical crises truly reflect the majestic momentum like the long river of mathematics. In the first mathematical crisis, irrational numbers became a member of the big family of mathematics, and reasoning and proof overcame intuition and experience, and a vast world appeared before us. But hippasus, who first discovered the root number 2, was thrown into the sea. In the second mathematical crisis, mathematical analysis was established on the strict basis of real number theory and really became the mainstream of mathematical development. But Newton looked pale and powerless under the attack of British Archbishop Becquerel. In the third mathematical crisis, "Russell Paradox" challenged the certainty of mathematics for the first time, completely shaken the foundation of mathematics and gave it a broader development space. However, Godel's incompleteness theorem completely shattered Hilbert's ambition to establish and perfect the mathematical formal system and solve the mathematical foundation. Genius is often ahead of its time, which is really hard for ordinary people to understand. But time will tell!

Mathematics is a historical or cumulative science. Important mathematical theories are always based on inheriting and developing the original theories. They will not overthrow the original theory until they are close, and they always contain the original theory. For example, the theoretical evolution of numbers shows obvious accumulation; In geometry, non-Euclidean geometry can be regarded as an extension of Euclidean geometry; Abstract algebra dating back to elementary algebra did not eliminate the former; Similarly, the generalization of functions, derivatives, integrals and other concepts in modern analysis includes the definition of Le Classic as a special case. It can be said that in the long evolution of mathematics, almost no previous building was completely overthrown. China's traditional mathematics has a long history and has its own unique ideological system and development approach. It is continuous, with a long development time and brilliant achievements, showing a distinct color of "oriental mathematics" and having a far-reaching impact on the historical process of world mathematics development. From ancient times to the Song and Yuan Dynasties, China has long been the mainstream of world mathematics development. After the Ming Dynasty, due to various political and social reasons, China's traditional mathematics was on the verge of extinction and was completely monopolized by the western Euclidean tradition. The development of mathematics in China for thousands of years has left us a lot of valuable historical materials.

Mathematics is a new problem from a cultural point of view. But I believe that once you step into the threshold of mathematical culture, you will be surprised to find that this is a beautiful and strange world. However, some of the things mentioned in the article are just the skins on the other side. It is believed that with the in-depth study of mathematical culture, a more wonderful world will be presented to mankind. In a word, mathematical culture is a wonderful culture, and it is an unknown culture for us teenagers. If we understand it, we will gradually realize it and have a general taste in it.

Reflection on Mathematical Culture 2 By chance, I wandered around the library in my spare time. I happened to look through the book Mathematical Culture written by Fang Yanming and turned over a few pages. I really felt good, so I borrowed it and spent a lot of time understanding some of it. After that, I also collected some related information on the Internet. This book is a new textbook for quality education in colleges and universities, which is characterized by studying mathematics as a culture. 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. People who have studied mathematics or have not studied mathematics can read this book and get help as long as they have a certain mathematical foundation. This book is divided into eight chapters, which briefly expounds the subject system of mathematical culture, as well as the main contents of philosophy, society, aesthetics, innovation and methodology of mathematical culture, and has a special chapter to introduce the development history of mathematical thought for thousands of years, giving readers a whole system of mathematical science development. In writing, this book insists on integrating theory with practice, pays attention to introducing ideas and methods, and pays attention to developing people's thinking and inspiring people's innovative consciousness. This book can be used as a professional teaching material for quality education of college students of arts, science and engineering, and also as a cultural reference book and extracurricular reading material for general humanities workers, social scientists, university teachers and graduate students, including national civil servants. No science can be favored by future generations like mathematics. When talking about mathematics, Einstein said: "Another reason why mathematics enjoys a high reputation is that mathematics gives a certain degree of reliability to the precise natural science. Without mathematics, these sciences cannot achieve this reliability. Klein said: "Mathematics is not only a method, an art or a language, but also a creative subject.

