Why did China call mathematics arithmetic in ancient times?

Arithmetic is the oldest, most basic and primitive part of mathematics. It studies the properties of numbers and their operations.

The word "arithmetic" is the general term for all mathematics in ancient China. As for the names of many branches of mathematics, such as geometry and algebra, they came into being very late. Foreign language books that systematically collate predecessors' mathematical knowledge were first written by Euclid of Greece. There are fifteen volumes in The Elements of Geometry, and the last two volumes are supplemented by people. Most of the books belong to geometry knowledge. The seventh, eighth and ninth volumes discuss the properties and operations of numbers, which belong to arithmetic. Now the Latin word "arithmetic" comes from the Greek word "number and number (phonology, sh? The technology of number three has changed. The ancient meaning of the word "suan" in China also means "number", which means bamboo pieces used for calculation. In ancient China, all complicated numerical calculations used calculation. So "arithmetic" includes all the mathematical knowledge and calculation skills at that time. The earliest handed down Nine Chapters Arithmetic, the lost Xu Shang Arithmetic and Du Zhong Arithmetic are all discussing the solutions to various practical mathematical problems.

Generation of arithmetic

About the generation of arithmetic, we still have to talk about numbers. Numbers are used to express and discuss quantitative problems. There are different types of quantities and also different types of numbers. As early as the initial stage of ancient development, due to the needs of human daily life and production practice, the simplest concept of natural numbers came into being in the initial stage of cultural development. One of the characteristics of natural numbers is that they are composed of inseparable individuals. For example, two things, a tree and a sheep, if two trees are in tandem; If there are three sheep, it is one, one after another. But you can't say that there are half trees and half sheep. Half a tree or half a sheep can only be counted as wood or mutton at best, but not as trees and sheep. However, natural numbers are not enough to solve the common division problems in life and production, so the concept of numbers has been expanded for the first time. Fractions are produced by the division of another quantity. For example, length is an infinitely divisible quantity. In order to express these quantities, only fractions are used. From the existing literature, we can know that human beings have long known the history of natural numbers and fractions. For example, the ancient Egyptian Rhineland papyrus handed down around 2000 BC recorded the calculation method of scores; There are also many natural numbers in Oracle Bone Inscriptions left over from the Yin Dynasty in China, with a maximum of 30,000, and they are all counted in decimal places. Natural numbers and fractions have different properties, and there are also different relationships between numbers. In order to calculate these numbers, there are methods of addition, subtraction, multiplication and division. These four methods are four operations. The oldest mathematics, arithmetic, is formed by accumulating and sorting out the properties of numbers and the experience of four operations between numbers in the application process. The development of arithmetic in the process of arithmetic development, due to the requirements of practice and theory, many new problems have been raised. In the process of solving these new problems, ancient arithmetic has been further developed from two aspects. On the one hand, in learning the four operations of natural numbers, it is found that only division is more complicated, some can be divided, some can be divided, some cannot be decomposed, some are greater than the common divisor of 1, and some cannot. In order to seek the laws of these numbers, it has developed into an independent branch of mathematics, called integer theory or elementary number theory, which specializes in the properties of numbers and is independent from ancient arithmetic, and has made new development in the future. On the other hand, various types of application problems and various methods to solve these problems are discussed in ancient arithmetic. In the long-term research, it will naturally inspire people to seek general methods to solve these application problems. That is to say, can we find a universal and more universal method to solve the same type of application problems, so we invented abstract mathematical symbols, which developed into another ancient branch of mathematics, namely elementary algebra. With the development of mathematics, arithmetic is no longer a branch of mathematics. Now what we usually call arithmetic is only a teaching subject in primary schools. The purpose is to enable students to understand and master the most basic knowledge about quantitative relations and spatial forms, correctly and quickly perform the four operations of integers, decimals and fractions, initially understand some of the simplest ideas in modern mathematics, and have preliminary logical thinking ability and spatial concepts. The specific content of modern primary school mathematics is basically the knowledge of ancient arithmetic, which means that many contents of ancient arithmetic and modern arithmetic are the same. However, there are differences between modern arithmetic and ancient arithmetic. First of all, the content of arithmetic is the research object of ancient adults, including mathematicians, and now it has become children's mathematics. Secondly, in modern primary school mathematics, the basic operation properties summarized for a long time are summarized, namely, the exchange law and associative law of addition and multiplication, and the distribution law of multiplication to addition. These five basic algorithms are not only the important properties of number operation learned in primary school mathematics, but also the main properties of the whole mathematics, especially algebra. Thirdly, in modern primary school mathematics, the ideas of basic mathematical concepts such as set and function in modern mathematics are also bred. For example, the change of sum, difference, product and quotient, the corresponding relationship between numbers, ratio and proportion. In addition, primary school mathematics now includes decimals and their four operations, which only appeared in16th century. It should be pointed out that the decimal fraction is not a new number, and it can be regarded as another way to write the fraction with the denominator of 10. We list arithmetic as the first branch here, mainly to emphasize that all ancient mathematics is called arithmetic, and modern algebra and number theory originally developed from arithmetic. Later, the concepts of arithmetic and mathematics appeared, which replaced the meaning of arithmetic and included all mathematics, and arithmetic became a branch. So it can also be said that arithmetic is the oldest branch. Why did China call "mathematics" arithmetic and "arithmetic" before? Now, arithmetic is a branch of mathematics, which includes natural numbers, properties generated by various operations, operation rules and practical applications. However, in the history of mathematical development, the meaning of arithmetic is much broader than it is now. In ancient China, it was a bamboo computing device. Arithmetic refers to the technology of operating this computing device, and also refers to all the mathematical knowledge related to calculation at that time. The word arithmetic officially appeared in Nine Chapters of Arithmetic. The Nine Chapters Arithmetic is divided into nine chapters, namely Tian Fang and Su. These are mostly practical names. For example, "square field" refers to the shape of land, and the calculation of land area belongs to the scope of geometry; "Millet" is a synonym for grain, which talks about the exchange of various grains, mainly involving proportion, and belongs to the category of today's arithmetic. It can be seen that "arithmetic" at that time refers to the whole of mathematics, which is different from the present meaning. It was not until the Song and Yuan Dynasties that the word "mathematics" appeared. At that time, mathematics and arithmetic were often used together. Of course, the mathematics here only refers to the mathematics in ancient China, which is different from the mathematical system in ancient Greece, and it focuses on the study of algorithms. From19th century, some western mathematics disciplines including algebra and trigonometry were introduced into China. Western missionaries mostly used mathematics, Japanese later used the word mathematics, and China still used "arithmetic" in ancient arithmetic. 1953, chinese mathematical society established a committee to examine mathematical terms, and established the present meaning of "arithmetic", but arithmetic and mathematics still coexist. 1937, Tsinghua University also had a "computing department". 1939, for the sake of unification, it was not until today that the special "mathematics" was determined.