In China, the origin of mathematics can also be traced back to ancient times. By the Western Zhou Dynasty (BC 1 1 century to the 8th century), "number", as one of the "six arts" that noble disciples must learn (ritual, music, shooting, calligraphy and number), had formed specialized knowledge, and some knowledge later became the first two mathematical works handed down from generation to generation in China-Zhouyi suan.

Zhou Shu suan Jing is also an astronomical work with unknown author, and it was written no later than the 2nd century BC. The most important mathematical aspects of Zhou Tao and Shu Jing are Pythagorean theorem, fractional operation and measurement.

There is no proof of Pythagorean Theorem in The Classic of Weekly Parallel Calculations, but the Pythagorean Square Theory in Zhao Shuang's Annotation in The Classic of Weekly Parallel Calculations contains the earliest proof of Pythagorean Theorem in ancient China. Zhao Shuang, whose real name is Jun Qing, was born and died in an unknown year, and lived in the Three Kingdoms period of the Later Han Dynasty. The Pythagorean Graph Theory is just over 500 words, which summarizes the main achievements of Pythagorean arithmetic in the whole Han Dynasty.

Nine Chapters Arithmetic is the most important classical mathematics in ancient China, which has a far-reaching influence on the development of ancient mathematics in China. Liu Hui's "Nine Chapters Arithmetic Preface" said that "Nine Chapters" was developed from the "Nine Numbers" of the Zhou Dynasty, and was deleted and supplemented by Zhang Cang and Geng Shouchang in the Western Han Dynasty. There are some contents similar to Jiusuan (unearthed in 1984) in the bamboo slips of the early Han Dynasty tomb in Zhangjiashan, Hubei, which were discovered in recent years. It can be considered that Nine Chapters Arithmetic started from the pre-Qin period, and was finally written in the middle of the Western Han Dynasty (the first century BC) after a long period of compilation and revision by many scholars.

"Nine Chapters Arithmetic" takes the form of examples of commands in art and literature. The book contains 246 math problems, which are divided into nine chapters (① Square Field, ② Millet, ③ Decreasing Score, ④ Less Generality, ⑤ Quotient Work, ⑤ Loss, ⑦ Profit and Loss, ⑧ Equation and ⑨ Pythagoras). The mathematical achievements contained in Nine Chapters Arithmetic are rich and varied, among which the most famous ones are fractional arithmetic, double-seeking method ("remainder"), open method, elimination method of linear equations ("equation") and introduction of negative numbers ("addition and subtraction"), which are of world significance.

China was the first country in the world to adopt decimal system for counting, which was widely used in the Spring and Autumn Period and the Warring States Period, that is, it strictly followed decimal system. Now the only information about counting methods is in the calculation of Sun Tzu's Art of War. Sun Tzu's Calculations is a three-volume book with unknown author's name, which was written in the 4th century. The first volume of this book is a systematic introduction to the calculation rules, and the second volume has the famous title of "I don't know how many things there are", also called "grandson problem".

Suan Qiujian Suanjing-Baijishu

According to Qian Baoyu's research, Zhang Qiujian, a native of Qinghe (now Linqing, Shandong Province) in the Northern Wei Dynasty, was written in 466-485 AD. The application of the least common multiple, the mutual summation of arithmetic progression elements and "Hundred Chicken Skills" are his main achievements. "Hundred Chickens Skill" is a world-famous indefinite equation problem. /kloc-Fibonacci calculation in Italy in the 3rd century, and/kloc-Alkasi in Arabia in the 5th century < < The Key to Arithmetic > and other works all have the same problems.

Jia Xian: Nine Chapters of the Yellow Emperor Calculate Fine Grass. "

China's classical mathematicians reached their peak in the Song and Yuan Dynasties, and the prelude of this development was the discovery of "Jiaxian Triangle" (binomial expansion coefficient table) and the establishment of higher-order open method ("increase, multiply and open method") closely related to it. Jia Xian, a native of Northern Song Dynasty, completed Nine Chapters of Fine Grass in Huangdi Neijing about 1050. The original book was lost, but the main contents were copied by Yang Hui's works (about13rd century), which can be handed down from generation to generation. Yang Hui's Detailed Explanation of Nine Chapters' Algorithms (126 1) has a picture of "Learning the Original Prescription", which means "Jia Xian used this technique". This is the famous "Jiaxian Triangle", or "Yang Hui Triangle". At the same time, it records Jia Xian's "method of increasing, multiplying and opening" to the root of higher order.

Jiaxian Triangle is called Pascal Triangle in western literature and was rediscovered by French mathematician B Pascal in 1654.

Qin: Counting Books and Nine Chapters.

Qin (about 1202 ~ 126 1), a native of Anyue, Sichuan, once served as an official in Hubei, Anhui, Jiangsu, Zhejiang and other places, and was exiled to Meizhou (now Meixian, Guangdong) around 126 1, and soon died. Qin, Yang Hui and Zhu Shijie are also called the four great mathematicians in Song and Yuan Dynasties. In his early years, he studied mathematics in seclusion in Hangzhou, and wrote the famous Shu Shu Jiu Zhang in 1247. The book "Shu Shu Jiu Zhang" 18, 8 1 title, is divided into nine categories (Wild Goose, Shi Tian, Tianjing, Prospecting, Foraging, Qian Gu, Architecture, Military Service, Market Changes). Its most important mathematical achievements —— "Dayan summation method" (one-time congruence group solution) and "positive and negative leveling method" (numerical solution of higher-order equations) made this Song Dynasty arithmetic classic occupy a prominent position in the history of medieval mathematics.