A rich knowledge system is very useful to natural scientists, social scientists, philosophers, logicians and artists, and also influences the theories of politicians and theologians. Satisfied human curiosity to explore the universe and meditation on beautiful music; Sometimes it may even subtly affect the process of modern history, but there is no doubt about it. In fact, in modern empirical science, whether to accept mathematical methods has increasingly become the main criterion for the success of this subject. As early as May 1 959, the famous mathematician Hua published the article "The Great Use of Mathematics" in * * *, which brilliantly discussed the ubiquitous and important contributions of mathematics in "the size of the universe, tiny particles, the speed of rockets, the cleverness of chemical engineering, the change of the earth, the mystery of biology and the complexity of daily life". The contribution of mathematics is particularly emphasized in the topic "Today's Mathematics and Its Application" drafted by Mr. Wang Zikun, Department of Mathematical Physics, China Academy of Sciences. He said: "The contribution of mathematics lies in promoting and improving the whole scientific and technological level, cultivating and nourishing scientific and technological talents, prospering economic construction and benefiting all the people.

The cultivation of learning thinking and cultural quality plays an extremely great role, which is unmatched by other disciplines. The intersection of mathematics and education, mathematics and culture, mathematics and history, mathematics and philosophy, mathematics and sociology, mathematics and high technology. , have derived some new academic growth points. Take the combination of mathematics and economics as an example: mathematics and economics can be said to be inseparable, so that it is impossible to study economy without understanding mathematics today. In macroeconomic activities, how to stop economic prosperity in time without falling into the danger of catastrophic economic recession can rely on optimal control theory. It is precisely because of the application of cybernetics and gradient method that people have solved the optimal planning model of Korean economy.

Type. Mathematics plays an extremely extensive role in microeconomics. For example, when improving the success rate of products, if the quality of products depends on several factors, and each of these factors is limited by some conditions, then how to choose the best collocation is actually a problem of statistical experimental design (SED). In today's world, mathematics is used to establish economic models, seek the best scheme in economic management, organize, schedule and control production processes by mathematical methods, and obtain economic information from data processing. , so that algebra, analysis, probability theory, statistical mathematics and many other mathematical thinking methods enter economics, which in turn promotes the development of mathematics. Today, an economist who doesn't know mathematics will never be an outstanding economist. Mathematics is one of the basic disciplines of human science and culture. It has typical discipline independence and is not restricted by other disciplines. Unlike physics, chemistry and astronomy, it lacks independence. There are two main characteristics of innovation in mathematics: one is originality (invention and discovery) and the other is inheritance (that is, creative perfection). Aesthetics of mathematical culture is an important content of mathematical culture. Proch Ras, an ancient philosopher and mathematician, asserted: "Where there are numbers, there is beauty." Kepler also said, "Mathematics is the prototype of beauty in this world". The pursuit of mathematical cultural aesthetics has become an important driving force for the development of mathematics. From this, the French poet Novali once sang: "Pure mathematics is also a science and an art." "Mathematicians who are both scientists and artists are the only lucky ones in the world." Throughout the ages, many mathematicians and philosophers have regarded "beauty" as the evaluation scale for determining the topic selection, topic selection criteria and success criteria, and even put "beauty consideration" above everything else. The famous mathematician von Neumann once wrote: "I think mathematicians are mainly aesthetic when choosing themes and judging success." Poincare put it more clearly: "Mathematicians are not."

Always pay attention to whether their methods and theories are beautiful, not flashy. So, what makes us feel that it is a beautiful answer and a beautiful proof? That is harmony, symmetry and proper balance between the parts. In a word, it is orderly, unified and coordinated, which makes us have a clear understanding and understanding of the whole and details, which is where great achievements are produced. Mathematics is a new problem from a cultural point of view. But I believe that once you step into the threshold of mathematical culture, you will be surprised to find that this is a beautiful and strange world. And some of the things mentioned in the article are just the fur of watching the fire from the other side. It is believed that with the in-depth study of mathematical culture, a more wonderful world will be presented to mankind.

In a word, mathematical culture is a wonderful culture, and it is an unknown culture for us teenagers. If we understand it, we will gradually realize it and have a general taste in it.