2 (600-5th century BC) Ancient Greek Mathematics: Demonstrating the Origin of Mathematics, European Geometry.
3 (3rd century-14th century) China mathematics, Indian mathematics and Arabic mathematics in the middle ages: the brilliance of practical mathematics.
4 (12nd century-17th century) The rise of modern mathematics: the development of algebra and the birth of analytic geometry.
The Establishment of Calculus in the 5th Century (14th Century-18th Century): Newton and Leibniz's Establishment of Calculus.
6 (18th century-19th century) era of analysis: the application of calculus in various fields.
The rebirth of 7 (19th century) algebra: the generation of abstract algebra (modern algebra).
The Transformation of 8 (19th Century) Geometry: Non-Euclidean Geometry
The rigidity of 9 (19th century) analysis: the rigidity of calculus foundation.
10 the trend of pure mathematics in the 20th century
The world of applied mathematics in 2 1 century
The Historical Process of Mathematics in China
China was a leading country in mathematics in the world in ancient times. If classified by modern disciplines, we can see that it is very developed in arithmetic, number, geometry and trigonometry. Now let's briefly review the development history of elementary mathematics in China.
(1) is an arithmetic material.
About 3,000 years ago, China knew four operations of natural numbers, and these operations were just some results, which were preserved in ancient words and books. The operation rules of multiplication and division were recorded in detail in Sun Tzu's Art of War (3rd century AD). China used chips to count in ancient times. In our ancient counting, we used the same bit rate as now. The method of counting chips is to use vertical chips to represent the number of units, hundreds of digits and tens of thousands of digits. Use horizontal chips to represent tens, thousands, etc. It is also obvious in the operation process. Sun Tzu's Calculations is expressed in sixteen words. "From one to ten, one hundred stands upright and thousands of faces are equal."
Like other ancient countries, the multiplication table has existed in China for a long time. China's multiplication table was called Jiujiu in ancient times. It is estimated that China had this table 2,500 years ago. At that time, people used 99 to represent mathematics. Now we can still see the wooden slips with multiplication formula of 99 left over from the Han Dynasty (1st century BC).
According to the existing historical data, the fractional arithmetic in China's ancient mathematical work Nine Chapters Arithmetic (AD 1 century or so) is the earliest document in the world, and the fractional arithmetic in Nine Chapters Arithmetic is almost exactly the same as what we use now.
In ancient times, learning arithmetic also began to know fractions from the measurement of quantity. Sun Tzu's Calculations of Classics (3rd century A.D.) and Summer Sun's Calculations of Classics (6th and 7th centuries A.D.) both started to talk about weights and measures before discussing scores. After describing weights and measures, Xiahou Yang's Jing suan records: "Ten times one, a hundred times two, a thousand times three and a thousand times four; One tenth, two percent, three thousandths, four thousandths. " This power of ten is undoubtedly China's earliest discovery.
In the notation of decimals, in Yuan Dynasty (A.D.13rd century), it was expressed in small letters, such as 13.56 1356. Arithmetically, we should also put forward the problem of "Sun Tzu's calculation of classics" in the third century A.D., and develop it into the "big extension and seeking skills" of Qin in the Song Dynasty (A.D. 1247). This is China's remainder theorem, and the same method was only studied in Europe in19th century.
In the book written by Yang Hui in the Song Dynasty (A.D. 1274), there was a table of factors within 1-300. For example, 297 is represented by "three factors plus one loss", that is, 297=3× 1 1×9, (165438). Yang Hui also used the term "conjoined addition" to describe prime numbers within 20 1-300.
(2) Materials belonging to algebra
Since he explained equations in the eighth volume of Nine Chapters Arithmetic, China has kept brilliant achievements in the field of numerical algebra.
The equation chapter of "Nine Chapters Arithmetic" first shows that the positive and negative techniques are accurate and unchangeable, just as we are learning elementary algebra from the four operations of positive and negative numbers, and the appearance of negative numbers enriches the content of numbers.
In the first century BC, there were several kinds of equations in ancient China, such as multivariate equation, univariate quadratic equation and indefinite equation. Prove the quadratic equation of one variable by using geometric figures. The emergence of indefinite equation in China more than two thousand years ago is a subject worthy of attention, which is more than three hundred years earlier than the Greek Diophantine equation we are familiar with now. Cubic equations in the form of x3+px2+qx=A and x3+px2=A were recorded by China in Wang Xiaotong's "Several Ancient Classics" in the 7th century A.D., and the digital solution was obtained by "dividing from the square" (unfortunately, the original solution was lost). It is not difficult to imagine Wang Xiaotong's pleasure when he got this solution. He said that whoever can change a word in his work will get thousands of dollars.
