Zhu Shijie
Zhu Shijie (1249-1314), courtesy name Hanqing and nickname Songting, Han nationality, surnamed Yanshan (now Beijing), was a mathematician and educator in the Yuan Dynasty. He has been engaged in mathematics education all his life. He is known as "the greatest mathematician in the medieval world".
Zhu Shijie developed the "quaternary technique" based on the Tianyuan technique at that time, which is to list the four-dimensional high-order polynomial equations and the elimination method to solve them. In addition, he also created the "stack product method", which is the summation method of high-order arithmetic sequences, and the "recruitment method", which is the high-order interpolation method.
The main works are "Arithmetic Enlightenment" and "Siyuan Jade Mirror".
Chinese name: Zhu Shijie
Alias: courtesy name Hanqing, nickname Songting
Nationality: Yuan
Ethnicity: Han
Birthplace: Yanshan (now Beijing)
Birthdate: 1249
Death date: 1314
Occupation: Mathematician
Belief: Science
Main achievements: Creation of "Four Elements Technique"
Creation of "Stacking Technique" and "Recruitment Technique"
Representative Works: "Arithmetic Enlightenment" and "Four Yuan Jade Mirror"
Character Profile
Zhu Shijie "traveled around the world as a famous mathematician for more than 20 years" and "scholars gathered at his door" (Mo Ruo and Zu Yi: Preface to "Siyuan Jade Mirror").
In the Song and Yuan Dynasties, the most outstanding mathematicians in the heyday of Chinese mathematics were "Qin Jiushao, Li Ye, Yang Hui, and Zhu Shijie", and Zhu Shijie was one of them. Zhu Shijie is a civilian mathematician and mathematics educator. Zhu Shijie studied "Nine Chapters of Arithmetic" diligently throughout his life, bypassed various other algorithms, and became a famous mathematician in the Yuan Dynasty.
Life experience
After the Yuan Dynasty unified China, Zhu Shijie traveled around as a mathematician for more than 20 years. Many people studied with him. When he arrived in Guangling (now Yangzhou) Scholars gathered at the door." He comprehensively inherited the mathematical achievements of his predecessors, absorbing not only the Tianyuan technique from the north, but also the positive and negative square root techniques from the south, various daily algorithms and popular songs. On this basis, he conducted creative research and wrote a summary and summary. "Arithmetic Enlightenment" (3 volumes), which aimed to popularize various mathematical knowledge at that time, was also written into the representative work of the Four Elements - "Si Yuan Jade Mirror" (3 volumes), which was published in 1299 and 1303. "Arithmetic Enlightenment" goes from the shallower to the deeper, starting from single-digit multiplication and continuing to the latest mathematical achievement at that time - Tianyuan Shu, which seems to form a complete system.
The book clearly puts forward the multiplication rules of positive and negative numbers, gives the concept and basic properties of reciprocals, outlines a number of new multiplication formulas and radical operation rules, summarizes a number of shortcut formulas for multiplication and division, and provides auxiliary The method of unknowns is used to solve systems of linear equations. The main content of "Siyuan Jade Mirror" is the method of quaternion, that is, the establishment and solution method of multivariate higher-order equations. Qin Jiushao's numerical solution to higher-order equations and Li Ye's Tianyuan technique are both included.
Among the mathematical heroes of the Song and Yuan Dynasties, Zhu Shijie’s work was of special significance. If many mathematicians are compared to mountains, Zhu Shijie is the tallest and most majestic mountain. Standing at the height of Zhu Shijie's mathematical thoughts and overlooking traditional mathematics, you will have the feeling of "seeing all the mountains at a glance".
