Open any history of China's mathematics development, it is not difficult to find that every step forward of Chinese ancestors is accompanied by the sweat of struggle. China's mathematics originated from ancient times to the end of Western Han Dynasty, and China's mathematics reached its peak from the middle of Sui Dynasty to the end of Yuan Dynasty. Next, from the end of Yuan Dynasty to the middle of Qing Dynasty, mathematics in China developed slowly. When the development of mathematics in China was slow, western mathematics had made great strides, so in the history of China's mathematics development, there appeared a confluence period of Chinese and western mathematics development, which was about1840 ~1911year. The beginning of modern mathematics is mainly concentrated in the period of191~1949. Although China is now in a backward position in the field of mathematics in the world, it is still unknown whether it can become a winner in the future.
catalogue
The source of 1
2 period of development and prosperity
3 heyday
4 slow development period
5 Chinese and Western Confluence Period
The source of 1
2 period of development and prosperity
3 heyday
4 slow development period
5 Chinese and Western Confluence Period
6 the beginning of modern mathematics
7 People's Republic of China (PRC)'s development after its founding.
8 ancient achievements
9 related items
10 reference
Open any history of China's mathematics development, it is not difficult to find that every step forward of Chinese ancestors is accompanied by the sweat of struggle. China's mathematics originated from ancient times to the end of Western Han Dynasty, and China's mathematics reached its peak from the middle of Sui Dynasty to the end of Yuan Dynasty. Next, from the end of Yuan Dynasty to the middle of Qing Dynasty, mathematics in China developed slowly. When the development of mathematics in China was slow, western mathematics had made great strides, so in the history of China's mathematics development, there appeared a confluence period of Chinese and western mathematics development, which was about1840 ~1911year. The beginning of modern mathematics is mainly concentrated in the period of191~1949. Although China is now in a backward position in the field of mathematics in the world, it is still unknown whether it can become a winner in the future.
A Brief History of Mathematics Development in China-Origin
The ancient Greek scholar Pythagoras (about 580-500 BC) famously said, "Everything counts". Indeed, a world without numbers is unimaginable.
Today, people will disdain such a trivial matter as counting from 1 to 10, but tens of thousands of years ago, it was a painstaking matter. 7,000 years ago, they couldn't even count two. If you ask them how many four wild animals they have caught, they will answer: "Many". If anyone could count to 10 at that time, it would be considered an outstanding genius. Later, people will gradually associate numbers with hands. Take one thing in each hand, which is 2. On the count of three, I was stumped again, so I put the third thing at my feet and the "problem" was solved.
In this way, in the gradual exploration, the ancestors of the Chinese nation came out of the chaotic world.
First, knot counting, and then developed into "calligraphy." Five or six thousand years ago, people could write the number 1 ~ 30. By the Spring and Autumn Period more than 2,000 years ago, our ancestors could not only write more than 3,000 kinds of mathematics, but also had the consciousness of addition, subtraction, multiplication and division. There is a passage in Jin Wenzhou's Ding: "The East Palace says: Pay ten tablets, and keep ten tablets as one. If you pay it next year, you will pay it. " This passage contains a question of rolling interest. That is to say, if you borrow 10 bundle of millet, you will return it later, and it will change from 10 bundle to 20 bundles. If you return it every other year, you have to increase it from the borrowed 10 bundle to 40 bundles. Expressed by mathematical formula:
10+ 10=20
20×2=40
In addition to the great progress in counting and algorithm, the ancestors of the Chinese nation also began to record some digital knowledge in books. Bagua appeared in Zhouyi, one of the classic works revised by Confucius in the Spring and Autumn Period (5565438 BC+0-479 BC). This magical gossip is still the research object of Chinese and foreign people, and it plays an important role in mathematics, astronomy and physics.
