A brief history of the development of mathematics in China. Open category: Mathematical Society

Looking through any history of the development of mathematics in China, it is not difficult to find that every step forward for the Chinese ancestors was accompanied by struggle. of sweat. Chinese mathematics originated from ancient times to the end of the Western Han Dynasty. The heyday of Chinese mathematics was from the middle Sui Dynasty to the late Yuan Dynasty. Next, from the late Yuan Dynasty to the mid-Qing Dynasty, the development of Chinese mathematics was slow. While the development of Chinese mathematics was slow, Western mathematics had made great strides ahead. Therefore, there was a period of confluence of the development of Chinese and Western mathematics in the history of the development of Chinese mathematics. This period was approximately between 1840 and 1911 AD. The beginning of modern mathematics was mainly concentrated in the period from 1911 to 1949 AD. Although China is currently lagging behind in the world of mathematics, it is still unclear who will win in the future.

Contents

1 Origin

2 Development and prosperity period

3 Heyday period

4 Slow development period< /p>

5 The period of confluence of China and the West

1 Origin

2 Period of development and prosperity

3 Heyday

4 Slow development Period

5 The period of confluence of China and the West

6 The beginning of modern mathematics

7 Development after the founding of the People's Republic of China

8 Ancient achievements

10 Reference materials

Looking through any history of the development of Chinese mathematics, it is not difficult to find that every step forward for the Chinese ancestors was accompanied by the struggle. Sweat. Chinese mathematics originated from ancient times to the end of the Western Han Dynasty. The heyday of Chinese mathematics was from the middle Sui Dynasty to the late Yuan Dynasty. Next, from the late Yuan Dynasty to the mid-Qing Dynasty, the development of Chinese mathematics was slow. While the development of Chinese mathematics was slow, Western mathematics had made great strides ahead. Therefore, there was a period of confluence of the development of Chinese and Western mathematics in the history of the development of Chinese mathematics. This period was approximately between 1840 and 1911 AD. The beginning of modern mathematics was mainly concentrated in the period from 1911 to 1949 AD. Although China is currently lagging behind in the world of mathematics, it is still unclear who will win in the future.

A brief history of the development of Chinese mathematics - origin

The ancient Greek scholar Pythagoras (about 580 BC ~ 500 BC) had a famous saying: "Everything is number". Indeed, a world without numbers is unimaginable.

Today, people would disdain such trivial matters as counting from 1 to 10, but tens of thousands of years ago, this matter was something that people took great pains to do. 7,000 years ago, they couldn't even count numbers above 2. If you were to ask them how many beasts they caught, they would answer: "Many." If someone could count to 10 at that time, he would have been considered an outstanding genius. Later, people gradually associated numbers with hands. Take one thing in each hand, that's 2. When I counted to 3, I was stumped again, so I put the third item at my feet, and the "problem" was solved.

In this way, through gradual exploration, the ancestors of the Chinese nation emerged from the chaotic world.

First it was knotted ropes for counting, and then it developed into "book deeds". Five or six thousand years ago, numbers from 1 to 30 could be written. By the Spring and Autumn Period more than 2,000 years ago, ancestors could not only write 3,000 The above mathematics also has the awareness of addition and multiplication. There is a passage in Jin Wenzhou's "※Ding": "The East Palace said: To pay back ten grains of grain, and leave ten grains of grain as yarn grains, and if the repayment is not enough next year, then the grains will be paid." This passage contains a compound interest. question. What it means is that if you borrow 10 bundles of millet and return it later, the 10 bundles you borrowed will become 20 bundles. If you pay it back every other year, it will increase from the 10 bundles you borrowed to 40 bundles. Expressed in mathematical formulas:

110=20

20×2=40

In addition to greater understanding of counting and algorithm In addition to progress, the ancestors of the Chinese nation also began to record some numerical knowledge in books. Bagua appeared in "The Book of Changes", one of the classical books revised by Confucius (551 BC - 479 BC) during the Spring and Autumn Period.

