Traditional Chinese arithmetic is characterized by its

Traditional Chinese arithmetic is characterized by its (applied) nature.

Mathematics is the science of studying the spatial forms and quantitative relationships of objective things. It is not subject to any limitation of time and space and strongly reveals this essential attribute.

However, in the different cultural traditions of various periods of antiquity, the manifestations of mathematics are often different, each presenting its own characteristics. For example, classical Chinese mathematics is quite different from other cultural traditions, especially ancient Greek mathematics, in many aspects, such as its form of expression, mode of thinking, relationship with social reality, center of research, and course of development.

First of all, it is the form of its expression, which here mainly refers to the form of the writings of the mathematical classics. Ancient Greek mathematics often took the form of abstract axiomatization, whereas classical Chinese mathematics was in the form of the articulated examples. The two different forms represent two very different styles.

These two forms and styles are equally useful for elucidating the foundations of mathematical theory. Some people tend to ignore this point and generalize ancient Chinese mathematical works into the form of application problem sets.

A careful analysis and comparison of the mathematical works themselves makes it easy to see that this conclusion is grossly incorrect. For example, in the most important work, the Nine Chapters of Arithmetic, of its nine chapters, the entirety of the six chapters on the square field, the corn, the lesser breadth, the work of the merchants, the surplus and the deficiency, the equations, and the parts of the three chapters on the decaying fraction, the even loss, and the hook and the strand, are either listed as one or a few examples, and then given in a very abstract manner as the "art;"

Only about one-fifth of the Nine Chapters of Arithmetic is summarized as a collection of applied problems. of the Nine Chapters on Arithmetic, i.e., about 50 questions in the chapters on Decaying Fractions, Mean Loss, and Gouxun, can be described as a collection of application problems.

The conclusion that the Nine Chapters of the Art of Arithmetic is a collection of application problems is inappropriate, and the correct way to refer to it is in the form of a collection of examples of the Art of Arithmetic. The main body of the later "Sun Zi Shu Jing" and so on should be said to be in the form of a collection of application problems, but put some preparatory knowledge to the beginning of the volume.

Song and Yuan mathematical climax of the writings, Jia Xian "Huang Di nine chapters of the calculation of the fine grass" abstraction is higher than the "nine chapters of the arithmetic", other writings due to the algorithm is more complex, algorithms of the abstract nature of the algorithm is sometimes not up to the degree of the "nine chapters", but also made valuable efforts, such as the "book of nine chapters of the total number of the art of the Danyan" and its core The technique of "Da-Yan for one" is the total technique for solving congruence formula.