1 1 century Jia Xian has invented the same numerical equation solution as Horner (1786- 1837), and we can't forget the great contribution of China13rd century mathematician Qin.
In the history of mathematics in the world, the original records of equations have different forms, but in comparison, we have to push the simplicity of China's magic. The four-element technology is the inevitable product of the development of celestial technology.
Serials are ancient things. Two thousand years ago, arithmetic progression and geometric sequence were discussed in Zhou Zhi than Jing and Nine Chapters Arithmetic. /kloc-At the beginning of the 4th century, China should give high praise to the calculation of Zhu Shijie series in Yuan Dynasty. Some of his works are recorded in the works of Europe18th and 9th centuries. In the 1 1 century, China had a complete binomial coefficient table and a method for compiling it.
Historical documents show that the famous surplus and deficiency calculation technology was spread to Europe from China.
The calculation of interpolation method can be traced back to Liu Zhuo in the 6th century in China, and the monks and nuns had interpolation methods with unequal intervals at the end of the 7th century.
Before14th century, China was one of the advanced countries that studied many problems in algebra.
That is, 18 and the 9th century, Li Rui (1773- 18 17) and Wang Lai (1768- 1865438) went to Li (/kloc).
(3) Materials belonging to geometry.
From the late Ming Dynasty (16th century) to the publication of some Chinese versions of Euclid's Elements of Geometry, China's geometry has been developing independently. We should pay attention to many ancient handicrafts and achievements in architectural engineering and water conservancy engineering, which contain rich geometric knowledge.
China's geometry has a long history, and reliable records can be traced back to BC15th century. In Oracle Bone Inscriptions, there are two words: rules and moments. Rules are used to draw circles and moments are used to draw squares.
The shape of moments in stone carvings in the Han Dynasty is similar to that of right-angled triangles. Around the 2nd century BC, China recorded the famous Pythagorean Theorem (Pythagoras originated relatively late).
The study of circle and square plays an important role in the development of ancient geometry in China. Mozi's definition of a circle is: "A circle is equal in length." A circle whose center is equal to the circumference is called a circle, which was explained more than 100 years before Euclid.
And Liu Xin (? 23), Zhang Heng (78- 139), Liu Hui (263), Wang Fan (2 19-257), Zu Chongzhi (429-500), Zhao Youqin (A.D.13rd century) and others, among whom Liu Fan.
Zu Chongzhi got the result π=355/ 133 more than one thousand years earlier than Europe.
In Liu Hui's notes on Nine Chapters of Arithmetic, his genius for the concept of limit has been revealed many times. In plane geometry, right-angled triangles or squares are used, and in solid geometry, cones and rectangular cylinders are used for displacement, which constitute the characteristics of ancient geometry in China.
Chinese mathematicians are good at applying algebraic results to geometry, and using geometric figures to prove the organic combination of algebra, numerical algebra and intuitive geometry, which has achieved good results in practice.
This just shows that in18th century and 9th century, mathematicians in China studied the proportion of tangent circle, and Mingda Xiang (1789- 1850) used tangent circle to calculate ellipse circumference. These are obtained by inheriting ancient methods and exerting them (of course, we also need to absorb the essence of foreign mathematics).
(4) triangular materials.
Trigonometry came into being because of measurement. First, the development of astronomy produced the spherical triangle. China's ancient astronomy was very developed, because the knowledge of spherical measurement had existed for a long time, and the position of constant stars could be determined. Plane measurement has been recorded in Weekly Shooting of Shu Jing. If the depth and distance are measured by moments.
Liu Hui secant method calculates the length of each side of regular hexagon and dodecagon in a circle in radius. This answer is consistent with the value of 2sinA (A is half of the central angle), and the same principle is also applicable to Zhao Youqin's calculation of a regular quadrilateral on a circle in the12nd century. From the calculations of Liu Hui and Zhao Youqin, we can get 7.5o, 15o, 22.5o and 3000.
In the ancient calendar, there was a sundial with 24 solar terms, and an eight-foot-long "table" stood upright on the ground. Due to the rotation of the earth, the sunlight projected on this "table" on the ground by each solar term is different. The ratio of these shadow lengths to the "eight-foot table" constitutes the cotangent function table (although there was no such name at that time).
