History of Mathematics Development in China Song and Yuan Dynasties Mathematics Ancient mathematics in China reached the peak of prosperity in Song and Yuan Dynasties, and a large number of accomplished mathematicians emerged. Among them, Qin, Yang Hui and Zhu Shijie have the most outstanding achievements, and are known as "the four great mathematicians in Song and Yuan Dynasties". Qin (A.D. 1202- 126 1) was from Anyue. His father, Qin, was born as a scholar. He is a doctor and a secretary with little supervision. Qin is clever and diligent. In the fourth year of Song Shaoding (123 1), he was a scholar in the Qin examination, and served as a county magistrate, judge, senator, state defender, farmer and temple official. He was once an official in Hubei, Anhui, Jiangsu, Zhejiang and other places, and was demoted to Meizhou (now Meixian County, Guangdong Province) around 126 1, and soon died. In his spare time in government affairs, he devoted himself to the study of mathematics, and extensively collected almanac, mathematics, astrology, temperament, architecture and other materials for analysis and research. During the period of four to seven years (1244 to 1247), while mourning for his mother, Song Chun edited and sorted out the long-term accumulated mathematical knowledge and research results, wrote the famous book "Nine Chapters of Mathematics" and created "Seeking a Skill". This was not only in the leading position in the world at that time, but also played an important role in modern mathematics and modern electronic calculation design, and was called "China's remainder theorem". His theory of "pros and cons" is called "Qin scheme". Now, almost all countries in the world have been exposed to his theorems, laws and problem-solving principles in mathematics courses from primary schools to middle schools to universities. Qin's achievements in mathematics were more than 800 years earlier than those of British mathematicians. Ye Li (1 192- 1279) is an expert in ancient algebra in China. Her real name is Ren Qing, whose name is Jingzhai, and she is from Luancheng County (now Luancheng County, Hebei Province). At the beginning of 1234, the rulers were finally destroyed by Mongolia. The demise of the Jin Dynasty brought misfortune to Ye Li's life, but because he no longer served as an official, he objectively gave him enough time for scientific research. His research work in Tongchuan is multifaceted, including mathematics, literature, history, astronomy, philosophy and medicine. The most valuable work is a comprehensive summary of celestial science written in the history of mathematics. Yang Hui was an outstanding mathematician and mathematical educator in the Southern Song Dynasty. /kloc-in the middle of the 0/3rd century, he was active in Suzhou and Hangzhou with many works. His famous math books have five kinds and 21 volumes. There are twelve volumes (126 1 year), two volumes (1262 year), three volumes (1274 year) and two volumes (field ratio multiplication and division algorithm). Yang Hui's mathematical research and education work focuses on computing technology. He summed up and developed agile algorithms for calculating multiplication and division, and some even made up songs, such as Nine Centralized Decisions. In his Algorithm for Extracting Odds from Ancient Times, he introduced various forms of "vertical and horizontal graphs" and related construction methods. "Overlap" was Yang Hui's research on higher-order arithmetic progression after Shen Kuo's "Gap Product". In Classification, Yang Hui reclassified 246 problems in Nine Chapters of Arithmetic into nine categories, such as multiplication and division, coincidence, interchange, quadratic decline and Pythagoras, according to the order of solving problems from shallow to deep. He attaches great importance to the popularization and development of mathematics education. Under the background of algorithm reform, Yang Hui's Learning Plan for Beginners is an important document in the history of Chinese mathematics education. Zhu Shijie (about 1300) was born in Songting, Han Qing, and lived in Yanshan (now near Beijing). He "traveled around the lake and sea for more than twenty years as a famous mathematician" and "gathered scholars by following the door". Zhu Shijie's representative works in mathematics include "Arithmetic Enlightenment" (1299) and "Meeting with the Source" (1303). "Arithmetic Enlightenment" is a well-known mathematical masterpiece, which spread overseas and influenced the development of mathematics in Korea and Japan. "Thinking of the source meets" is another symbol of the peak of China's mathematics in the Song and Yuan Dynasties, among which the most outstanding mathematical creations are "thinking of the source" (the formulation and elimination of multivariate higher-order equations), "overlapping method" (the summation of higher-order arithmetic progression) and "seeking difference method" (the high-order interpolation method). China, a mathematician in Yuan Dynasty, made an in-depth study on the solution of multivariate higher-order equations, higher-order arithmetic progression summation and higher-order interpolation. He wrote three volumes, Arithmetic Enlightenment (1299) and Four-element Jade Mirror (1303). In these three volumes, he discussed the solution of high-order simultaneous equations with up to four elements, and the expression and connection of polynomials. Mathematics in Song and Yuan Dynasties includes about 400 years from the Northern Song Dynasty to the end of Yuan Dynasty. During this period, many outstanding mathematicians emerged, among which the most outstanding representatives, such as Yang Hui, Zhu Shijie, etc. Li Shangyin, who is usually called "four outstanding figures in Song and Yuan Dynasties", occupies an important position in the history of mathematics. At the same time, Europe is in the Middle Ages, and the brilliant achievements of China mathematicians in solving some problems are far ahead of the world. Mathematics in Song and Yuan Dynasties was developed on the basis of mathematics in Han and Tang Dynasties. Not only the mathematical works of Jia Xian, Yang Hui and Qin are called "Nine Chapters", but the first two books are even the compilation of problems in the nine chapters, and more mathematical problems come from the nine chapters, such as the achievements of Guo Shoujing. Due to the development of block printing, the Northern Song Dynasty published ten arithmetic classics such as Nine Chapters Arithmetic since Han and Tang Dynasties from the official "Secretary Province" in the seventh year of Yuanfeng, and used them as school textbooks [1]. As a textbook, Ten Books of Calculation Classics was printed and published, which had a great influence on mathematics education and even mathematics research in Song and Yuan Dynasties. The famous mathematician and his work Zhang Qiujian-