By the Warring States period, the knowledge of mathematics had far exceeded the level of 1~3000. At this stage, they began to cultivate and sow in the fields of arithmetic, geometry and even modern applied mathematics. In the field of arithmetic, four arithmetic operations were established in this period, and the formulas in multiplication have appeared sporadically in Guanzi, Xunzi and Zhouyi Shu, and fractional calculation has also been applied to farming and grain distribution. In the field of geometry, Pythagorean theorem appeared. In the field of algebra, the concept of negative number has sprouted. The most surprising thing for later generations is that in this period, the bud of "game theory" appeared, which is a problem in the field of modern applied mathematics. It is a branch of operational research, which mainly uses mathematical methods to study whether two parties with conflicting interests have their own optimal strategies to win each other in competitive activities and how to find out these strategies. As a discipline, this branch of mathematics was formed during or after the Second World War in this century, but as early as more than 2,000 years ago, Sun Bin, a famous strategist in the Warring States Period (360-330 BC), put forward the problem of "Touma", the content of which reflected the mathematical thought of striving for overall optimization in game theory. The problem with "Touma" is that Qi Weiwang wants to compete with General Tian Ji, and everyone has 1 horse. Compared with Qi Weiwang, Tian Ji's three horses are slightly inferior. If the tournament method corresponding to the same level is adopted, Tian Ji will undoubtedly lose, and Tian Ji is so anxious that he doesn't know what to do. At this moment, Sun Bin nudged on the sidelines, and Tian Ji won Qi Weiwang 2-/kloc-0-0 with Sun Bin's method.
What method did Sun Bin use? Please refer to the following schematic diagram:
Qi Weiwang, Tian Ji.
A good horse. A good horse.
Medium horse, medium horse
Inferior horse
Seeing this, don't you think our ancestors were really smart?
When history advanced to the Qin and Han Dynasties, ancestors no longer carved words on bones. They write everything they need to remember on bamboo and wood chips with a brush. This kind of written bamboo and wood chips is called "Jane" or "Solution". This kind of bamboo slips or bamboo slips was handed down most in the Western Han Dynasty.
From those Han bamboo slips, we found that the examples of multiplication and division in arithmetic in Qin and Han dynasties increased obviously, and there were also intermediate formulas of multi-step multiplication and division and 99-99 method. In geometry, I have a lot of research on the calculation of rectangular area and volume.
The most noteworthy things in this period are calculation and decimal system. With them, ancestors will no longer worry about the lack of suitable calculation methods. This computing system was used in ancient China until the Tang Dynasty.
The exact origin time of calculation and compilation is not clear, only that the system has been formed before and after Qin and Han Dynasties.
To understand how to calculate financing, we must first know what financing is. The chip is a small stick with a diameter of 1 and a length of 6. These sticks are made of bamboo, wood, bone, iron and copper. Their functions are similar to abacus beads. At present, many batches of protrusions have been unearthed. 197 1 year, found in a rectangular male and female tomb unearthed in Qianyang County, Shaanxi Province, the man's body was tied with a silk bag with a raised bone in it. 1980 a batch of early bone fragments unearthed in the southern suburbs of Shijiazhuang also hung on the waist of the deceased. As can be seen from the quotation, calculation and financial management have been widespread among intellectuals in the Han Dynasty. As for how to use the chip, according to the record, it is like this: when calculating, put the chip in a special box or put it casually. For numbers below 5, put a few chips, while for the four numbers from 6 to 9, you need to use a horizontal or vertical chip as 5, and put a few chips in the rest of the numbers.
For the convenience of calculation, the ancients stipulated the vertical and horizontal representation. The vertical bar indicates the number of digits used for a single number and one hundred thousand digits; Horizontal representation is used for tens or thousands of digits, and when zero is encountered, one digit is empty.
Decimalization is the common decimal method in our daily life today. That is to say, for positive integers or positive decimals, base on ten, every ten into one, every hundred into two, every thousand into three and so on. The appearance of decimal system has created good conditions for the development of four operations.
A Brief History of Mathematics Development in China —— Period of Development and Prosperity
The prosperous period of mathematics in China was from the end of Western Han Dynasty to the middle of Sui Dynasty. This is the first peak of China's mathematical theory. The symbol of this peak is the birth of the mathematical monograph "Nine Chapters of Arithmetic". Nine chapters of arithmetic have at least 1800 years. Who is its author? Who made it up? So far, there is no research. Historians only know that it was the crystallization of China's mathematical knowledge in Qin and Han Dynasties, and it was spread and used in the 1 century.
This book is divided into nine chapters:
① Square field (operation of four fractions and plane shape method for finding area).
(2) Corn (the calculation method of grain trade).
③ Decay (calculation method of distribution ratio).
④ Less and wider (square root and opening method)
⑤ quotient work (solid volume method)
⑥ Equal loss (calculation method for managing the average burden of grain transportation).
