After the demise of the Tang Dynasty, the Five Dynasties and Ten Kingdoms remained the continuation of the warlord melee. Until the Northern Song Dynasty unified China, agriculture, handicrafts and commerce flourished rapidly, and science and technology advanced by leaps and bounds. From the 11th century to the 14th century (Song and Yuan Dynasties), computational mathematics reached its peak, which was the unprecedented prosperity and fruitful heyday of ancient mathematics in China. During this period, a number of famous mathematicians and mathematical works appeared. They are listed as follows: Nine Chapters of the Yellow Emperor by Jia Xian (165438+mid-20th century), On the Origin of Ancient Times by (65438+mid-2nd century) and Nine Chapters of Shu by Qin (65438). Yang Hui's algorithm (126 1), daily algorithm (1262) and Yang Hui's algorithm (1274-65438).

Around 1050, Jia Xian of the Northern Song Dynasty (the year of birth and death is unknown) created the method of increasing, multiplying and opening any height in the Nine Chapters of the Yellow Emperor. It was not until A.D. 18 19 that William George Horner, an Englishman, came up with the same method. Jia Xian also listed the binomial theorem coefficient table until17th century in Europe.

During the period of 1088- 1095, Shen Kuo put forward the "gap product method" from the production practice problems such as the number of restaurants and the volume of terraces, and began to study the high-order arithmetic progression summation, and established the correct summation formula. Shen Kuo also put forward "the skill of meeting circles" and obtained the first approximate value of arc length in the history of ancient mathematics in China.

In A.D. 1247, Qin in the Southern Song Dynasty popularized the multiplication and division method in Shu Shu Jiu Zhang, and described the numerical solution of higher order equations. He listed more than 20 solutions of higher-order equations from practice, the highest of which was a decagonal equation. It was not until16th century in Europe that the Italian Scipio Del Ferro proposed the solution of cubic equation. Qin also systematically studied the theory of a congruence.

In A.D. 1248, Li Zhi (A.D. 1 192- 1279) wrote "The Sea Mirror for Measuring the Circle", which was the first work to systematically discuss the "celestial technique" (one-dimensional higher-order equation) and was an outstanding achievement in the history of mathematics. In the Preface, Ye Li criticized the fallacy of belittling scientific practice and treating mathematics as "poor skills" and "playing with things and getting tired of it".

In A.D. 126 1 year, Yang Hui (date of birth and death unknown) used "stacking technique" to find the sum of several high-order arithmetic progression. In A.D. 1274, he also described the "nine-return method" and introduced various calculation methods of multiplication and division.

In A.D. 1303, Zhu Shijie of Yuan Dynasty (date of birth and death unknown) wrote a jade mirror with four elements. He extended "Tianshu" to "Quaternary" (Quaternary high-order simultaneous equation) and put forward the elimination method. It was not until A.D. 1775 that etienne bezout, a Frenchman in Europe, proposed the same solution. On this basis, the interpolation formula of higher-order difference is obtained. The general interpolation formula was put forward by Englishman James Gregory in Europe until 1670 and Isaac Newton from 1676 to 1678.

In14th century, people in China used abacus. Before modern computers appeared, abacus was a simple and effective computing tool in the world.

Characteristics and limitations of China's mathematics

(1) takes algorithm as the center and belongs to applied mathematics. China's mathematics is not divorced from the reality of social life and production, and aims at solving practical problems. Mathematical research centers on establishing algorithms and improving computing technology.

(2) It has strong sociality. In China's traditional mathematical culture, mathematics is one of the six arts (ritual, music, shooting, imperial, calligraphy and mathematics), which is cultivated by Confucianism. Its function is to "understand the gods, obey life, manage the world like everything", so China's traditional mathematics is always branded with China's philosophy and ancient academic thought, which is often related to the number of skills.

(3) The theory is highly generalized. Because China's traditional mathematics pays attention to solving practical problems, and because of China's comprehensive inductive thinking, China's traditional mathematics doesn't care about the formalization of mathematical theory, but this doesn't mean that China's tradition only stays at the empirical level without theoretical achievements. China's mathematical algorithms actually contain the theoretical basis for establishing these algorithms. Mathematicians in China are used to building mathematical concepts and methods on a few self-evident and intuitive mathematical principles, such as the theory of rate in algebra, the principle of complementary entry and exit in plane geometry, Yang Equestrian in solid geometry, the principle of section in surface theory (or Liu Zu's principle, that is, principle) and so on.

The Influence of China's Mathematics on the World

Mathematical activities have two basic tasks-proof and calculation. The former is because of accepting the axiomatic (deductive) mathematical cultural tradition, while the latter is because of accepting the mechanized (algorithmic) mathematical cultural tradition. In the world mathematical culture tradition, Greek mathematics represented by Euclid's Elements of Geometry is undoubtedly the basis of western deductive mathematics tradition, while China mathematics represented by Nine Chapters of Arithmetic is undoubtedly the oriental algorithmic mathematics tradition.

China's mathematics spread to India and Arabia through the Silk Road, and later to the West through Arabs. Moreover, in the cultural circle of Chinese characters, it has been affecting the mathematical development of Asian countries such as Japan, Korean Peninsula and Vietnam.