The significance of Zhu Shijie's work lies in summarizing Song and Yuan mathematics and bringing it to a new height in theory. This is mainly manifested in the following three areas. The first is equation theory. In terms of formulating equations, Jiang Zhou's segmentation method prepared the work for Tianyuan Shu. He already had the idea of ????finding equivalent polynomials. Dongyuan Ma and Xindao were the pioneers of Tianyuan Shu, but their derivation of equations was still bound by geometric thinking. , Li Ye basically got rid of this shackles and summed up a fixed set of Tianyuan Technique procedures, which brought Tianyuan Technique into a mature stage. In terms of solving equations, Jia Xian gave the multiplication method, Liu Yi used positive and negative square roots to find the positive roots of the fourth-order equation, and Qin Jiushao solved the numerical solution problem of higher-order equations on this basis. At this point, the establishment and solution of higher-order equations of one variable have been achieved. The system of linear equations has existed since ancient times, so it has the conditions for the generation of multivariate higher-order equations. Li Desai's dual art and Liu Dajian's ternary art appeared one after another. Zhu Shijie's quaternary art is the summary and improvement of dual art and ternary art. Since the quaternion has occupied the upper, lower, left and right sides of the constant terms, the development of the equation theory has obviously come to an end at this point. From the perspective of the types of equations, the equations before the emergence of Tianyuan Shu were all integral equations.
From Dongyuan to Li Ye, fractional equations were gradually developed.
Zhu Shijie broke through the limitations of rational equations and began to deal with irrational equations. The second is the study of higher-order arithmetic series. Shen Kuo's gap product technique pioneered the study of high-order arithmetic series, and Yang Hui gave a series of second-order arithmetic series summation formulas including gap product technique. On this basis, Zhu Shijie successively studied the summation problem of second-order, third-order, fourth-order and even fifth-order arithmetic series, thereby discovering its rules and mastering the unified formula of triangular stacks. He also discovered the intrinsic connection between the stacking method and the interpolation method, and used the stacking formula to give a standardized fourth-order interpolation formula. The third is the study of geometry. Before the Song Dynasty, geometric research was inseparable from Pythagorean and area and volume. Jiang Zhou's "Yi Gu Ji" also takes the area problem as its research object. Li Ye began to notice the relationship between the elements in the Yuancheng factor and obtained some theorems, but failed to extend them to more general situations. Zhu Shijie not only summarized the previous Pythagorean and quadrature theories, but also went a step further based on Li Ye's thoughts, conducted an in-depth study of the quantitative relationship between the geometric elements within the Pythagorean shape and the circle, and discovered two important theorems - Projection theorem and chord power theorem. In solid geometry, he also began to notice the relationship between elements within figures. Zhu Shijie's work made the object of geometric research go from the whole figure to the interior of the figure, reflecting the progress of mathematical thinking.
Famous anecdotes
At the end of the 13th century, the war-torn motherland was unified by the Yuan Dynasty, and the destroyed economy and culture quickly prospered. In order to prosper and secure the country, the Mongolian rulers respected knowledge, selected talents, and pushed various sciences to new heights.
One day, a teacher came to the beautiful Slender West Lake in Yangzhou and hung a signboard in front of his apartment. It read in big characters: "Mr. Zhu Songting of Yanshan, specializes in teaching four yuan." technique". Within a few days, Zhu Shijie's front door was bustling with people seeking knowledge. When Zhu Shijie was receiving student registrations, a sudden shouting and cursing caught his attention.
I saw an old lady wearing silk and silver, chasing a young girl, beating and scolding: "You bitch, if you don't get a lot of money, do you want to be a lady?" , I'm afraid you were born in the wrong child, and you won't be able to think about it in the next life." The girl was beaten to pieces, and even her inner clothes were torn. The girl huddled up in a ball and let her beat her, but refused to go back with her. When Zhu Shijie saw the injustice, he stepped forward to ask. When the old lady saw a nosy person appearing, she laughed and said, "Do you want to fight the injustice? If you give me 50 taels of silver, this girl will be yours." !"
When Zhu Shijie saw this, he said angrily: "I can't afford 50 taels of silver, but I can do this in broad daylight. Isn't it possible for me to do this without the king's law?"
The old lady sarcastically said: "You poor devil, why are you talking about royal law? Silver is royal law. If you can take out 50 taels of silver, I will not fight."