⑦ Profit and loss (profit and loss problem's solution also involves other types of problems that this solution can handle).
⑧ Equation (solution of linear equations and positive and negative skills).
Pet-name ruby Pythagorean Theorem (Pythagorean Theorem Application and Solution of Simple Measurement Problem).
The book contains 246 mathematical application problems, each of which is divided into questions, answers and technical solutions. Some have one topic and one skill, and some have three parts. Each chapter is closely related to social production.
The birth of this book not only shows that China has formed a complete mathematical system in ancient times, but also it is difficult to find another mathematical monograph with comparable performance in the world.
At the peak of the development of this mathematical theory, in addition to the magnum opus Nine Chapters Arithmetic, Liu Hui's Nine Chapters Arithmetic also appeared, as well as his mathematical monographs Calculating Classics on the Island, Calculating Classics by Sun Tzu (the author is unknown), Calculating Classics by Xiahou Yang, Calculating Classics by Zhang Qiu, and Compiling Zu Chongzhi.
The outstanding figures who made new achievements in mathematics in this period were Zhao Shuang of Three Kingdoms, Liu Hui of Wei and Jin Dynasties and Zu Chongzhi of Southern Dynasties.
A Brief History of Mathematics Development in China —— Its heyday
The heyday of mathematics in China was from the middle of Sui Dynasty to the end of Yuan Dynasty.
The scientific development of any country cannot be separated from a clean and enlightened social environment and a solid economic foundation. From the middle of Sui Dynasty to the end of Yuan Dynasty, because the rulers summed up the lessons of overthrowing the dynasty and adopted a series of enlightened policies, the economy developed rapidly and science and technology were greatly improved, and mathematics, as a part of science and technology, also entered its heyday at this time.
During this period, the normalization of mathematics education and the emergence of mathematics talents are the most important characteristics.
Before the Sui Dynasty, school education did not attach importance to mathematics, so there was no mathematics major. In the Sui Dynasty, this situation was broken, and arithmetic majors were set up in schools equivalent to universities. In the Tang Dynasty, imperial academy, the highest institution of higher learning, also set up a mathematics museum, in which doctors and teaching assistants were readily available to train mathematics talents. At this time, the importance of mathematics education is also reflected in the issue of selecting officials. According to the ancient book "History", there is a story that there was a great official named Yang Shi in the Tang Dynasty. He asked his staff to recommend an excellent staff member for promotion. There are thousands of choices, and when there are two people left, I can't decide which one to get rid of. Because these two clerks have the same conditions in all aspects: the same position, the same "length of service" and similar comments ... who should I choose? I have no choice but to hand in contradictions. After learning this news, Yang Yang also spent a lot of time thinking over and over again, and finally decided to test them with a math problem. He said to the two candidates, "As a clerk, your occupation determines that you should have the ability to calculate quickly. If I give a question, whoever answers correctly first will be promoted. " Later, the first person who answered correctly was naturally promoted, and the other person returned to his original position with conviction. This shows that the Tang Dynasty attached importance to mathematics.
Majored in mathematics. Good teaching materials are indispensable. In the meantime, there is also Li (? ~ AD 7 14) and others, on the orders of the imperial court, made a special textbook for imperial academy computer library after research and screening. This textbook is called Ten Books on Calculating Classics, with a full set of ten books: Weekly Calculations, Nine Chapters Calculations, Sunzi Calculations, Cao Wu Calculations, Xiahou Yang Calculations, Zhang Qiu Calculations, Island Calculations, and Five Classics Arithmetic and Composition.
For this set of professional teaching materials, imperial academy has also stipulated the study period and established a system of taking exams once a month. Since then, mathematics education has gradually improved.
Under the increasingly perfect mathematics education system, a generation of famous mathematics masters have emerged, namely, Wang Xiaotong, his party, Shen Kuo, Jia Xian, Yang Hui, Qin, Guo Shoujing and Zhu Shijie. ...
Science has always been the wealth of all mankind. At that time, China's mathematics level quickly attracted the attention of North Korea and Japan, and they began to send overseas students and booksellers to China. After a period of study, knowledge about fields, land rent and grain exchange was introduced into the algorithm. Imperial academy's curriculum and examination system have been absorbed into running schools. From this perspective, at this stage, China has been at the forefront of the development of mathematics in the world.
