Zhu Shijie (1300 or so), Zhu Shijie, whose real name is Han Qing, was born in Songting, Yanshan (now Beijing). Engaged in mathematics research and education for a long time. He traveled around the world as a famous mathematician for more than 20 years, and many people came from all directions to study. His main works are "Arithmetic Enlightenment" in three volumes and "Meeting with Siyuan" in three volumes. ), "traveling around the lake and sea with famous mathematicians for more than 20 years" and "following the door to gather scholars". 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. He is familiar with the formula of higher-order differential method, which is 400 years earlier than the west. Chinese and foreign mathematical historians have a high opinion of Zhu Shijie and his masterpiece "Four Jade Juanjian". Zhu Shijie was an outstanding mathematical scientist in Yuan Dynasty. /kloc-At the end of 0/3, the war-torn motherland was unified by the Yuan Dynasty, and the destroyed economy and culture flourished rapidly. For the sake of national prosperity and security, Mongolian rulers respect knowledge, select talents and push all sciences to a new height. One day, by the scenic Slender West Lake in Yangzhou, a teacher came and hung a sign in front of his apartment, which read in big letters: "Teacher Zhu Songting of Yanshan specializes in teaching four elements." A few days later, Zhu Shijie's front door was crowded with people who were curious about knowledge. Just as Zhu Shijie was accepting students' registration, suddenly, a lot of yelling caught his attention. I saw a semi-old Xu Niang dressed in satin and silver, chasing a young girl, beating and cursing: "You bitch, didn't you catch a lot of money?" Do you want to be a good family? I am afraid that you voted for the wrong baby and will not think about it in the next life. " The girl was beaten so badly that even the clothes inside her were torn. The girl curled up into a ball and asked her to fight, but she didn't go back with her. When Zhu Shijie saw that the road was rough, he came forward to ask. Xu Niang, a half-aged man, saw a nosy person and sneered, "Do you want to be keen? You give me fifty taels of silver, and the girl is yours! " Zhu Shijie was furious at this. "Can't I pay fifty taels of silver?" . You can't run amok in broad daylight. Is there no king's law? "Old Xu Niang said sarcastically," you poor wretch, what are you talking about? Silver is the king. I won't fight if you can pay fifty taels of silver. Zhu Shijie was so angry that he took out 50 taels of silver from his pocket, threw it in front of Xu Niang, picked up the girl and went back to his teaching place. "。 It turned out that Xu Niang, who was half-aged, was the madam of a prostitute's family. The girl's father borrowed 10 silver from the madam, but he could not pay back the money due to natural disasters, so he had to sell his daughter to pay off his debts. I happened to meet Zhu Shijie today and let this girl out of her misery. Later, under the careful instruction of Zhu Shijie, the girl also learned a lot of mathematics and became Zhu Shijie's right-hand man. In a few years, the two became husband and wife. Therefore, there is a saying among Yangzhou people: Zhu Hanqing taught and educated people in Yuan Dynasty. Saving people from fire and water, a big marriage. The above story is hard to tell, but it shows that Zhu Shijie has a loving heart while studying. In addition, in mathematical science, Zhu Shijie comprehensively inherited the mathematical achievements of Qin, Yang Hui and others, and creatively developed them. He wrote such famous works as Arithmetic Enlightenment, Meeting with Siyuan, which pushed the ancient mathematics in China to a new height and formed the highest peak of China's mathematics in the Song and Yuan Dynasties. The Enlightenment of Arithmetic was published by Zhu Shijie in Yuan Chengzong Dade for three years (1299). There are 20 books in three volumes, with 259 questions and corresponding answers. Since the multiplication and division method, this book has been talking about the highest achievement of mathematics development at that time, "Tianyuan Shu", which comprehensively introduced all aspects of mathematics at that time. Its system is complete, the content is simple and easy to understand, and it is a very famous enlightenment reading. This book was later spread to Korea, Japan and other countries, and reprinted and annotated editions were published