Zhu Shijie was already angry. Extremely, he took out 50 taels of silver from his pocket, threw it in front of the old lady, picked up the girl and returned to his teaching place. It turned out that the old lady was the madam of a brothel, and the girl's father borrowed 10 taels of silver from the madam. Due to natural disasters, he could not repay the money, so he had to sell his daughter to pay off the debt. Today I happened to meet Zhu Shijie and saved the girl from suffering.
Later, under Zhu Shijie’s careful instruction, the girl also knew some mathematics and became Zhu Shijie’s right-hand assistant. Within a few years, the two got married. Therefore, there is still a saying among the people in Yangzhou: Zhu Hanqing in the Yuan Dynasty taught and educated people. Save people from suffering and make their marriage successful.
Related writings
Zhu Shijie has been engaged in mathematics research and education for a long time. He has traveled around the world as a famous mathematician for more than 20 years, and many people from all over the world come to study. Zhu Shijie's representative works on mathematics include "Arithmetic Enlightenment" (1299) and "Siyuan Jade Mirror" (1303). "Arithmetic Enlightenment" is a popular mathematics masterpiece that has been spread overseas and influenced the development of mathematics in North Korea and Japan. "Siyuan Jade Mirror" is another symbol of the peak of mathematics in the Song and Yuan Dynasties in China. Among the most outstanding mathematical creations are "Siyuan Shu" (multiple higher-order equations and elimination method), "Stacking Product Method" (high (summation of order arithmetic sequence) and "recruitment technique" (high-order interpolation method).
In mathematical science, Zhu Shijie comprehensively inherited the mathematical achievements of Qin Jiushao, Li Ye, and Yang Hui, and gave creative development, writing famous works such as "Arithmetic Enlightenment" and "Siyuan Jade Mirror" , pushed ancient Chinese mathematics to a higher level and formed the highest peak of Chinese mathematics in the Song and Yuan Dynasties.
"Arithmetic Enlightenment" was published by Zhu Shijie in the third year of Dade of Chengzong in the Yuan Dynasty (1299). It has three volumes, 20 subjects, and a total of 259 questions and corresponding answers. This book starts from the operations of multiplication and division to the "Tian Yuan Shu", the highest achievement in the development of mathematics at that time, and comprehensively introduces 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 book. This work later spread to Korea, Japan and other countries, and had reprinted and annotated editions published, exerting a certain influence. And "Four Yuan Jade Mirror" is a masterpiece of mathematics with brilliant achievements. It is highly praised by researchers in the history of modern mathematics and considered to be the most important and most contributing mathematical masterpiece among ancient Chinese mathematical science works. "Siyuan Yujian" was written in the seventh year of Dade (1303). It has three volumes, 24 subjects, and 288 questions. It introduces Zhu Shijie's solution to multivariate higher-order equations - the quaternary technique, as well as high-order arithmetic. Calculation of series - research and achievements in stacking techniques, recruiting techniques, etc.
"Tian Yuan Shu" is to assume that "Tian Yuan is so-and-so", that is, so-and-so is x. But when there is more than one unknown number, in addition to the unknown number Tian Yuan (x), it is also necessary to set up the Earth Yuan (y), the Human Yuan (z) and the Material Yuan (u), and then list the high values ??of two yuan, three yuan or even four yuan. The system of secondary equations is then solved. In Europe, solving simultaneous linear equations began in the 16th century, and research on multivariate higher-order simultaneous equations only happened in the 18th to 19th centuries. Another major contribution of Zhu Shijie is the research on "Stacking Technique". He studied a series of new stack-shaped series summation problems, and summarized them into the formula of "triangular stack". In fact, he obtained a systematic and universal formula for this type of arbitrary high-order arithmetic series summation problems. solution. Zhu Shijie also quoted the triangular stack formula into the "Differentiation Technique" and pointed out that the coefficients in the Triangular Stack Formula are exactly the products of each triangular stack in turn, thus obtaining the Differential Triangulation Formula containing four times of difference.
