Introduction to the origin
Ancient Greek scholar Pythagoras (approximately 580 BC to approximately 500 BC) famously said: "Everything is numbered." Indeed, an uncountable world is unimaginable.
Today, people are dismissive of such trivial things as counting from 1 to 10. However, tens of thousands of years ago, this matter could make people take great pains. Before 7000, they couldn't even count the number above 2. If they were to ask how many four beasts they caught, they would answer: "Many." If someone were to count to 10 at that time, they would be considered an outstanding genius. Later, people slowly associate numbers with their hands. Take one thing in each hand, which is 2. When I counted to 3, I was stumped again, so I put the third thing by my feet, and the "difficulty" was solved.
In this way, in the gradual exploration, the ancestors of the Chinese nation came out of the chaotic world.
Firstly, the knots were counted, and then it developed into the "book deed". Five or six thousand years ago, numbers from 1 to 30 were written. By the Spring and Autumn Period more than 2,000 years ago, the ancestors could not only write 3000 The above mathematics also has the awareness of addition and multiplication. In the "Ding" of Bronze Inscription Zhou, there is a passage: "Donggong said: pay the ten zi for hehe, and pay the ten zi for the remnant, and pay the zi for the next year." This passage contains a question of profit. What is said is that if you borrow 10 bundles of millet and return it later, it will change from 10 bundles to 20 bundles. If you pay it back the next year, you will have to go from 10 bundles to 40 bundles when you borrowed it. Expressed by mathematical formula:
10+10=20
20×2=40
In addition to the larger number and algorithm In addition to progress, the ancestors of the Chinese nation began to record some digital knowledge in books. Gossip appeared in one of the classical books revised by Confucius in the Spring and Autumn Period (551-479 BC). This magical gossip is still the object of people's hard work in China and foreign countries, and it plays a role in mathematics, astronomy, physics and many other aspects that cannot be underestimated.
By the time of the Warring States Period, the knowledge of mathematics has far exceeded the level of 1~3000. At this stage, they began to cultivate seeds in the fields of arithmetic, geometry, and even modern applied mathematics. In the field of arithmetic, the four arithmetic operations have been established during this period. The tactics of multiplication have appeared scattered in books such as,, and etc., and fraction calculation has also begun to be applied to planting land and distributing food. In the field of geometry, the Pythagorean theorem appeared. In the field of algebra, the germ of the concept of negative numbers appeared. The most surprising thing for posterity is that during this period, the budding of "game theory" appeared, and 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 who have conflicts of interest. In competitive activities, whether there is an optimal strategy for defeating the other party, and how to find these strategies and other issues. This branch of mathematics was formed as a discipline during or after the Second World War of this century, but as early as 2000 years ago, the famous military strategist Sun Bin (360-330 BC) proposed it during the Warring States Period. Going through the "horse fighting" problem, and the content of this problem exactly reflects the mathematical thinking of striving for the overall best in game theory. The "Equestrian Fighting" question is that King Qi Wei wants to race horses with General Tian Ji. Each of them has one upper, middle, and lower horse. Tian Ji's three horses are slightly inferior to those of King Qi Wei. For one thing, if you use the corresponding contest of the same level, Tian Ji will undoubtedly lose. Tian Ji is so anxious that he doesn't know what to do. At this time, Sun Bin called from the side, and Tian Ji used Sun Bin's method to win King Qi Wei 2:1.
What method did Sun Bin use? Please see the diagram below:
Tian Ji and Qi Wei Wang
Wait for the inferior horse immediately
The superior horse, the medium horse
The medium horse Inferior horse
Seeing this, don’t you think our ancestors were really smart?
When history advanced to the Qin and Han dynasties, the ancestors no longer engraved on the bones. They write all the things they need to remember with a brush on bamboo or wood chips. This kind of bamboo or wood chips with written characters is called "Jian" or "Jian". This kind of bamboo slips or slips have been handed down most in the Western Han Dynasty.
From those Han bamboo slips, we found that in the Qin and Han dynasties, there was a significant increase in arithmetic examples of multiplication and division, as well as the emergence of multi-step multiplication and division and the more complete nine-nine multiplication formula. In terms of geometry, knowledge of the calculation of rectangular area and volume is also available.
The most worth mentioning of this period is the counting and decimal system. With them, ancestors no longer worry about not having suitable calculation methods. In ancient my country, this computing system was used until the Tang Dynasty.