This magical gossip is still the object of research and study by people in China and foreign countries. It plays an important role in mathematics, astronomy, physics and many other aspects that cannot be underestimated.

By the Warring States Period, mathematical knowledge had far exceeded the level of counting from 1 to 3,000. At this stage, they began to cultivate and sow seeds in the fields of arithmetic, geometry, and even modern applied mathematics. In the field of arithmetic, the four arithmetic operations were established during this period. Multiplication formulas have appeared sporadically in works such as Guanzi, Xunzi, and Zhou Yishu. Fractional calculations have also begun to be used in planting land, distributing food, etc. aspect. In the field of geometry, the Pythagorean theorem appeared. In the field of algebra, the concept of negative numbers appeared. What is most surprising to future generations is that during this period, the emergence of "game theory" emerged. Game theory is a problem in the field of modern applied mathematics. It is a branch of operations research, which mainly uses mathematical methods to study the two parties with conflicting interests. In competitive activities, whether there is an optimal strategy for defeating the other party, and how to find out these strategies. This branch of mathematics was only formed as a subject during or after the Second World War in this century. However, as early as more than 2,000 years ago, the famous military strategist Sun Bin (360 BC ~ 330 BC) during the Warring States Period proposed We have passed the "horse fighting" problem, and the content of this problem reflects the mathematical idea of ??striving for the overall optimal in game theory. The question of "horse fighting" is that King Wei of Qi is going to race a horse with General Tian Ji. Each of them has an upper, middle and lower horse. Tian Ji's three horses are slightly inferior to those of King Wei of Qi. First of all, if we use the corresponding competition method of the same level, Tian Ji will definitely lose. Tian Ji is so anxious that he doesn't know what to do. At this time, Sun Bin gave advice from the side, and Tian Ji used Sun Bin's method to defeat King Qi Wei 2:1.

What method did Sun Bin use? Please look at the schematic diagram below:

Tian Ji Qi Weiwang

High-grade horse and waiting horse

Medium-grade horse and medium-grade horse

Inferior 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 characters on bones. They used brushes to write down the things they needed to remember on pieces of bamboo or wood. Such written bamboo or wood pieces were called "jians" or "slips". This kind of slips or slips has been handed down the most from the Western Han Dynasty.

From those Han bamboo slips, we found that in the Qin and Han dynasties, there was a significant increase in multiplication and division examples in arithmetic, and there were also multi-step multiplication and division methods and the nine-nine multiplication formula that tended to be complete. In terms of geometry, the knowledge of calculating the area and volume of a rectangle is also acquired.

The most noteworthy thing about this period is the arithmetic and decimal system. With them, ancestors no longer have to worry about not having suitable calculation methods. In ancient my country, this calculation system was used until the Tang Dynasty.

The exact origin time of calculation is still unclear. It is only known that around the Qin and Han Dynasties, calculation had already formed a system.

To understand what is going on, you must first know what betting is. Chips are small sticks with a diameter of 1 minute and a length of 6 minutes. The materials of these small sticks include bamboo, wood, bone, iron, copper, etc. Their function is similar to that of abacus beads. At present, many batches of physical chips have been unearthed. In 1971, it was found in a rectangular tomb of a man and a woman unearthed in Qianyang County, Shaanxi Province. The male corpse had a silk bag tied to his crotch, and the bag contained a handful of bone chips. A batch of early bone chips unearthed in the southern suburbs of Shijiazhuang in 1980 were also hung on the waists of the deceased. It can be seen from the quotation that arithmetic was already common among intellectuals in the Han Dynasty. Regarding how to use chips, according to records, this is the following: When calculating, place the chips on a special case, or place them casually. For numbers below 5, put as many counters as there are numbers. For the four numbers 6 to 9, you need to use one counter placed horizontally or vertically as 5. The remaining numbers are still placed as many as they are. Root calculation.