A Brief History of Mathematics Development in China —— The Period of Slow Development
Next, from the end of Yuan Dynasty to the middle of Qing Dynasty, the development of mathematics in China was slow, almost eclipsed by the aforementioned flourishing age of mathematics.
From the end of Song Dynasty to the establishment of centralization of authority in Yuan Dynasty, the land of China was ravaged by years of war, and no one cared about science and technology, and a lot of valuable mathematical heritage suffered losses.
After the establishment of the Ming Dynasty, production developed briefly, but it quickly declined due to the corruption of feudal rule, and it was not relieved until the early years of the Qing Dynasty.
In such an environment of political corruption, economic backwardness and peasant uprising, it is reasonable for mathematics to fall into a trough.
However, the trend of world development never waits for people. With the decline of mathematics in China, western mathematics quietly caught up with it, which in turn penetrated into China.
When western capitalism began to sprout, in order to seek development, Catholic missionaries, pirates and businessmen flocked to China. In addition to taking away raw materials, markets and cheap labor from China, they also brought some cultural knowledge.
Matteo Ricci (1552~ 10), an Italian, had the greatest influence among the missionaries who came to China in 65438 ~ 18. From 1583 to 1599, when he lived in Zhaoqing, Shaozhou, Nanchang and Nanjing in China, he met many famous scholars in China, such as Li Zhi, Xu Guangqi and Li Zhi. The mentality of these people is that they are not satisfied with empty talk about Neo-Confucianism and are eager to enrich Qiang Bing. Therefore, they are eager for the latest scientific and technological achievements in the world. The arrival of Matteo Ricci undoubtedly played a hit-it-off role.
Matteo Ricci, Xu Guangqi and Li Zhizao jointly translated two mathematical works in the same language: Elements of Geometry and Calculating Fingers.
Among them, The Elements of Geometry is very popular, and there is almost no omission. Although there were no ready-made China words in the Latin original at that time, Xu Guangqi overcame difficulties and created many appropriate translations, which made the book reach the level of faithfulness, expressiveness and elegance.
Since Matteo Ricci cooperated with China scholars in the translation of monographs, the spread of western learning to the east has been growing.
So what is China's own mathematical "specialty" in this period? This is an abacus.
During the Sui and Tang Dynasties, people began to make improvement plans. They try to simplify calculation methods and make up formulas ... but in the rapidly developing field of mathematics, calculation algorithms will inevitably be replaced by other algorithms.
At the end of the Yuan Dynasty, a small and light abacus appeared. People are overjoyed at this new tool, which is simple in calculation and easy to carry. Some people even write it into proverbs, poems and lyrics.
The appearance of abacus soon led to books on abacus formulas and abacus algorithms. 16,17th century, among a large number of abacus books in China, the most famous one is Cheng Dawei's "Pointing at Arithmetic". After the popularity of abacus calculation, calculation automatically disappeared.
Shortly after China invented the abacus, Pascal (A.D. 1623~ 1662), a 9-year-old French mathematician, introduced the world's earliest computer. At present, although the world has entered the computer age, the abacus still has its place. Someone has tried it, and it is even faster than a small calculator in addition and subtraction.
A Brief History of Mathematics Development in China —— Combination of Chinese and Western.
When the development of mathematics in China was slow, western mathematics had made great strides forward. Therefore, in the history of China's mathematics development, there was an intersection of Chinese and western mathematics development, which was about1840 ~191year.
As mentioned earlier, around the16th century, western missionaries brought some new mathematical knowledge. Although some foreigners have personal goals, in any case, the introduction of new knowledge is always beneficial to the progress of mathematics in China. However, when Yong Zhengdi 1723 ascended the throne, it was suggested that a large number of missionaries were in China, which was unfavorable to his rule. The emperor also wanted to think. Immediately ordered, except for a few foreigners who made a new calendar in China, all other missionaries stayed behind.
The consequence of this order is that it is difficult to "import" western mathematical knowledge in the next 100 years; Mathematicians in China have to turn their eyes from learning new western knowledge to studying their own old achievements.
The light of ancient mathematics did not last long. After the defeat of the Opium War, China was closed to the outside world, imperialist powers came in to carve up China, and China once became a semi-colonial and semi-feudal society.