The exact time of origin of the counting chips is still unclear. It is only known that around the Qin and Han dynasties, counting chips have formed a system.
To understand what is going on, you must first know what is called. Chips are small sticks with a diameter of 1 minute and a length of 6 minutes. These small sticks are made of bamboo, wood, bone, iron, and copper. Their function is similar to that of abacus beads. At present, many batches of raised objects have been unearthed. In 1971, it was discovered in a rectangular co-educational tomb unearthed in Qianyang County, Shaanxi Province. The male corpse was tied with a silk sac on the crotch and contained a bone chip. A batch of early bone chips unearthed in the southern suburbs of Shijiazhuang in 1980 were also hung on the waist of the deceased. It can be seen from the citation that calculation chips have been commonly used among intellectuals in the Han Dynasty. Regarding how to use the chips, according to the record, it is like this: When calculating, place the chips on a special case, or place them casually. For numbers below 5, just put a few chips, and for the 4 numbers 6-9, you need to use a horizontal or vertical counting chip as 5, and the remaining numbers still have a few chips. Calculate the bargain.
For the convenience of calculation, the ancients stipulated the vertical and horizontal notation. Vertical notation is used for digits, one hundred, and ten thousand digits; horizontal notation is used for tens and thousands digits. When it encounters zero, one digit is left blank.
The decimal system is exactly the method of every decimal that we commonly use in our daily lives today. That is to say, for positive integers or positive decimals, it is based on ten, every tenth is one, every hundred is two, every thousand is three, and so on. The emergence of the decimal system has created good conditions for the development of the four arithmetic operations.
Prosperous period of development
The prosperous period of Chinese mathematics development was approximately from the late Western Han Dynasty to the middle of the Sui Dynasty. This is the first peak of Chinese mathematical theory. The sign of this peak is the birth of mathematics monographs. At least there is "Nine Chapters of Arithmetic" from 1800. Who is the author? Who compiled it? So far there is no research. Historians only know that it is the crystallization of mathematics knowledge from the Qin and Han Dynasties in China for one or two hundred years, and it began to be used in the first century AD.
This book is divided into nine chapters:
①Fang Tian (Four Algorithms of Fractions and Method of Finding Area of Plane Shape).
②Corn (calculation method of grain transaction).
③Attenuation (calculation method of distribution ratio).
④Shaoguang (square root and open method)
⑤Shang Gong (three-dimensional shape finding volume method)
⑥Equal loss (management of uniform grain transportation) Calculation method of burden).
⑦Insufficient profit (the solution to profit and loss problems, and other types of problems that can be dealt with by this solution).
⑧Equations (a system of linear equations solution and plus and minus arithmetic).
⑨Pythagorean (application of the Pythagorean theorem and simple solution to measurement problems).
The book contains 246 mathematical application questions. Each question is divided into three parts: question, answer, and technique (solution. Some have one problem, one technique, and some have multiple techniques), and each chapter The content of this is inextricably linked to social production.
The birth of this book not only shows that a complete mathematics system in ancient China has been formed, but also in the world, it was difficult to find another mathematics monograph that was instinctively comparable at that time.
At the peak of the development of mathematical theory, in addition to "Nine Chapters Arithmetic", Liu Hui's "Nine Chapters Arithmetic" and his writing, (author unknown) appeared. ,, and Zu Chongzhi's and other mathematics monographs.
In 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.
The heyday of Chinese mathematics
The heyday of Chinese mathematics is from the middle of Sui Dynasty to the late Yuan Dynasty.
The development of science in any country is inseparable from Qingping’s enlightened social environment and strong economic foundation. From the middle of the Sui Dynasty to the end of the Yuan Dynasty, as the rulers summarized the lessons of the overthrow of the dynasties and adopted a series of enlightened policies, the economy developed rapidly, and science and technology were greatly improved. At this time it entered its heyday.
During this period, the regularization of mathematics education and the emergence of mathematics talents were the most important features.