Wei, Jin, southern and northern dynasties

During the Wei and Jin Dynasties, China's mathematics developed greatly in theory. Among them, the work of Zhao Shuang (unknown year of birth and death) and Liu Hui (unknown year of birth and death) is considered as the beginning of China's ancient mathematical theory system. Zhao Shuang, a native of Wu in the Three Kingdoms, was one of the earliest mathematicians who proved mathematical theorems and formulas in ancient China. He made a detailed annotation on Zhou pian Shu Jing, and strictly proved the pythagorean theorem in pythagorean square diagram by geometric method. His method embodies the idea of cut-and-fill principle. Zhao Shuang also put forward a new method to solve quadratic equation by geometric method. In 263, Liu Hui, Ren Wei of the Three Kingdoms, annotated Nine Chapters Arithmetic, which not only explained and deduced the methods, formulas and theorems of the original book as a whole, but also systematically expounded the theoretical system and mathematical principles of China's traditional mathematics. His discussion was creative and created the secant method in Volume 1 Square Field (that is, the method of infinitely approaching the area of a circle by connecting regular polygons in a circle). It lays a theoretical foundation for the study of pi and provides a scientific algorithm. He obtained the approximate value of pi by the method of "secant circle" as 3927/ 1250 (i.e. 3. 14 16). "Shanggongpian" constructs the geometric model of "Mouhe Square Cover", which solves the problem of spherical volume formula and opens the way for Zuxuan to get the correct result. In order to establish the polyhedral volume theory, Yang successfully proved equestrian by the limit method. He also wrote Calculation of Islands, which developed the ancient Pythagorean measurement method-gravity difference technique.

The society in the Southern and Northern Dynasties was in a state of war and division for a long time, but the development of mathematics was still vigorous. There are some books on arithmetic, such as Sun Tzu's Art of War, Xiahou Yangbing Law and Zhang Qiu's Art of War. Written in the 4th-5th century A.D., Sunzi Suanjing gave the question "Things are unknown" and gave the answer, which led to the solution of a congruence group of China. The "Hundred Chickens Problem" in Zhang Qiujian suan Jing leads to three unknown indefinite equations.

During the Wei and Jin Dynasties, China's mathematics developed greatly in theory. Among them, the work of Zhao Shuang (unknown year of birth and death) and Liu Hui (unknown year of birth and death) is considered as the beginning of China's ancient mathematical theory system. Zhao Shuang, a native of Wu in the Three Kingdoms, was one of the earliest mathematicians who proved mathematical theorems and formulas in ancient China. He made a detailed annotation on Zhou pian Shu Jing, and strictly proved the pythagorean theorem in pythagorean square diagram by geometric method. His method embodies the idea of cut-and-fill principle. Zhao Shuang also put forward a new method to solve quadratic equation by geometric method. In 263, Liu Hui, Ren Wei of the Three Kingdoms, annotated Nine Chapters Arithmetic, which not only explained and deduced the methods, formulas and theorems of the original book as a whole, but also systematically expounded the theoretical system and mathematical principles of China's traditional mathematics. His discussion was creative and created the secant method in Volume 1 Square Field (that is, the method of infinitely approaching the area of a circle by connecting regular polygons in a circle). It lays a theoretical foundation for the study of pi and provides a scientific algorithm. He obtained the approximate value of pi by the method of "secant circle" as 3927/ 1250 (i.e. 3. 14 16). "Shanggongpian" constructs the geometric model of "Mouhe Square Cover", which solves the problem of spherical volume formula and opens the way for Zuxuan to get the correct result. In order to establish the polyhedral volume theory, Yang successfully proved equestrian by the limit method. He also wrote Calculation of Islands, which developed the ancient Pythagorean measurement method-gravity difference technique.

The society in the Southern and Northern Dynasties was in a state of war and division for a long time, but the development of mathematics was still vigorous. There are some books on arithmetic, such as Sun Tzu's Art of War, Xiahou Yangbing Law and Zhang Qiu's Art of War. Written in the 4th-5th century A.D., Sunzi Suanjing gave the question "Things are unknown" and gave the answer, which led to the solution of a congruence group of China. The "Hundred Chickens Problem" in Zhang Qiujian suan Jing leads to three unknown indefinite equations. During the Wei and Jin Dynasties, China's mathematics developed greatly in theory. Among them, the work of Zhao Shuang (unknown year of birth and death) and Liu Hui (unknown year of birth and death) is considered as the beginning of China's ancient mathematical theory system. Zhao Shuang, a native of Wu in the Three Kingdoms, was one of the earliest mathematicians who proved mathematical theorems and formulas in ancient China. He made a detailed annotation on Zhou pian Shu Jing, and strictly proved the pythagorean theorem in pythagorean square diagram by geometric method. His method embodies the idea of cut-and-fill principle. Zhao Shuang also put forward a new method to solve quadratic equation by geometric method. In 263, Liu Hui, Ren Wei of the Three Kingdoms, annotated Nine Chapters Arithmetic, which not only explained and deduced the methods, formulas and theorems of the original book as a whole, but also systematically expounded the theoretical system and mathematical principles of China's traditional mathematics. His discussion was creative and created the secant method in Volume 1 Square Field (that is, the method of infinitely approaching the area of a circle by connecting regular polygons in a circle). It lays a theoretical foundation for the study of pi and provides a scientific algorithm. He obtained the approximate value of pi by the method of "secant circle" as 3927/ 1250 (i.e. 3. 14 16). "Shanggongpian" constructs the geometric model of "Mouhe Square Cover", which solves the problem of spherical volume formula and opens the way for Zuxuan to get the correct result. In order to establish the polyhedral volume theory, Yang successfully proved equestrian by the limit method. He also wrote Calculation of Islands, which developed the ancient Pythagorean measurement method-gravity difference technique.

The society in the Southern and Northern Dynasties was in a state of war and division for a long time, but the development of mathematics was still vigorous. There are some books on arithmetic, such as Sun Tzu's Art of War, Xiahou Yangbing Law and Zhang Qiu's Art of War. Written in the 4th-5th century A.D., Sunzi Suanjing gave the question "Things are unknown" and gave the answer, which led to the solution of a congruence group of China. The "Hundred Chickens Problem" in Zhang Qiujian suan Jing leads to three unknown indefinite equations.