For the convenience of calculation, the ancients prescribed the vertical and horizontal representation. Vertical notation is used for numbers in units, hundreds, and thousands; horizontal notation is used for numbers in tens and thousands. When zero is encountered, one digit is left blank.

The decimal system is the decimal system commonly used in our daily life today.

That is to say, for positive integers or positive decimals, ten is used as the basis, and every tenth is added to one, every hundred is added to two, every thousand is added to three, and so on. The emergence of the decimal system created good conditions for the development of the four arithmetic operations.

A brief history of the development of Chinese mathematics - a period of development and prosperity

The period of development and prosperity of Chinese mathematics was from the late Western Han Dynasty to the middle of the Sui Dynasty. This was the first peak period of Chinese mathematical theory. The symbol of this peak is the birth of the mathematical treatise "Nine Chapters on Arithmetic". There is "Nine Chapters on Arithmetic" from at least 1800. Who is its author? Who made it up? So far there is no way to verify it. Historians only know that it is the crystallization of mathematical knowledge from the Qin and Han Dynasties in China for one or two hundred years, and it began to be spread and used in the 1st century AD.

This book is divided into nine chapters:

①Fang Tian (Four Fraction Algorithms and Plane Area Method).

②Corn (calculation method of grain transactions).

③ Decline score (calculation method of distribution ratio).

④ Shao Guang (square root and square root method)

⑤ Shang Gong (method of finding the volume of three-dimensional shapes)

⑥ Uniform transportation (managing grain transportation evenly burden calculation method).

⑦Insufficient profit (the solution to profit and loss problems also involves other types of problems that can be solved with this solution).

⑧Equations (solution of linear equations and positive and negative techniques).

⑨Pythagorean (application of the Pythagorean theorem and solutions to simple measurement problems).

The book contains 246 mathematical application problems. Each question is divided into three parts: questions, answers, and techniques (solutions. Some problems have one technique, and some problems have multiple techniques), and each chapter The contents are inextricably linked with social production.

The birth of this book not only showed that a complete mathematical system in ancient China had been formed, but also that it was difficult to find another comparable mathematical monograph in the world at that time.

During the peak period of the development of this mathematical theory, in addition to the masterpiece "Nine Chapters of Arithmetic", Liu Hui's "Nine Chapters of Arithmetic" and his "Island Arithmetic Classic" also appeared , "Sun Zi Suan Jing" (author unknown), "Xia Houyang Suan Jing", "Zhang Qiu Jian Suan Jing" and Zu Chongzhi's "Zhu Shu" and other mathematical monographs.

During this period, the outstanding figures who created new achievements in mathematics were: Zhao Shuang from the Three Kingdoms, Liu Hui from the Wei and Jin Dynasties, and Zu Chongzhi from the Southern Dynasties.

A brief history of the development of Chinese mathematics - the heyday

The heyday of Chinese mathematics was from the middle Sui Dynasty to the late Yuan Dynasty.

The scientific development of any country is inseparable from a peaceful and enlightened social environment and a strong economic foundation. From the middle of the Sui Dynasty to the end of the Yuan Dynasty, as the rulers summed up the lessons of the overthrow of previous dynasties and adopted a series of enlightened policies, the economy developed rapidly and science and technology also improved greatly. Mathematics, which is part of science and technology, also At this time it entered its heyday.

During this period, the most important features were the formalization of mathematics education and the emergence of mathematical talents in large numbers.