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.

Ye Li: Circular Sea Mirror-Kaiyuan Art

With the development of numerical solution technology of higher-order equations, the sequential equation method came into being, which is called "Kaiyuan technique". Among the mathematical works handed down from Song Dynasty to Yuan Dynasty, Ye Li's "Measuring the Round Sea Mirror" is the first work that systematically expounds Kaiyuan.

Ye Li (1 192 ~ 1279), formerly known as Li Zhi, was born in Luancheng, Jin Dynasty. He used to be the governor of Zhou Jun (now Yuxian County, Henan Province). Zhou Jun was destroyed by the Mongolian army in 1232, so he studied in seclusion. He was hired by Kublai Khan of Yuan Shizu as a bachelor of Hanlin for only one year. 1248 was written into "Circle Survey Mirror", the main purpose of which was to explain the method of establishing equations by using Kaiyuan. "Kai Yuan Shu" is similar to the column equation method in modern algebra. "Let Tianyuan be so-and-so" is equivalent to "Let X be so-and-so", which can be said to be an attempt of symbolic algebra. Ye Li also has another mathematical work Yi Gu Yan Duan (1259), which also explains Kaiyuan.

Zhu Shijie: Four Yuan Jade Sword

Zhu Shijie (about 1300) was born in Songting, Han Qing, and lived in Yanshan (now near Beijing). He "traveled around the lake and sea for more than twenty years as a famous mathematician" and "gathered scholars by following the door". Zhu Shijie's representative works in mathematics include "Arithmetic Enlightenment" (1299) and "Meeting with the Source" (1303). "Arithmetic Enlightenment" is a well-known mathematical masterpiece, which spread overseas and influenced the development of mathematics in Korea and Japan. "Thinking of the source meets" is another symbol of the peak of China's mathematics in the Song and Yuan Dynasties, among which the most outstanding mathematical creations are "thinking of the source" (the formulation and elimination of multivariate higher-order equations), "overlapping method" (the summation of higher-order arithmetic progression) and "seeking difference method" (the high-order interpolation method).

Hua

"Mathematics, like music, is famous for its geniuses. These geniuses are smart even without formal education. Although Hua modestly avoids using the word "wizard", it appropriately describes the outstanding China mathematician-G B Kolata.

Hua is a legend and a self-taught mathematician.

He was born in Jintan County, Jiangsu Province,19101012. 1June, 985 102, Hua, a superstar in China's mathematics field, died of myocardial infarction while giving lectures in Japan.

Hua is a famous mathematician at home and abroad. He is the founder and pioneer of China's research on analytic number theory, canonical group, matrix geometry, automorphism, multiple complex functions and so on. His famous academic paper "On Functions of Multiple Complex Variables in Typical Fields" has done pioneering work in the field of mathematics because it has applied methods that have never been used before, and won the first prize of 1957 China Science. His research results were named "Fahrenheit Theorem" and "Brouwer-Gadang-Hua Theorem" by the international mathematical community. Hua worked tirelessly all his life, struggled ceaselessly, wrote books, set forth opinions and covered a wide range. He has published about 200 academic papers, including Heap Prime Theory, Introduction to Advanced Mathematics, Estimation of Exponential Sum and Its Application in Number Theory, Typical Groups, Analysis of Typical Fields in the Theory of Functions of Multiple Complex Variables, Introduction to Number Theory, Numerical Integral and Its Application, Starting from the Unit Circle and Optimization Method.