Before the Sui Dynasty, school education did not pay much attention to mathematics, so there was no such thing as a mathematics major. In the Sui Dynasty, this situation was broken, and a school equivalent to a university began to set up mathematics majors. In the Tang Dynasty, Guozijian, the highest institution of higher learning, also added a mathematics hall, where doctors and teaching assistants were all available to train mathematics talents. At this time, the importance of mathematics education was also reflected in the issue of selecting officials. According to ancient books, there is a story: There was a high official in the Tang Dynasty named Yang Xi. He asked his people to recommend a good clerk for promotion. After a thousand selections of people under his team, when there are two people left at the end, it is uncertain which one should be removed. Because these two clerks have the same conditions in all aspects: the same position, the same "senior years", and similar comments...Who should I choose? There is no other way but to turn in the contradiction. After Yang Xiao learned the news, he took a lot of thoughts and thoughts, and finally decided to put out a math question to test them. He said to the two candidates: "As a clerk, you should have the ability to calculate quickly as a clerk. If I ask a question, whoever answers the correct answer first will be promoted." Later, the person who answered the correct answer was naturally promoted. The other person also returned to his original position convincingly. This shows that the Tang Dynasty paid much attention to mathematics.
With a major in mathematics. Good textbooks are indispensable. During this period, Tang Dynasty mathematician Li Chunfeng (?~AD 714) and others were ordered by the government to study and screen them, and stipulated a special textbook for the Guozijian School. The name of this set of textbooks is a full set of ten: "Nine Chapters of Mathematics>,,,,,,, and.
For this set of professional teaching materials, the Imperial College also stipulated the length 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 masters, who are famous in history, have emerged: Wang Xiaotong, Liu Zhuo, Yi Yi, Shen Kuo, Li Ye, Jia Xian, Yang Hui, Qin Jiuzhao, Guo Shoujing, 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, knowledge about fields, rent payment, grain exchange, etc. was introduced in the algorithm; the curriculum and examination system of the Imperial College were absorbed in running the school. From this point of view, at this stage, China is already at the forefront of world mathematics development.
Slow development period
Next, from the late Yuan Dynasty to the middle Qing Dynasty, the development of Chinese mathematics was slow. Compared with the mathematics boom mentioned above, this stage was almost eclipsed.
From the end of the Song Dynasty to the establishment of a centralized power system in the Yuan Dynasty, there were wars on the land of China for years, science and technology were ignored, and a lot of valuable mathematical heritage was lost.
After the establishment of the Ming Dynasty, production developed in a short period of time, but immediately declined due to the corruption of the feudal rule. It was not until the early years of the Qing Dynasty that it eased.
In such an environment of political corruption, economic backwardness, and peasant uprisings one after another, it is reasonable for mathematics to fall into a trough.
However, the trend of world development has always been waiting for no one. Taking advantage of the decline of Chinese mathematics, Western mathematics has quietly caught up and infiltrated China in turn.
When Western capitalism began to sprout, in order to seek development, Catholic missionaries, pirates, and businessmen flooded into China. 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 centuries, the Italian Matteo Ricci (1552-AD 1610) had the most 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 dissatisfaction with philosophical philosophies and longing for a prosperous country and a strong military. For this reason, they eagerly hope for the latest scientific and technological achievements in the world. And the arrival of Matteo Ricci is undoubtedly a hit.
Matthew Ricci, Xu Guangqi and Li Zhizao respectively co-translated two mathematics works:.
The text of "Geometric Yuanyuan" is popular, with few omissions. Although there was no ready-made Chinese vocabulary for the Latin in the original work at that time, Xu Guangqi still overcame the difficulties and created many appropriate translations to make the book reach the level of faithfulness, expressiveness and elegance.
Starting from the co-translation of monographs by Matteo Ricci and Chinese scholars, the momentum of western learning has been increasing.
So what is China's own mathematics "special product" in this period? It is abacus.
During the Sui and Tang Dynasties, people have already begun to think about improving their calculations. They try to simplify the calculation method and compose formulas... However, in the rapidly developing field of mathematics, the calculation algorithm will inevitably be replaced by other algorithms.
At the end of the Yuan Dynasty, a small and handy abacus appeared. People look at this new tool that is simple to calculate and easy to carry. Some people even edit it into colloquial sayings, poems, and lyrics.
The appearance of the abacus soon led to books on abacus formulas and abacus algorithms. In the 16th and 17th centuries, among a large number of books on abacus in China, the most famous is Cheng Dawei’s "Direct Point Algorithm" Tongzong. After the popularization of abacus, the calculation automatically disappeared.
Shortly after the Chinese invented abacus, in 1642, 19-year-old French mathematician Pascal (AD 1623~1662) launched the world's first computer. At present, although the world has entered the computer age, abacus still has its place. Someone has tried, in addition and subtraction operations, its speed even exceeds that of small calculators.