Before the Sui Dynasty, school education did not attach great importance to mathematics, so there was no such thing as a mathematics major. By the Sui Dynasty, this situation was broken, and arithmetic majors began to be established in schools equivalent to universities. In the Tang Dynasty, the Imperial Academy, the highest institution of higher education, also established a mathematics school, including doctors and teaching assistants, specializing in cultivating mathematical talents. At this time, the emphasis on mathematics education was also reflected in the issue of official selection. According to the ancient book "History of Tang Que", there is such a story: There was a high official in the Tang Dynasty named Yang Sun. He asked his staff to recommend an outstanding clerk for promotion. The people under his command have been screened and selected, and when there are only two left, I am not sure which one is better to get rid of. Because the conditions of these two clerks are so similar in all aspects: the same position, the same "service length", and similar comments...who should I choose? I had no choice but to hand over the conflict. After Yang Sun learned the news, he put a lot of thought into it, considered it again and again, and finally decided to come up with a math problem to test them. He said to the two candidates: "As clerks, your career determines that you should have the ability to calculate quickly. I will ask a question, and whoever answers correctly first will be promoted." Later, the person who answered correctly first was promoted as a matter of course, and The other man also returned to his original position convinced. It can be seen from this that the Tang Dynasty attached great importance to mathematics.

With a mathematics major. Good teaching materials are indispensable. During this period, the Tang Dynasty mathematician Li Chunfeng (? ~ 714 AD) and others, under the orders of the government, after studying and selecting, prescribed special textbooks for the Imperial Academy of Statistics.

This set of textbooks is called "Ten Books of Suanjing". There are ten books in the set: "Zhou Bi Suan Jing", "Nine Chapters Suan Jing", "Sun Tzu Suan Jing", "Wucao Suan Jing", "Xiahou Yang Suan Jing" Sutra", "Zhangqiu Jian Suan Jing", "Haidao Suan Sutra", "Five Classics Sushu", "Zhu Shu" and "Ji Gu Su Su Jing".

For this set of professional textbooks, the Imperial College also stipulated the number of years of study and established a monthly exam system. Mathematics education began to gradually improve from this time.

Under the increasingly perfect mathematics education system, a generation of mathematics leaders who will go down in history have emerged. They are: Wang Xiaotong, Liu Zhuo, Yi Xing, Shen Kuo, Li Ye, Jia Xian, Yang Hui, Qin Jiushao, Guo Shoujing, and Zhu Shijie. ...

Science has always been the common 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 students and booksellers to China. After a period of study, I introduced knowledge about acres, rent, and grain exchange in Algorithm; I absorbed the curriculum and examination system of the Imperial College in running a school. From this point of view, at this stage, China is already at the forefront of the development of mathematics in the world.

A brief history of the development of Chinese mathematics - the slow development period

From the late Yuan Dynasty to the mid-Qing Dynasty, the development of Chinese mathematics was slow. Compared with the prosperous age of mathematics mentioned above, this stage Almost eclipsed.

From the end of the Song Dynasty to the establishment of a centralized system in the Yuan Dynasty, wars raged in China for many years, science and technology were not taken seriously, and a large amount of precious mathematical heritage was lost.

After the establishment of the Ming Dynasty, production developed for a brief period, but immediately declined due to the corruption of feudal rule. It was not until the early years of the Qing Dynasty that things eased.

In such an environment of political corruption, economic backwardness, and recurring peasant uprisings, it is reasonable for mathematics to fall into a trough.

However, the trend of world development has always waited for no one. Taking advantage of the decline of Chinese mathematics, Western mathematics quietly caught up and penetrated into China.

When Western capitalism began to sprout, Catholic missionaries, pirates, and businessmen poured into China in search of development. In addition to taking away raw materials, markets, and cheap labor from China, they also brought some cultural knowledge.

Among the missionaries who came to China from the 16th to the 18th century, the Italian Matteo Ricci (1552~1610 AD) had the greatest influence. From 1583 to 1599, when he was active in Zhaoqing, Shaozhou, Nanchang, Nanjing and other places in China, he met many famous Chinese scholars, such as Li Zhi, Xu Guangqi, Li Zhizao and others. These people are in a state of mind that is dissatisfied with empty talk about Neo-Confucianism and longs for a rich country and a strong military. For this reason, they eagerly hope for the latest scientific and technological achievements in the world. The arrival of Matteo Ricci undoubtedly played a role in hitting it off.

Matteo Ricci, Xu Guangqi and Li Zhizao jointly translated two mathematical works respectively: "Elements of Geometry" and "Tongwen Suanzhi".