successively, which had a certain influence. Philip Burkart Meeting is a brilliant mathematical masterpiece. It has been highly praised by researchers in the history of modern mathematics, and is considered as the most important and greatest mathematical masterpiece among China's ancient mathematical scientific works. "Siyuan Encounter" was written in the seventh year of Dade (1303), with three volumes, 24 doors and 288 questions. This paper introduces Zhu Shijie's research and achievements in solving multivariate higher-order equations-Quaternary method and calculating higher-order arithmetic progression-superposition method and differential method. "Tianyuan Shu" means "Tianyuan is XXX", that is, XXX is X. But when there is more than one unknown, in addition to the unknown Tianyuan (X), it is necessary to set geographical elements (Y), humanistic elements (Z) and material elements (U), and then list the high-order binary, ternary or even quaternary equations before solving them. In Europe, the solution of linear equations began in16th century, and the study of high-order simultaneous equations was from 18 to19th century. Another great contribution of Zhu Shijie is the study of "piling". He studied a series of new summation problems of crib-shaped sequences, which were summarized as "triangular crib" formula. In fact, he obtained a systematic and universal solution to this kind of arbitrary high-order arithmetic progression summation problem. Zhu Shijie also introduced the triangle crib formula into the unique skill, pointing out that the coefficient in the unique skill formula is just the product of the triangle crib in turn, thus obtaining the unique skill formula with the fourth difference. He also extended this formula to include any higher-order difference, which is the first time in the history of mathematics in the world, nearly four centuries earlier than the same achievement of Newton in Europe. Because of this, Zhu Shijie and his "Meet with Siyuan" enjoy a high reputation in the world. In modern Japan, France, the United States, Belgium and many countries in Asia, Europe and the United States, people introduce homesickness to their countries. Sutton, a famous American historian of science, commented on Zhu Shijie in this way: "(Zhu Shijie) is the most outstanding mathematical scientist of the Chinese nation, the era in which he lived, and also throughout the ages. "Philip Burkart Meets" is the most important mathematical work of China and one of the most outstanding mathematical works in the Middle Ages. It is a rare treasure in the world mathematics treasure house. "It can be seen that scientists and their works in the Song and Yuan Dynasties played an inestimable role in the history of world mathematics. In addition to the above achievements, Zhu Shijie also put forward many noteworthy contents in his works: 1. In the history of Chinese mathematics, he formally put forward the correct law of positive and negative multiplication for the first time; 2. He discussed the calculation of sphere surface area, which is the only discussion in China's classical mathematics. Although the conclusion is incorrect, the innovative spirit is valuable; 3. In "Arithmetic Enlightenment", he recorded a complete formula of "nine normalization and one division", which is almost the same as the abacus formula. In a word, Zhu Shijie inherited and developed the mathematical achievements of predecessors and made indelible contributions to the development of ancient mathematical science in China. Zhu Shijie deserves to be a famous mathematician in the history of mathematics in China and even in the world. Thanks to the joint efforts of Zhu Shijie and other contemporary algebras, mathematics in Song and Yuan Dynasties reached a brilliant height, ranking among the top in the world in many aspects. Since Zhu Shijie, the highly developed situation of mathematics in China has not been developing all the time. On the contrary, many achievements were lost in the Ming and Qing Dynasties. This is really a great pity in the history of science. Mr. Zhu Songting of Yanshan was an outstanding mathematician in Yuan Dynasty. Yuan Yu's Four Lessons and Arithmetic Enlightenment written by him are important milestones in the development of ancient mathematics in China and precious legacies of ancient mathematics in China. Zhu Shijie's adolescence is exactly the same as that after the Mongolian army destroyed the gold. But before the destruction of gold, Zhongdu (now Beijing) was