He also extended this difference formula to include any high-order difference. This was the first time in the history of mathematics in the world, and it was nearly 4 centuries earlier than the same achievement of Newton in Europe. Because of this, Zhu Shijie and his book "Siyuan Jade Mirror" enjoy huge international reputation. In modern times, people from Japan, France, the United States, Belgium and many countries in Asia, Europe and the United States introduced the "Siyuan Jade Mirror" to their own countries. Sutton, the late famous American historian of science, commented on Zhu Shijie this way: "(Zhu Shijie) is the most outstanding mathematical scientist of the Chinese nation, the era in which he lived, and throughout ancient and modern times." "Siyuan Jade" "Jian" is the most important Chinese mathematical work and one of the most outstanding mathematical works in the Middle Ages. It is a rare treasure in the world's mathematical treasure house. "It can be seen from this that the scientists and their works in the Song and Yuan Dynasties. It has played an inestimable role in the history of world mathematics.
Character Contributions
Zhu Shijie’s main contribution is to create a complete set of unknown elimination methods, called the four-element elimination method. This method has been in the leading position in the world for a long time. It was not until the 18th century that the French mathematician Bezout proposed a general solution to higher-order equations, surpassing Zhu Shijie. In addition to the Four Elements Technique, there are two other important achievements in the "Si Yuan Jade Mirror", namely the creation of a general high-order arithmetic series summation formula and an equal-spaced fourth-order interpolation formula. The latter is often called a move. Different skills. This book represents the highest level of mathematics in the Song and Yuan Dynasties. American science historian G. Sarton praised it as "the most important work on Chinese mathematics and one of the outstanding mathematical works in the Middle Ages." Zhu Shijie was in the heyday of the development of traditional Chinese mathematics. At that time, the society "respected arithmetic, the subject gradually became popular", and mathematical works were widely disseminated.
He has done in-depth research on the solution of multivariate higher-order equations, the summation of higher-order arithmetic series, and higher-order interpolation methods. He is the author of "Arithmetic Enlightenment" (1299), "Siyuanyu" "Jian" (1303) each has 3 volumes. In the latter, the solution method of higher-order simultaneous equations with up to four elements, the expression and operation of polynomials and the elimination method are discussed, which is close to modern mathematics and is at the forefront of the world. He is in the leading position. He is proficient in the formulas of the high-level recruitment method, four hundred years earlier than the West. Chinese and foreign historians of mathematics speak highly of Zhu Shijie and his famous work "Four Yuan Jade Mirror".
The extension of Tianyuan Shu to high-order simultaneous equations of two, three and four elements is another outstanding creation of mathematicians in the Song and Yuan Dynasties. The one that has been handed down to this day and systematically discusses this outstanding creation is Zhu Shijie's "Four Yuan Jade Mirror". "Siyuan Jade Mirror" was written in 1303.
The book has 3 volumes, 24 subjects, and 288 questions. It mainly discusses the solution of higher-order equations (this is also Zhu Shijie's greatest contribution), the summation of higher-order arithmetic series, and higher-order interpolation methods. It is an important masterpiece that has been passed down to this day and systematically discusses the Four Elements Art.