The text of "Elements of Geometry" is simple and has few omissions. Although there were no ready-made Chinese words to compare the Latin in the original work at that time, Xu Guangqi still overcame the difficulties and created many appropriate translations, making the whole book reach the level of honesty, expressiveness and elegance.

Since Matteo Ricci and Chinese scholars jointly translated the monograph, the spread of Western learning to the East has gained momentum.

So what was China’s own mathematical “specialty” during this period? It's abacus.

During the Sui and Tang Dynasties, people had already begun to make plans for improvement. They try to simplify calculation methods and compile formulas... However, in the rapidly developing field of mathematics, calculation methods will inevitably be replaced by other algorithms.

At the end of the Yuan Dynasty, the small and flexible abacus appeared. People were extremely excited to see this new tool that was simple to calculate and easy to carry. Some people even incorporated it into proverbs, poems, and lyrics.

The emergence of the abacus soon led to abacus formulas and abacus algorithm books. In the 16th and 17th centuries, among a large number of books on abacus in China, the most famous one was Cheng Dawei's "Zhizhi Algorithm" Tongzong". After the popularity of abacus, abacus calculations automatically disappeared.

Not long after the Chinese invented the abacus, in 1642, the 19-year-old French mathematician Pascal (AD 1623~1662) launched the world's earliest computer. At present, although the world has entered the computer age, abacus still has its place. Someone tried it, and it was even faster than a small calculator in addition and subtraction operations.

A brief history of the development of Chinese mathematics - the period of confluence of Chinese and Western mathematics

While the development of Chinese mathematics was slow, Western mathematics had made great strides ahead, so a Chinese-Western mathematics system emerged in the history of the development of Chinese mathematics. The confluence period of development, this period is approximately between 1840 and 1911 AD.

As mentioned earlier, around the 16th century, Western missionaries brought some new mathematical knowledge. Although some foreigners have their own personal goals, in any case, new knowledge can be introduced, which is always good for the progress of Chinese mathematics. However, when Emperor Yongzheng of the Qing Dynasty came to the throne in 1723, some people suggested that a large number of missionaries in China would be detrimental to their rule. When the emperor thought about it, it was the same. So he immediately ordered that except for a few foreigners who compiled the new calendar in China, no other missionaries would be allowed to stay.

The consequence of this order was that in the next 100 years or so, it would be difficult to "import" Western mathematical knowledge; Chinese mathematicians had to shift their focus from learning new Western knowledge to returning to Study your old results.

The return of ancient mathematics did not last long. The Opium War failed, and the situation of seclusion was broken. Imperialist powers came in to carve up China one after another, and China became a semi-colonial and semi-feudal society for a while.

Beginning in the 1860s, Zeng Guofan, Li Hongzhang and others launched the "Westernization Movement" in order to maintain the corrupt Qing government. At this time, a group of intellectuals represented by Li Shanlan, Xu Shou, and Hua Hengfang, as mathematicians, scientists, and engineers, participated in activities such as introducing Western learning, setting up factories, and schools. Through their unremitting efforts, they laid the foundation for modern science and technology, and modern times. The foundation of the development of mathematics in China.

When the "Westernization Movement" ended in military failure in 1894, factories, railways, and schools were preserved, and scientific and technological knowledge also spread to a certain extent.

This period was characterized by the fusion of China and the West. The so-called merging of China and the West does not mean total Westernization. Mathematicians studied traditional mathematics while absorbing new methods. For a time, there was a good momentum of talented people and numerous writings.

At this time, Chinese mathematicians had independently obtained some calculus results in power series, apices, etc., and also achieved outstanding results in indefinite analysis and combinatorial analysis. However, even so, China still has not reached a leading position among its peers in the world.

A brief history of the development of Chinese mathematics - the beginning of modern mathematics

The beginning of modern mathematics was mainly concentrated in the period from 1911 to 1949 AD.

