The research on the history of mathematics culture shows that ancient human mathematics, as a subsystem of operation and expression in the cultural system, has dual functions (or dual features) from the beginning, namely quantitative functions and mysterious functions (Note: Wang Xianchang's Mathematics and Human Civilization, Yan 'an University Press, 1990, pp. 58-70). )。 However, numbers or mathematics in different national cultures have a certain mystery in a specific cultural atmosphere, and the development path of mathematics mystery in different national cultures is different.
In the development of ancient Greek culture, primitive mathematics has always developed along the track of unified inheritance of mystery and quantity. The combination of ancient Greek mathematics and mystery makes them pursue the absoluteness of mathematics and explain the universal position of the world from the religious and philosophical levels, which is the cultural background that ancient Greek mathematics is completely divorced from practical problems and pursues the rigor of logical deduction.
Therefore, in the sense of the history of mathematical culture, western mathematics originated in ancient Greece is not only an operation system with mathematical significance, but also a rational interpretation system that plays a leading role in the cultural system, or a normative model of rational construction. In western culture, western mathematics explains the changes of the universe, guides the development of reason and participates in the expression of the material world. The construction of any discipline must imitate and apply mathematical models according to the requirements of cultural rationality. Explaining everything with mathematics is a value concept acquired by western mathematics in its adapted culture.
In the development of China culture, the calculation system formed by the mechanized operation of ancient mathematical calculation in China originated from the evolution of bamboo stick operation as primitive mathematics in the historical process.
In ancient times, China was a country that used bamboo sticks as special objects to perform numerical and mathematical operations. Ancient mathematics in China has dual functions of external calculation and internal calculation, namely, the arithmetic function of "counting everything" and the explanatory function of mysticism.
Therefore, China's ancient mathematics not only failed to form its own thinking method and structural form at the religious and philosophical levels, but also formed the characteristics of studying specific mathematical problems. The value orientation of China's ancient mathematics in the cultural tradition is to try to construct a concise operation method under the condition of mechanical repetition of planning and operation, and to solve specific problems raised in practice accurately and quickly.
China's traditional values and the technical value orientation of calculation determine the development and construction mode of ancient mathematics in China. This value orientation of computational mathematics has ensured the development direction of the characteristics of ancient mathematics mechanization in China, the practical application level of mathematics has been continuously developed, and the technology and level of mechanized calculation have been continuously improved. With the help of this special tool, the ancient people in China classified all kinds of practical problems, effectively sorted out and deduced them, and made brilliant achievements in comparison algorithm, "equation" technique, square root technique, tangent circle technique, great derivation technique, celestial element technique, four elements technique and product-difference technique, which reached the climax of mathematics in the Song and Yuan Dynasties. The abacus system developed after Yuan Dynasty is the development, reform and continuation of the calculation system. It can be said that the traditional mathematics in China is based on the calculation system, aiming at improving the mechanized calculation technology to solve practical problems. At the same time, the traditional characteristics of cultural values have also created a group of people who spread and develop mathematics as a skill, which is the talent advantage to promote the development of mathematics mechanization, especially in a relatively stable cultural environment, and its traditional values have played an important role.
From the analysis of the development stage of the cultural value system, China's calculation system and model reached the peak of mathematics in the Song and Yuan Dynasties, and the mechanization of the algorithm reached the highest level to a great extent. Jia Xian's trigonometry, multiplication and division is a great improvement and creation of the root-seeking program since nine chapters. Qin's positive and negative root-seeking method has developed the multiplication and division method to a very complete situation, and its major derivation and calculation have also developed the solution of the problem of "unknown things" to the most general mechanized program on the basis of the calculation of the previous dynasties. Ye Li's celestial sphere technology is a great improvement and breakthrough to the algorithm of sequence equation, and also a perfect embodiment of geometric algebra. It is an inevitable result and requirement to develop into multivariate higher order equations. Therefore, in the Song and Yuan Dynasties, China's algorithm mechanization reached an unprecedented height, which is consistent with the requirements of traditional mathematical cultural values. It is the natural development of China's planning cultural arrangement mode and transformation technology after long-term accumulation. Solving a specific problem quickly, accurately and concisely is the inevitable trend and result of mathematical calculation in China's planning system.