On the basis of Tianyuan Shu, Zhu Shijie established the "four-element higher-order equation theory". He placed the constant term in the center (i.e. "Tai"), and then "established the Tianyuan one below and the earth yuan one below." On the left, the human element is on the right, and the material element is on the top." The four "elements" of "heaven, earth, people, and things" represent unknown numbers, (that is, equivalent to today's x, y, z, w,) the four "elements" The powers of are placed in the four directions of up, down, left and right, and other items are placed in the four quadrants. If we use modern x, y, z, w to represent heaven, earth, people, and things, then we can express it by Zhu Shijie's method of setting up high-order multivariate equations: And the above two graphics "four-dimensional linear equation" and "four-dimensional linear equation" The equations represented by "quadratic equation" are: x+y+z+w=0
After using the above method to list the four-dimensional higher-order equations, then solve the system of equations simultaneously , the method is to use the elimination method to solve, first select one element as the unknown number, and the polynomial composed of other elements as the coefficient of the unknown number, then eliminate one element of the four-element four-element equation to become the three-element three-element equation, and then eliminate the one element to become the two-element two-element equation. , and then eliminate one yuan, you will get the Tianyuan opening method containing only one yuan, and then use the multiplication method to find the positive root. This is a major development in the solution of linear method groups. In the West, more systematic research on multivariate equations had to wait until the 16th century. The summation of high-order arithmetic series and the high-order interpolation method are also important contents of "Si Yuan Jade Mirror". The formula can be summarized from a series of triangular stack formulas in many summation problems. Zhu Shijie gave the formula when p=1, 2, 6 in the above formula. In addition, there are other higher-order arithmetic series summation formulas. In terms of the recruitment method, Zhu Shijie is equivalent to giving the recruitment formula, which is more than 400 years earlier than the West.
The famous American science historian Sutton commented: "Zhu Shijie was the most outstanding mathematician of his time and throughout ancient and modern times." "Siyuan Jade Mirror" is "a Chinese mathematical work." "Zhu Shijie is not only an outstanding mathematician, but also a mathematics educator who has traveled around the world and taught students for more than 20 years. He also personally compiled an introductory book on mathematics called "Arithmetic Enlightenment". In the second volume of "Arithmetic Enlightenment", Zhu Shijie proposed methods for solving the Pythagorean form with known chord sums and strand chord sums, which supplemented the shortcomings of "Nine Chapters of Arithmetic".
Historical evaluation
"Mr. Zhu Songting of Yanshan" was an outstanding mathematician in the Yuan Dynasty. The "Four Yuan Jade Mirror" and "Arithmetic Enlightenment" written by him are an important milestone in the development of ancient Chinese mathematics and a valuable legacy of ancient Chinese mathematics. In the middle of the 13th century, in addition to accepting the mathematical achievements of the north, Zhu Shijie also absorbed the mathematical achievements of the south, especially various daily algorithms, commercial arithmetic, popular songs, etc.
Zhu Shijie once "traveled around the world". In the preface of Mo Ruo (ancient mathematician), there is "Mr. Zhu from Songting in Yanshan has been traveling around the lakes and seas as a famous mathematician for more than 20 years. Scholars are coming from all over the world, so Mr. The wonder of "Nine Chapters" was invented by Shu Hou's illustrations, and the three volumes were called "Siyuan Jade Mirror". In the preface of Zu Yi, there is also "Han Qing is famous in the world, and his self-title is Song Ting Zhou." Traveling in all directions, he visited Guangling again, and scholars gathered at Heimen." After a long period of study tours, lectures and other activities, he finally published two of his mathematical masterpieces - "Arithmetic Enlightenment" and "Siyuan Jade Mirror" in Yangzhou in 1299 and 1303. The formula of elimination in Yang Hui's book was further developed in Zhu Shijie's "Arithmetic Enlightenment".
Luo Shilin of the Qing Dynasty believed: "During the Song and Yuan Dynasties, Han Qing, Qin Daogu (i.e. Qin Jiushao), and Li Renqing can be called three tripods. Daogu's positive and negative squares, Han Qing's Tianyuan are all equal to the top and bottom. Throughout the ages, the officials of the Han Dynasty have embraced everyone, tried their best to follow the same example, and were divine and enlightened, especially superior to those of Qin and Li." Wang Jian, a mathematician in the Qing Dynasty, said: "Mr. Zhu Songting is both the director of Qin and Li, and he is the author of a family of works." Zhu Shijie comprehensively inherited and creatively carried forward the mathematical achievements contained in the books of Qin and Li such as Tianyuan Shu, positive and negative methods, etc., and also included daily use, commercial use, and division formulas in Yang Hui's books, which were closely related to the social life at that time. Various related algorithms and made new developments.