From 65438 to 1960s, Zeng Guofan and Li Hongzhang launched the "Westernization Movement" to safeguard the corrupt Qing government. At this time, a group of intellectuals represented by Li, Xu Shou and Huawei, as mathematicians, scientists and engineers, participated in the activities of introducing western learning and running schools. Through their unremitting efforts, they laid the foundation for the development of modern science and technology and modern mathematics in China.
1894 When the Westernization Movement ended in military failure, factories, railways and schools still existed, and scientific and technological knowledge was spread to a certain extent.
This period is characterized by the combination of Chinese and western cultures. The so-called confluence of China and the West does not mean total westernization. Mathematicians absorb new methods while studying traditional mathematics. For a time, there was a good momentum of talented people and rich writings.
At this time, China mathematicians have made some independent calculus achievements in power series, sharp cone skills and so on, and have also made excellent achievements in indefinite analysis and combinatorial analysis. However, even so, China has not reached the leading position among its peers in the world.
A Brief History of Mathematics Development in China —— The Beginning of Modern Mathematics
The beginning of modern mathematics is mainly concentrated in the period of191~1949.
By the end of 65438+2009 and the beginning of the 20th century, great changes had taken place in the field of mathematics in China. Send a large number of international students, set up new schools, organize academic groups and have special periodicals. Since then, China has entered the research stage of modern mathematics.
From 1847, the first batch of students, represented by Hong Rong, went abroad, forming a climax of studying abroad. At that time, the number of people studying abroad reached thousands every year. After returning to China, they formed a modern scientific team that can not be ignored in China.
Among the early overseas students, few studied mathematics, among which Su, Chen, Zhou Weiliang, Hua and others made outstanding achievements.
After such a group of overseas students returned to China, there have been new changes in scientific research, education and academic exchanges.
In terms of scientific research, before 1949, * * * published 652 papers. Although the number is small and the scope is limited to pure mathematics, its level is not lower than that of international counterparts. You know, even this modest achievement was achieved by overcoming unimaginable difficulties in politics, economy and other aspects.
In education, a formal curriculum has been established, mathematics has more class hours than liberal arts, and textbooks have been updated. By the end of 1932, there was a team of 155 mathematics teachers in Chinese universities, who could offer more than 5 to 10 specialized courses.
In terms of academic exchange, chinese mathematical society was founded in July, 1935, and founded Journal of chinese mathematical society and Journal of Mathematics. China people participated in the 9th and 10 international mathematical congresses held from 1932 to 1936. At this time, mathematicians from all over the world were invited to give lectures in China, which brought a modern atmosphere to the mathematics field behind closed doors.
A Brief History of Mathematics Development in China —— Development after the Founding of the People's Republic of China
From 65438 to 0949, when New China was founded, the government attached great importance to the scientific cause, although the country was in a dilemma of lack of funds and everything was ready. China Academy of Sciences was established in 1949+065438+ 10, and the Institute of Mathematics was formally established in 1952. Then, chinese mathematical society and his publications resumed and created other special issues on mathematics, and some scientists' monographs were published in competition, paving the way for mathematical research.
During the 18 years after liberation, the number of published papers was more than three times that before liberation, many of which not only filled the gaps in China's past, but also reached the advanced level in the world.
When mathematicians catch up and try to restore the advanced position of China's mathematics in the world, a ruthless storm swept through China. In the decade of the Cultural Revolution, society was out of control, people were confused and science declined. In the garden of mathematics, except for Chen Jingrun and Huahe, several mathematicians struggled to blossom several flowers, which almost withered everywhere, leaving a blank.
When the political disaster of 10 passed, people looked up and saw that the mathematical research in other countries had already reached its peak, which required great efforts to catch up.
The Chinese nation has always had a glorious tradition of self-improvement and perseverance. After the catastrophe, with the publication of Mr. Guo Moruo's wonderful article "Spring of Science", the mathematics garden ushered in the spring of everything's recovery. From 65438 to 0977, Beijing formulated a new mathematical development plan, resumed the work of the Mathematical Society, re-published academic magazines, strengthened mathematics education and strengthened basic theoretical research. ...
Although China is now in a backward position in the field of mathematics in the world, we should know from a distance that Ma Quan is still an "X".
A Brief History of Mathematics Development in China-Ancient Achievements
In the history of ancient mathematics development in China, the gold medals won by our ancestors were enough to open an exhibition hall, and only a "list" was opened here, giving readers an intuitive impression.