China's ancient algebra should not be judged by the evaluation model and value standard of western mathematics.
From the comparative analysis of the cultural history of ancient mathematics between China and the West, it can be concluded that the differences in function and structure of ancient mathematics between China and the West are mainly caused by the differences in cultural levels and value orientations endowed by the cultural system. It can be said that the structural model and rational function of western mathematical works will not appear in China culture. Therefore, in the development of mathematics in ancient and modern times for thousands of years, it is inevitable to form two tendencies of Chinese and western mathematics in different periods and regions: the tendency of logical deduction and the tendency of mechanized algorithm. The tendency of logical deduction, represented by Euclid's Elements of Geometry in ancient Greece, and the tendency of mechanized algorithm, represented by Nine Chapters of Arithmetic, interact and "take turns to govern". * * * has contributed to the development of mathematics in the world with its own structural mode, mode of thinking, operation rules and structural features.
From the perspective of the history of mathematical culture, China's application-oriented operation and operation system gave birth to the success of mechanization of ancient mathematical algorithms in China. China mathematics, with its unique style and characteristics different from western mathematics, once occupied the focus of world mathematics research in the history of medieval mathematics and civilization. After the decline of brilliant ancient Greek mathematics, it reached the beginning of14th century. The brilliant achievements of China's traditional mathematics indicate the great success of the mechanized algorithm under the calculation system, and the application and development of abacus and abacus in the metaphase is the continuation of China's mechanized algorithm system, a major improvement and development of calculation tools, and a historical necessity of the change of calculation technology. The popularization and application of abacus greatly improves the calculation speed and efficiency, simplifies the mechanized operation procedures and tedious steps, and adapts to the practical needs of agriculture, handicraft industry and commercial development for a large number of complex calculations in mathematics. Therefore, the appearance, universal application and development of abacus and abacus are not only great inventions created by China's traditional mathematics, but also great contributions to world science and technology and civilization.
However, regarding the contribution of China's traditional mathematics and western mathematics to the world's scientific and technological civilization, for a long time, most of the mathematical evaluation criteria used by people are western centralism formed in western mathematics. This centrist believes that the great achievements of contemporary mathematics began in ancient Greece and developed along the only road of being king. Knowledge without strict deduction cannot be regarded as science, and only the relationship between western mathematics and other disciplines is the key necessary condition for the development of modern science.
The theoretical basis of the judgment standard of western centralism is the philosophy of western mathematics, which consciously or unconsciously takes the thinking mode and value standard of western mathematics as the only standard for evaluating mathematics (including traditional mathematics in China and even eastern mathematics) and science in different countries and regions of the world. The research on the history of mathematics culture shows that this judgment and comparison is not based on the rational speculation of ancient mathematics in China, but ignores the cultural characteristics of the evolution of bamboo slips mathematics in China and the cultural differences between western mathematics.
In a word, the difference of values between Chinese and western ancient mathematics in their national cultures is an issue that we should attach great importance to in the study of the history of mathematics. In the history of human culture, people can find that each cultural system has its own specific mathematical development and structural model. Comparing ancient human mathematics, we should extract the regularity of ancient human mathematics from the mathematical models of different cultural systems, and take it as the value scale to evaluate it objectively and fairly. China's ancient mathematics was developed in China culture, and it will not and cannot follow the pattern of western mathematics. Therefore, when we judge China's ancient algebra, we should not copy the evaluation of western mathematics.
In the differences between Chinese and western cultures, we deeply realize that the model of western mathematics cannot and cannot be the only development model of human mathematics, and the value standard of western mathematics should not and cannot be the only evaluation standard of ancient human mathematics. This is like N Wen Xi's question: "Why is the history of non-European civilization always judged by whether it is close to some aspects of early European science or modern science?" Why didn't early European science need to be tested? "