Related information
Before the Yuan Dynasty destroyed the Southern Song Dynasty, exchanges between the north and the south, especially academic exchanges, were almost severed.
Mathematicians in the South knew nothing about Tian Yuan Shu in the North, while mathematicians in the North were rarely influenced by the South.
From this point of view, in Zhu Shijie’s work, there are not only the achievements of northern mathematics represented by the solution of higher-order equations and Tianyuan Shu, but also the daily use reflected in Yang Hui’s work. The achievements of southern mathematics, such as commercial algorithms and various formulas, not only inherited the glorious legacy of ancient Chinese mathematics, but also made creative developments. Zhu Shijie's work, in a certain sense, can be regarded as a representative of Song and Yuan mathematics and the pinnacle of the development of ancient calculation systems. Even Western bourgeois scholars cannot deny this. George Sutton said: Zhu Shijie "is of the Han nationality, of the era in which he lived, and is also one of the most outstanding mathematicians throughout ancient and modern times." He said that "Si Yuan Jade" "Jian" "is the most important Chinese mathematical work and one of the most outstanding mathematical works in the Middle Ages." With his own outstanding works, Zhu Shijie pushed ancient Chinese mathematics to a higher level, added a new chapter to the glorious history of ancient Chinese mathematics, and formed the highest peak of the development of Chinese mathematics in the Song Dynasty.
Yangzhou Anecdotes
Based on this, we know that Zhu Shijie was born in Beijing. In the late 13th century, he traveled around the country as a famous mathematician for more than 20 years. Zhu Shijie finally lived in Yangzhou and engaged in mathematics. Through research and lectures, he attracted many scholars to gather in Yangzhou for academic exchanges. Yangzhou is located at the intersection of north and south, and various academic thoughts are integrated here. At that time, Yangzhou's printing industry was very developed and it was the country's book publishing center. Two works embodying Zhu Shijie's mathematical achievements, "Arithmetic Enlightenment" and "Siyuan Jade Mirror" " was printed and published in Yangzhou in the third year of Dade of the Yuan Dynasty (1299) and the seventh year of Dade of the Yuan Dynasty (1303).
The book "Mathematics Enlightenment" consists of ***3 volumes, divided into 20 subjects, and contains 259 mathematical problems. At the beginning of the book, Zhu Shijie gives 18 commonly used mathematical formulas and various commonly used mathematical constants, including: the nine-nine formula for multiplication, the nine-return formula for division (exactly the same as the later abacus division formula), and the formula for converting a kilogram into zero. , as well as calculation and counting rules, carry method for small and large numbers, conversion of weights and measures, pi, addition and subtraction of positive and negative numbers, multiplication rules, square root rules, etc. The main text includes multiplication and division operations and their shortcuts, multiplication method, Tianyuan technique, solution of linear equations, summation of high-order arithmetic series, etc. The whole book goes from shallow to deep and covers almost all aspects of mathematics at that time. , forming a relatively complete system, which can be said to be a good mathematics textbook. Luo Shilin, a Yangzhou scholar in the Qing Dynasty, said that "Arithmetic Enlightenment" "seems to be shallow but is actually deep". This comment is very pertinent.
"Four Yuan Jade Mirror" is Zhu Shijie's masterpiece that explains the results of many years of research. The book is divided into 3 volumes, 24 subjects, and 288 questions. All the questions in the book are related to solving equations or solving systems of equations. Among them, there are 7 questions about quaternary questions (those that require the establishment of four unknowns) and 13 questions about ternary questions. , 36 questions for the dualist, and 232 questions for the univariate. The beginning of the volume lists four types of five pictures, including Jia Xian's triangle, and gives examples of solutions to Tianyuan, Dual, Sanyuan, and Quaternary techniques; the latter three are respectively Dual, Sanyuan, and Quaternary higher order. Listing and solution of systems of equations. The greatest contribution of this book is the creation of the four-element elimination method to solve the problem of multivariate higher-order equations. Another major achievement in the book is the systematic solution of high-order arithmetic series summation problems and high-order difference method problems.