In the 10th century, China astronomer Guo Shoujing (1231-1316) discovered three formulas on a spherical triangle. Now we use trigonometric function terms: sine, cosine, tangent, cotangent, secant, cotangent, all of which were the names of China in16th century. At that time, adding the two functions of vector and cotangent was called eight lines.
/kloc-in the late 7th century, China mathematician Mei Wending (1633- 172 1) compiled a book about plane triangles and a book about spherical triangles. The book about plane triangle is called Outline of Plane Triangle, which contains the following contents: (1) the definition of trigonometric function; (2) Solving right triangle and oblique triangle; (3) The quadrature of a triangle containing a circle and a square; (4) measurement. This is not far from the content of modern plane triangle. Mei Wending also wrote a book about famous multiplication and difference formulas on triangles. /kloc-After the 8th century, China also published many trigonometry books.
The Book of Changes records that "there was a rule of tying ropes in ancient times, and later sages changed their books." There are many numerals in Oracle Bone Inscriptions unearthed in Yin Ruins. From one to ten, as well as hundreds, thousands and tens of thousands, are special notation, with 13 independent symbols. The notation is written in the combined document, including decimal notation, and the maximum number is thirty thousand.
Calculation is a calculation tool in ancient China, and this calculation method is called calculation. The age of calculation cannot be verified, but it is certain that calculation has been very common in the Spring and Autumn Period.
There are two ways to calculate numbers by counting chips, vertical and horizontal:
When representing multi-digits, the decimal numerical system is adopted, and the digits of each digit are arranged from left to right, criss-crossing (the rule is: one is vertical and ten is horizontal, a hundred stands, a thousand is relative to ten, and ten thousand is equal to a hundred), and a space is used to represent zero. Calculation and financing establish good conditions for addition, subtraction, multiplication and division.
Calculation was not gradually replaced by abacus until the end of Yuan Dynasty in15th century. It was on the basis of calculation that China ancient mathematics made brilliant achievements.
In geometry, according to Records of the Historian Xia Benji, Yu Xia used ruler, moment, ruler, rope and other drawing and measuring tools. And a special case of Pythagorean theorem has been found, which is called Pythagorean theorem in the west. During the Warring States Period, the Work Inspection Book written by Qi people summed up the technical specifications of handicrafts at that time, including some measurement contents and some geometric knowledge, such as the concept of angle.
A hundred schools of thought contended during the Warring States period also promoted the development of mathematics, and some schools also summarized many abstract concepts related to mathematics. As we all know, Mo Jing's definitions and propositions of some geometric terms, such as "a circle, an equal length", "flat, the same height" and so on. Mohist school also gave the definitions of finite and infinite. Zhuangzi records the famous theories of Hui Shi and others, and the topics put forward by debaters such as Huan Tuan and Gong Sunlong, emphasizing abstract mathematical ideas, such as "the greatest is the greatest, the smallest is the smallest", "one foot pestle, half a day, inexhaustible" and so on. Many mathematical propositions such as these definitions and limit ideas of geometric concepts are quite valuable mathematical ideas, but this new idea of attaching importance to abstraction and logical rigor has not been well inherited and developed.
In addition, the Book of Changes, which tells the gossip of Yin and Yang and predicts good and bad luck, has sprouted from combinatorial mathematics, reflecting the idea of binary system.
Second, the formation and foundation of China's mathematical system.
This period includes the 400-year history of mathematical development from Qin and Han Dynasties, Wei and Jin Dynasties and Southern and Northern Dynasties. The Qin and Han Dynasties was the formation period of China's ancient mathematical system. In order to systematize and theorize the growing mathematical knowledge, specialized mathematical books have appeared one after another.
The earliest mathematical monograph in the history of China is Shu Shu, a Han bamboo slip unearthed in Zhangjiashan, Jiangling, Hubei Province in 1984, which was written in the early years of the Western Han Dynasty. At the same time, a Resume of the Han Dynasty was written in the second year of Lv Hou (BC 186), so the book was written in BC 186 at the latest (it should be before).