easily captured by Genghis Khan in 12 15. Kublai Khan of Yuan Shizu moved his capital to Yanjing (later renamed Dadu, now Beijing) on 1264 (to 1266) to facilitate the rule of the Central Plains people. In 1960s, Yanjing was not only the political center of the whole country, but also an important cultural center of the whole country, especially in the north. Kublai Khan once recruited a large number of Han intellectuals as the brains of the Yuan Dynasty. Among them, Wang Xun (1235- 128 1), Guo Shoujing (123 1- 1279), (11. /kloc-In the middle of the 0/3rd century, a mathematical research center represented by Tian Yuanshu appeared in southern Hebei and southern Shanxi. In addition to the Purple Mountain in Wu 'an and the Phoenix Mountain in Yeli Yuanshi County, there are also Jiangzhou in Linfen, Shanxi Province, Li Wenyi in Lixian County, Hebei Province, and Shixin Island where deer are caught in Hebei Province. Are studying celestial magic. Zhu Shijie also inherited the main achievement of northern mathematics-astrophysics, and extended it from binary and ternary to the solution of quaternary equations. Zhu Shijie not only accepted the mathematical achievements of the North, but also absorbed the mathematical achievements of the South, especially various daily algorithms, business arithmetic and popular ballads. Before the Yuan Dynasty destroyed the Southern Song Dynasty, North-South exchanges, especially academic exchanges, were almost cut off. Mathematicians in the south know nothing about celestial science in the north, and mathematicians in the north are rarely influenced by the south. Zhu Shijie once "traveled around the world". In the preface of Muruo (an ancient mathematician), "Mr. Zhu Songting of Yanshan Mountain, as a famous mathematician, has traveled around the lake and sea for more than 20 years. There are more and more scholars all over the world, so Mr. Li invented Nine Wonders, and took the study of the soil after Shu as the three volumes of the book ... called "Philip Burkart meets", and in the preface of Zuyi, there is also "Han Qing is a famous hero in the world, and Song Ting has his own number. "Liu Zhou is everywhere, revisiting Guangling, and gathering people after the door." After a long period of investigation and lectures, his two mathematical masterpieces, The Enlightenment of Arithmetic and The Encounter of Thinking Source, were finally published in Yangzhou 1299 and 1303. The formula of eliminating songs in Yang Hui's book was further developed in Zhu Shijie's Arithmetic Enlightenment. In the Qing Dynasty, Luo Shilin thought: "Han Qing was the third best harmony between Qin Dynasty and Yuan Dynasty. There are pros and cons in the valley, and Tianyuan in Han Qing has ups and downs. There are all kinds of things, and the more the better, especially beyond Qin and Li. " Wang Jian, a mathematician in the Qing Dynasty, also said: "Mr. Zhu Songting is the director of Qin and Li, and has achieved great success." Zhu Shijie comprehensively inherited and creatively carried forward the mathematical achievements in Qin and Li's works, such as "Tian Mo" and "Forward-Inverse Method", and included various algorithms in Yang Hui's works that were closely related to social life at that time, and made new development. From this point of view, in Zhu Shijie's works, there are not only the achievements of northern mathematics, such as solving higher-order equations and celestial skills, but also the achievements of southern mathematics, such as daily and commercial algorithms and various songs, which are all reflected in Yang Hui's works. They not only inherited the glorious legacy of ancient mathematics in China, but also developed creatively. Zhu Shijie's work, in a sense, can be regarded as the representative of mathematics in Song and Yuan Dynasties and the peak of the development of ancient computer systems. Even western bourgeois scholars can't deny this. George Sarton said: Zhu Shijie "belongs to the Han nationality, belongs to the era in which he lived, and is also an outstanding mathematician in all previous dynasties", and called "Meet with Siyuan" the most important mathematical work in China and one of the most outstanding mathematical works in the Middle Ages ". With his outstanding works, Zhu Shijie pushed ancient mathematics in China to a new height, added a new chapter to the glorious history of ancient mathematics in China, and formed the highest peak of mathematics development in China-Song Dynasty.