Before Zhu Shijie, ancient Chinese mathematics had a method for solving equations - "Tian Yuan Shu". "Tian Yuan Shu" solved equations by assuming "Tian Yuan is so-and-so", and so-and-so is (x). Zhu Shijie not only inherited the Tianyuan technique, but also extended the method of solving equations from two-element and three-element to four-element. When there is more than one unknown number, in addition to the unknown number Tianyuan (x), also set up the earth element (y), human element (z) and matter element (u), and then list the higher-order simultaneous equations of two yuan, three yuan or even four yuan. group and then solve. In Europe, the solution of simultaneous linear equations began in the 16th century, and the research on multivariate higher-order simultaneous equations was only in the 18th and 19th centuries. Zhu Shijie's "Tian Yuan Shu" was more than 400 years earlier than Europe.
Zhu Shijie's research on "Stacking Technique" actually obtained a universal solution to the problem of summation of high-order arithmetic series.
Since the Song Dynasty, there has been research on the summation of high-order arithmetic series in my country. In the works of Shen Kuo (1031-1095) and Yang Hui (1261-1275), there are stacking problems. These stacking problems are Some involve high-order arithmetic series. Zhu Shijie further deepened the research on this issue in "Siyuan Jade Mirror" and obtained a series of formulas for triangular stacks.
"Si Yuan Jade Mirror" is a masterpiece of mathematics with brilliant achievements. It is the master of mathematics in Song and Yuan Dynasties, and it is also the highest level mathematics work in ancient my country. Researchers in the history of modern mathematics have spoken highly of "Siyuan Jade Mirror". George Sutton, a well-known expert on the history of science, said that "Siyuan Jade Mirror" "is the most important work on Chinese mathematics and one of the most outstanding mathematical works in the Middle Ages." Joseph Needham, who edited "History of Science and Technology in China", commented on Zhu Shijie and "Siyuan Jade Mirror": "None of the mathematicians before him could reach the mysterious truth contained in this profound work."
Unfortunately, after Zhu Shijie, no profound mathematical works appeared in the Yuan Dynasty. There were few new editions of mathematical works in the Han, Tang, Song and Yuan Dynasties, and many were even lost. When the Sikuquanshu library was opened in the thirty-seventh year of Qianlong (1772), many ancient mathematics classics were excavated, but Zhu Shijie's works were not discovered, so they were not included in the collection at first; in 1799, Ruan Yuan, Li Rui and others compiled The "Siyuan Jade Mirror" was not introduced in the biography of the mathematician "Chou Ren Zhuan". Soon after, Ruan Yuan visited this book in Zhejiang, and immediately compiled it into the "Si Ku Quanshu" and gave the manuscript to Li Rui for proofreading (it was not yet completed). Later, He Yuanxi engraved the manuscript according to this copy, which is "Si Yuan Quanshu". The first reprint of the Jade Mirror since its original publication in 1303. In 1839, after many years of research, Yangzhou scholar Luo Shilin published "Siyuan Jade Mirror" compiled by him. Luo made detailed notes on every issue in the book. When Luo Shilin was reprinting "Four Yuan Jade Mirror", "Arithmetic Enlightenment" was not yet available. Later, Luo Shilin "heard that North Korea used this book as a calculation subject to recruit scholars", so she asked someone to find a reprinted copy of "Arithmetic Enlightenment" engraved by Jin Shizhen, Yin of Quanzhou, North Korea in the 17th year of Shunzhi (1660). It was reprinted and published in Yangzhou. This is the master copy of the various existing editions of the book.
These two outstanding mathematical works by Zhu Shijie of the Yuan Dynasty were both completed and engraved in Yangzhou. After being lost for hundreds of years, they were discovered, collated, annotated and re-engraved in Yangzhou by Yangzhou scholars. Publication, this alone shows that Yangzhou has a very important position in the history of the development of mathematics in my country.