The confluence period of Chinese and Western mathematics
When the development of Chinese mathematics was slow, Western mathematics had already made great strides ahead, so there was a confluence of Chinese and Western mathematics development in the history of Chinese mathematics. One period was approximately between 1840 and 1911 AD.
As mentioned earlier, around the 16th century, Western missionaries brought some new mathematical knowledge. Although some foreigners have personal goals, in any case, new knowledge can be passed in, which is always good for the progress of mathematics in China. However, when Emperor Yongzheng of the Qing Dynasty ascended the throne in 1723, someone suggested that a large number of missionaries were in China, which would be detrimental to their rule. The emperor thought, too. So he immediately ordered that, except for a few foreigners who compiled the new calendar in China, no other missionaries would stay.
The consequence of this order is that in the next 100 years or so, Western mathematics knowledge will also be difficult to "import"; Chinese mathematicians had no choice but to shift their eyes from learning new Western knowledge back to Study my old results.
The situation of ancient mathematics did not last long. The Opium War failed and the situation of self-reliance was opened. The imperialist powers came in one after another to carve up China, and China was reduced to a semi-colonial and semi-feudal society for a while.
Beginning in the 1860s, Zeng Guofan, Li Hongzhang and others initiated 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 established the foundation of modern science and technology. The foundation for the development of mathematics in China.
When the "Westernization Movement" ended in a military defeat in 1894, the factories, railways, and schools were retained, and scientific and technological knowledge spread to a certain extent.
The characteristic of this period is the confluence of China and the West. The so-called confluence of Chinese and Western is not a complete Westernization. Mathematicians are studying traditional mathematics while absorbing new methods. For a while, there is a good momentum of abundant talents and writings.
At this time, Chinese mathematicians have independently obtained some calculus results in power series, apex technique, etc., and also obtained excellent results in indefinite analysis and combinatorial analysis. However, even so, among its peers in the world, China still has not achieved the leading position.
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 had taken place in the field of Chinese mathematics. A large number of foreign students were sent out, new schools were founded, academic groups were organized, and specialized journals were established. China has since entered the stage of modern mathematics research. .
From 1847, after the first batch of students, represented by Rong Hong, went abroad, there was a climax of studying abroad. At that time, the number of students studying abroad reached as many as thousands every year. After they returned to China, they formed a modern scientific team that cannot be ignored in China.
In the early days, there were not many people who studied mathematics. Among them, those who have 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, and academic exchanges.
In scientific research, a total of 652 papers were published before 1949. Although the number is small and the scope is limited to pure mathematics, the level is not lower than that of colleagues in the world. You must know that this meagre achievement was achieved after overcoming unimaginable difficulties in politics and economics.
In education, a formal curriculum has been established, mathematics has more hours than liberal arts, and textbooks have also been updated. By 1932, Chinese universities had a team of about 155 mathematics teachers who could offer 5 to 10 professional courses.
In terms of academic exchanges, the "Chinese Mathematical Society" was established in July 1935 to establish peace. 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 atmosphere to the field of mathematics that was retreat in the past.
Development after the founding of the People’s Republic of China
In 1949, at the beginning of the founding of the People’s Republic of China, although the country was in a predicament of lack of funds and waiting to be developed, the government has given great attention to scientific undertakings. Great concern. The Chinese Academy of Sciences was established in November 1949, and the Institute of Mathematics was formally established in July 1952. Subsequently, the Chinese Mathematical Society and its journals restored and created other mathematics special issues, and some monographs by scientists were also published. Mathematical research paved the way.
In the 18 years after liberation, the number of papers published accounted for more than three times the total number of papers before liberation. Many of these papers not only filled the gaps in the past in China, but some reached the world's advanced level.
Just as mathematicians rushed to catch up and tried to restore the advanced status of Chinese mathematics in the world, a ruthless storm swept across China. During the ten years of the Cultural Revolution, society was out of control, people's hearts were chaotic, and science declined. In the field of mathematics, with the exception of Chen Jingrun, Hua Luogeng, Zhang Guanghou and other mathematicians struggling to bloom a few flowers, they were almost withered and blank.