At the end of the 19th century and the beginning of the 20th century, great changes took place in the Chinese mathematics community. A large number of students were sent abroad, new schools were founded, academic groups were organized, and specialized journals were established. China has since entered the stage of modern mathematics research. .

Since 1847, the first batch of students represented by Rong Hong went abroad, forming a climax of studying abroad. At that time, thousands of people studied abroad every year. After they returned to China after completing their studies, they formed a modern scientific team in China that cannot be ignored.

Among those who studied abroad in the early days, not many studied mathematics. Among them, those who made outstanding achievements include: Su Buqing, Chen Jiangong, Chen Shengshen, Zhou Weiliang, Xu Bao, Hua Luogeng, Lin Jiaqiao and others.

After the return of such a group of overseas students, there have been new changes in scientific research, education, academic exchanges and other aspects.

In terms of scientific research, *** published 652 papers before 1949. Although the number was small and the scope was limited to pure mathematics, its level was not lower than that of its peers in the world. You must know that even this meager result was achieved after overcoming unimaginable difficulties in politics, economy and many other aspects.

In terms of education, a formal curriculum has been established, with more hours of mathematics than liberal arts, and textbooks have also been updated. By 1932, various universities in China had a team of about 155 mathematics teachers who could teach more than 5 to 10 professional courses.

In terms of academic exchanges, the "Chinese Mathematical Society" was established in July 1935, and the "Journal of the Chinese Mathematical Society" and "Journal of Mathematics" were founded. The 9th and 10th International Mathematics Conferences held from 1932 to 1936 were attended by people from China. At this time, mathematicians from various countries who were invited to give lectures in China also came in droves, bringing a modern flavor to the previously insular field of mathematics.

A brief history of the development of mathematics in China - Development after the founding of the People's Republic of China

In 1949, at the beginning of the founding of New China, although the country was in the predicament of lack of funds and a lot of waste to be developed, the government Great attention was given to scientific undertakings. The Chinese Academy of Sciences was established in November 1949, and the Institute of Mathematics was officially established in July 1952. Then, the Chinese Mathematical Society and its founded journals restored and created other mathematics special journals, and some scientists' monographs were also published. All of this contributed to the establishment of the Chinese Academy of Sciences. Mathematical research paves the way.

In the 18 years after liberation, the number of published papers accounted for more than three times the total number before liberation. Many of these papers not only filled the gaps in China's past, but some also reached the world's advanced level.

Just as mathematicians were catching up and trying to restore China's mathematics to its advanced status in the world, a ruthless storm swept through China. During the ten years of the Cultural Revolution, society was out of control, people were in chaos, and science was in decline. In the field of mathematics, except for Chen Jingrun, Hua Luogeng, Zhang Guanghou and other mathematicians who struggled to bloom a few flowers, almost everything was withered and completely blank.

After the political disaster of 10 years has passed, people look up and see that mathematics research in other countries has already reached peaks, and it will take a lot of effort 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 eloquent article "The Spring of Science", the mathematics field ushered in the spring of recovery of all things. In 1977, a new mathematics development plan was formulated in Beijing, the work of the Mathematics Society was resumed, academic journals were resumed and founded, mathematics education was strengthened, and basic theoretical research was strengthened...

Although China is currently in the world mathematics arena Already in a backward position, however, Lu Yao knows horse power, and who will win from now on will still be a "x".

A brief history of the development of Chinese mathematics - ancient achievements

In the history of the development of ancient Chinese mathematics, the gold medals won by our ancestors are enough to open an exhibition hall. Here is only a "list", Give readers an intuitive impression.

(1) Decimal notation and the adoption of zero. It originated from the Spring and Autumn Period, more than 1,000 years earlier than the second inventor, India.

(2) The origin of binary thought. The Bagua method originated from the "Book of Changes", more than 2,000 years before its second inventor, the German mathematician Leibniz (1646~1716 AD).

(3) The origin of geometric thought. The "Mo Jing" originated from Mo Zhai during the Warring States Period, more than 100 years before the second inventor Euclid (330 BC ~ 275 BC).