Zhou Kuai Shu Jing, compiled at the end of the Western Han Dynasty (the first century BC), is an astronomical work about Gai Tian's cosmology, but it contains many mathematical contents. There are two main achievements in mathematics: (1) puts forward the special case and universal form of Pythagorean theorem; (2) Chen Zi's method of measuring the height and distance of the sun is the pioneer of gravity difference's Pythagorean method. In addition, there are more complicated root-finding problems and fractional operations.
Nine Chapters Arithmetic is an ancient mathematical classic that has been compiled and revised by several generations. Written in the early years of the Eastern Han Dynasty (1st century BC). This book is written in the form of problem sets, collecting 246 questions and their answers, which belong to nine chapters: Tian Fang, Su Mi, Decline, Shao Guang, Shanggong, Equal Loss, Profit and Loss, Equation and Pythagoras. The main contents include four fractional and proportional algorithms, the calculation of various areas and volumes, and the calculation of pythagorean measurement. In algebra, the concept of negative number and the law of addition and subtraction of positive and negative numbers introduced in the chapter of equation are the earliest records in the history of mathematics in the world. The solution of linear equations in the book is basically the same as that taught in middle schools now. As far as the characteristics of Nine Chapters Arithmetic are concerned, it pays attention to the application and integration of theory with practice, and forms a mathematical system centered on calculation, which has had a far-reaching impact on the ancient calculation in China. Some of its achievements, such as decimal value system, modern skills and surplus skills, have also spread to India and Arabia, and through these countries to Europe, which has promoted the development of world mathematics.
During the Wei and Jin Dynasties, China's mathematics developed greatly in theory. Among them, the work of Zhao Shuang (unknown year of birth and death) and Liu Hui (unknown year of birth and death) is considered as the beginning of China's ancient mathematical theory system. Zhao Shuang, a native of Wu in the Three Kingdoms, was one of the earliest mathematicians who proved mathematical theorems and formulas in ancient China. He made a detailed annotation on Zhou pian Shu Jing, and strictly proved the pythagorean theorem in pythagorean square diagram by geometric method. His method embodies the idea of cut-and-fill principle. Zhao Shuang also put forward a new method to solve quadratic equation by geometric method. In 263, Liu Hui, a Ren Wei of the Three Kingdoms, annotated Nine Chapters Arithmetic, which not only explained and deduced the methods, formulas and theorems of the original book as a whole, but also systematically expounded the theoretical system and mathematical principles of China's traditional mathematics, which was creative and created the secant method in Volume 1 Square Field (that is, the method of connecting regular polygons in a circle to infinitely approximate the area of a circle). It lays a theoretical foundation for the study of pi and provides a scientific algorithm. He obtained the approximate value of pi by the method of "secant circle" as 3927/ 1250 (i.e. 3. 14 16). "Shanggongpian" constructs the geometric model of "Mouhe Square Cover", which solves the problem of spherical volume formula and opens the way for Zuxuan to get the correct result. In order to establish the polyhedral volume theory, Yang successfully proved equestrian by the limit method. He also wrote Calculation of Islands, which developed the ancient Pythagorean measurement method-gravity difference technique.
The society in the Southern and Northern Dynasties was in a state of war and division for a long time, but the development of mathematics was still vigorous. There are some books on arithmetic, such as Sun Tzu's Art of War, Xiahou Yangbing Law and Zhang Qiu's Art of War. Written in the 4th-5th century A.D., Sunzi Suanjing gave the question "Things are unknown" and gave the answer, which led to the solution of a congruence group of China. The "Hundred Chickens Problem" in Zhang Qiujian suan Jing leads to three unknown indefinite equations.
In the 5th century A.D., the most representative works in this period were Zu Chongzhi and Zuxuan. On the basis of Liu Hui's annotation of Nine Chapters Arithmetic, they greatly promoted traditional mathematics and became a model of attaching importance to mathematical thinking and reasoning. They also made outstanding contributions to astronomy. Their book seal script has been lost. According to historical records, they have made three great achievements in mathematics: (1) Calculate pi to the sixth place after the decimal point and get 3. 14 15926.
He Chengtian, a contemporary astronomer, invented the method of adjusting the sun, used rational fractions to approximate real numbers, and developed ancient indefinite analysis and numerical approximation algorithms.
Thirdly, the establishment of Chinese mathematics education system.
Large-scale architecture in Sui Dynasty objectively promoted the development of mathematics. At the beginning of the Tang Dynasty, Wang Xiaotong compiled the Classic of Ancient Calculations, mainly through practical problems such as earthwork calculation, engineering division and acceptance, and silo calculation, and discussed how to establish cubic polynomial equations by geometric methods, and developed the square root theory in Nine Chapters of Arithmetic.