(1) Decimal notation and the adoption of zero. Originated in the Spring and Autumn Period, earlier than the second inventor India 1000 years.
(2) The origin of binary system. The Eight Diagrams method, which originated in Zhouyi, was more than 2000 years earlier than the second inventor, the German mathematician Leibniz (A.D. 1646 ~ 17 16).
(3) that origin of geometric thought. The Mohist Classic originated in Mo Zhai during the Warring States Period, which was earlier than the second inventor Euclid (330-275 BC) 100 years.
(4) Pythagorean theorem (quotient height theorem). The inventor Shang Gao (from the Western Zhou Dynasty) was more than 550 years earlier than the second inventor Pythagoras (580-500 BC).
(5) Rubik's cube. The earliest records of magic methods in China are The Analects of Confucius and The Classic in the Spring and Autumn Period, while abroad, the Rubik's Cube appeared in the 2nd century A.D., more than 600 years earlier than in China.
(6) fractional arithmetic and decimals. China's complete fractional arithmetic appeared in "Nine Chapters of Arithmetic", and its transcript appeared in 1 century at the latest. The same law appeared in India in the 7th century, and it is considered as the "originator" of this law. China is more than 500 years earlier than Indian.
China used the least common multiple of western countries 1200 years ago. As early as 1 100 years ago, decimals were used in the west.
(7) The discovery of negative numbers. This discovery was first seen in Nine Chapters Arithmetic, more than 600 years earlier than India and 1600 years earlier than the West.
(8) Surplus is not surgery. Also known as double false positioning method. It was first seen in the seventh chapter of Nine Chapters Arithmetic. In the world, it was not until the 3rd century A.D./kloc-0 that the same method appeared in Europe, which was more than 200 years later than that in China.
(9) Equation technology. It first appeared in Nine Chapters Arithmetic, in which the method of solving linear equations was more than 600 years earlier than India and 1500 years earlier than Europe. China is 1800 years earlier than other countries in the world in solving linear equations by matrix arrangement method.
(10) The most accurate pi "ancestral rate". It is more than 1000 years earlier than other countries in the world.
(1 1) equal product principle. Also known as the "ancestral declaration" principle. Keep the world record of 1 100.
(12) quadratic interpolation method. Liu Zhuo, an astronomer in Sui Dynasty, first invented it, which was more than 1000 years earlier than Newton, the world runner-up (1642 ~ 1727).
(13) multiplication and division method. In modern mathematics, it is also called Horner method. Jia Xian, a mathematician of the Song Dynasty in China, was first invented in1/century, which was about 800 years earlier than that proposed by Horner, a British mathematician (A.D. 1786~ 1837).
(14) Yang Hui Triangle. It is actually a binomial expansion coefficient table. Originally created by Jia Xian, it can be found in his book The Nine Chapters of Yellow Emperor's Fine Grass Algorithm. Later, this book was lost, and Yang Hui, a native of the Southern Song Dynasty, compiled this table in his "Detailed Explanation of Nine Chapters of Algorithms", hence the name "Yang Hui Triangle".
In the world, besides China's Jia Xian and Yang Hui, the second inventor is French mathematician Pascal (A.D. 1623~ 1662). His invention date was 1653, which was nearly 600 years later than that of Jia Xian.
(15) China's remainder theorem. In fact, it is the way to solve the problem of simultaneous congruence. This method was first seen in Sun Tzu's calculation. 180 1 year, German mathematician Gauss (A.D. 1777~ 1855) put forward this solution in "Arithmetic Inquiry". Westerners believe that this method is the first in the world and call it "Gauss Theorem", but it was later discovered than China.
(16) digital higher-order equation method, also known as "astrophysics". In the Jin and Yuan Dynasties, China mathematician Ye Li invented the equation method of setting unknowns, and skillfully expressed it in the calculation. This method is more than 300 years earlier than other countries in the world, which lays a good foundation for solving multivariate higher-order equations in the future.
(17) calls for differences. Namely the high-order arithmetic progression summation method. Since the Northern Song Dynasty, many mathematicians in China have studied this problem. In the Yuan Dynasty, Zhu Shijie first invented the technique of calling the difference, which always solved this problem. In the world, Newton, who was nearly 400 years later than Zhu Shijie, got the same formula.