(4) Pythagorean theorem (Shanggao theorem). The inventor, Shang Gao (from the Western Zhou Dynasty), was more than 550 years earlier than the second inventor, Pythagoras (580 BC ~ 500 BC).

(5) Magic square. The earliest records of magic methods in my country are the "Analects of Confucius" and "Shu Jing" of the Spring and Autumn Period. Overseas, the appearance of magic methods occurred in the 2nd century AD, and our country was more than 600 years earlier than abroad.

(6) Fractional operation rules and decimals. China's complete fraction calculation rules appear in "Nine Chapters of Arithmetic", and its biography appeared as late as the 1st century AD. The same law appeared in India in the 7th century AD and is considered the "originator" of this method. Our country predates India by more than 500 years.

China used the least common multiple 1,200 years earlier than the West. The use of decimals predates the West by more than 1,100 years.

(7) Discovery of negative numbers. This discovery was first seen in "Nine Chapters of Arithmetic", which was more than 600 years earlier than India and more than 1,600 years earlier than the West.

(8) Gain is not a technique. Also known as the double false position method. It was first seen in Chapter 7 of "Nine Chapters of Arithmetic". In the world, the same method did not appear in Europe until the 13th century, more than 1,200 years later than China.

(9) Equation technique. It first appeared in "Nine Chapters of Arithmetic", in which the method of solving simultaneous linear equations was more than 600 years earlier than India and more than 1,500 years earlier than Europe. In terms of using the matrix arrangement method to solve linear equations, our country is more than 1,800 years ahead of other countries in the world.

(10) The most accurate "ancestral rate" of pi. More than 1,000 years earlier than other countries in the world.

(11) Equal product principle. Also known as the "ancestral principle". It has held the world record for more than 1,100 years.

(12) Quadratic interpolation method.

The astronomer Liu Zhuo of the Sui Dynasty first invented it, more than 1,000 years before the "world runner-up" Newton (1642~1727 AD).

(13) Multiplication method. Also known as "Horner's method" in modern mathematics. The Chinese mathematician Jia Xian of the Song Dynasty first invented it in the 11th century, about 800 years earlier than the time proposed by the British mathematician Horner (1786~1837 AD).

(14) Yang Hui Triangle. It is actually a binomial expansion coefficient table. It was originally created by Jia Xian and was found in his book "The Yellow Emperor's Nine-Chapter Algorithm". Later, the book was lost. Yang Hui of the Southern Song Dynasty compiled this table in his "Detailed Explanation of the Nine-Chapter Algorithm", hence the name "Yang Hui's Triangle" .

In addition to China’s Jia Xian and Yang Hui, the second inventor in the world is the French mathematician Pascal (1623~1662 AD). His invention was in 1653, nearly later than Jia Xian. 600 years.

(15) Chinese Remainder Theorem. In fact, it is a method of solving simultaneous linear congruences. This method was first seen in "Sun Tzu's Sutra". In 1801, the German mathematician Gauss (1777~1855 AD) proposed this solution in "Arithmetic Inquiry". Westerners thought this method was the first in the world and called it "Gauss' Theorem". , but later it was discovered that it was more than 1,500 years later than China, so it was renamed "Chinese Remainder Theorem".

(16) Digital higher-order equation method, also known as "Tian Yuan Shu". During the Jin and Yuan Dynasties, Chinese mathematician Li Ye invented the equation method for setting unknown numbers and cleverly expressed it in calculations. This method is more than 300 years earlier than other countries in the world, laying a good foundation for the solution of multivariate higher-order equations that will appear in the future.

(17) Recruitment technique. That is, the high-order arithmetic series summation method. Since the Northern Song Dynasty, many mathematicians in China have studied this problem. In the Yuan Dynasty, Zhu Shijie first invented the recruitment technique, which solved this problem. In the world, Newton obtained the same formula nearly 400 years later than Zhu Shijie.