After 10 years of political disasters passed, people looked up and saw that mathematics research in other countries had already peaked one after another, and it took 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 brilliantly literary "Science Spring", the mathematics field ushered in the spring of recovery. In 1977, a new mathematics development plan was formulated in Beijing, the work of the Mathematical Society was resumed, the publication of academic journals was resumed, and the academic journals were reissued, and mathematics education was strengthened. Already in a backward position, however, Lu Yao knows horsepower, and who will be the winner in the future will still be an "x".
Ancient achievements
In the history of the development of ancient Chinese mathematics, the gold medals won by the ancestors are enough to open an exhibition hall. Only a "list" is opened here to give readers an intuitive impression. .
(1) The use of decimal notation and zero. It originated in the Spring and Autumn Period, more than 1,000 years earlier than the second inventor, India.
(2) The origin of binary system thinking. The gossip method derived from the "Book of Changes" was more than 2000 years earlier than the second inventor, German mathematician Leibniz (AD 1646~1716).
(3) The origin of geometrical thought. Mo Jing originated from Mo Di during the Warring States Period, which predates the second inventor Euclid (330-275 BC) more than 100 years ago.
(4) Pythagorean theorem (theorem of Shanggao). The inventor, Shang Gao (a native of Western Zhou Dynasty), predates the second inventor Pythagoras (580 to 500 BC) by more than 550 years.
(5) Magic square. The earliest records of magic methods in our country are the "Analects" and "Book of Books" in the Spring and Autumn Period. In foreign countries, magic squares appeared in the second century AD, and our country predates foreign countries by more than 600 years.
(6) Fraction algorithm and decimals. The complete Chinese fraction algorithm appeared in "Nine Chapters of Arithmetic", and its biography had appeared in the first century AD at the latest. The same law only appeared in India in the 7th century, and it is considered the "originator" of this law. Our country predates India more than 500 years.
China used the least common multiple for 1200 years earlier than the West. The use of decimals is more than 1,100 years earlier than in the West.
(7) The discovery of negative numbers. This discovery was first seen in "Nine Chapters Arithmetic", which was more than 600 years earlier than India and more than 1,600 years earlier than the West.
(8) Surplus is not a technique. Also known as double false position method. 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) Equations. 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 the use of matrix arrangement method to solve linear equations, my country is more than 1,800 years earlier than other countries in the world.
(10) The most accurate "ancestor rate" of pi. It is more than 1,000 years earlier than other countries in the world.
(11) Principle of equal area. Also known as "Zu Xuan" principle. Keep the world record for more than 1,100 years.
(12) Quadratic interpolation. The earliest invention by Liu Zhuo, an astronomer in the Sui Dynasty, was more than 1,000 years earlier than the "world runner-up" Newton (1642-1727 AD).
(13) Method of multiplying and opening. Also known as "Horner's method" in modern mathematics. Jia Xian, a mathematician in Song Dynasty in my country, was first invented in the 11th century, about 800 years earlier than the time proposed by the British mathematician Horner (1786~1837).
(14) Yang Hui triangle. It is actually a table of binomial expansion coefficients. It was originally created by Jia Xian and found in his book "The Yellow Emperor's Nine Chapters Algorithm". Later this book was lost. The Southern Song dynasty Yang Hui compiled this table in his "Detailed Explanation of the Nine Chapters Algorithm", hence the name "Yang Hui Triangle." .
In the world, apart from Jia Xian and Yang Hui of China, the second inventor is the French mathematician Pascal (AD 1623~1662). His invention was in 1653, which was nearly later than Jia Xian. 600 years.
(15) The Chinese Remainder Theorem. In fact, it is a method of solving simultaneous congruences. This method was first seen in "Sun Tzu Suan Jing". In 1801, the German mathematician Gauss (1777~1855 AD) proposed this solution in "Arithmetic Inquiry". Westerners think this method is the best in the world, and it is called "Gauss Theorem." , But it was later discovered that it was more than 1,500 years later than China, so it was named the "Chinese Remainder Theorem".
(16) Digital higher-order equation method, also known as "Tian Yuan Shu". During the Jin Yuan Dynasty, Chinese mathematician Li Ye invented an equation method for setting unknowns and cleverly expressed it in his calculations. This method is more than 300 years earlier than other countries in the world, and lays 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, there have been many scholars studying this problem in China. In the Yuan Dynasty, Zhu Shijie first invented the technique of recruitment, which always solved this problem. In the world, Newton obtained the same formula nearly 400 years later than Zhu Shijie.