The Sui and Tang Dynasties was the period when the feudal bureaucratic system in China was established. With the establishment of imperial examination system and imperial academy system, mathematics education has made great progress. In 656, imperial academy established a Mathematics Museum with doctors and teaching assistants in mathematics. Taishi ordered Li and others to compile and annotate ten calculation books (including Weekly Calculation, Nine Chapters of Arithmetic, Island Calculation, Sunzi Calculation, Zhang Qiu Calculation, Xiahou Yang Calculation and Ji Gu Calculation). It has played an important role in preserving ancient mathematical classics.
With the implementation of some important astronomical discoveries in the Southern and Northern Dynasties in the calendar compilation at the turn of Sui and Tang Dynasties, some important mathematical achievements appeared in the calendar of Tang Dynasty. In 600 A.D., the Sui Dynasty put forward the world's first quadratic interpolation formula with equal spacing when solving Huang Shi, which was an outstanding creation in the history of mathematics. In the Tang Dynasty, monks and their followers developed it into a quadratic interpolation formula with unequal intervals in Yan Li.
In the late Tang Dynasty, the computing technology was further improved and popularized, and many practical arithmetic books appeared, trying to simplify the multiplication and division algorithm.
Fourthly, the peak of mathematics development in China.
After the demise of the Tang Dynasty, the Five Dynasties and Ten Kingdoms remained the continuation of the warlord melee. Until the Northern Song Dynasty unified China, agriculture, handicrafts and commerce flourished rapidly, and science and technology advanced by leaps and bounds. From 1 1 century to14th century (Song and Yuan Dynasties), computational mathematics reached its peak, which was the heyday of unprecedented prosperity and fruitful achievements in ancient Chinese mathematics. During this period, a number of famous mathematicians and mathematical works appeared, which are listed as follows: Jia Xian's Nine Chapters of the Yellow Emperor (165438+mid-20th century), The Origin of Ancient Times (65438+mid-2nd century) and Qin's Nine Chapters. Yang Hui's algorithm (126 1), daily algorithm (1262) and Yang Hui's algorithm (1274-65438). Mathematics in Song and Yuan Dynasties reached the ancient mathematics in China in many fields, which was also the peak of mathematics in the world at that time. The main tasks are:
Around A.D. 1050, Jia Xian of the Northern Song Dynasty (the year of birth and death is unknown) created a method of "increasing, multiplying and opening" in the Nine Chapters of the Yellow Emperor to open any higher power. It was not until A.D. 18 19 that the Englishman William George Horner came up with the same method. Jia Xian also listed the binomial theorem coefficient table, and the similar "Basga Triangle" did not appear in Europe until17th century. (The Nine Chapters of the Yellow Emperor Arithmetic Fine Grass has been lost)
During the period of 1088- 1095, Shen Kuo put forward the "gap product method" from the production practice problems such as the number of restaurants and the volume of terraces, and began to study the high-order arithmetic progression summation, and established the correct summation formula. Shen Kuo also put forward the theory of "meeting circle" and obtained the first approximate formula of arc length in the history of ancient mathematics in China. He also used the idea of logistics to analyze and study the relationship between logistics supply and the advance and retreat of troops.
In A.D. 1247, Qin in the Southern Song Dynasty popularized the multiplication and division method in Shu Shu Jiu Zhang, and described the numerical solution of higher order equations. He listed more than 20 solutions of higher-order equations from practice, the highest of which is the decagonal equation. It was not until16th century in Europe that the Italian Scipio Del Ferro proposed the solution of cubic equation. Qin also systematically studied the theory of primary congruence.
In A.D. 1248, Ye Li (Li Zhi, 1 192- 1279) wrote The Sea Mirror for Measuring the Circle, which was the first work to systematically discuss the "celestial technique" (one-dimensional higher-order equation) and was an outstanding achievement in the history of mathematics. In the round sea mirror? In the Preface, Ye Li criticized the fallacy of belittling scientific practice and treating mathematics as "poor skills" and "playing with things and getting tired of it".
In A.D. 126 1 year, Yang Hui (the year of birth and death is unknown) in the Southern Song Dynasty used "piling technique" to find the sum of several kinds of high-order arithmetic progression. In A.D. 1274, he also described the "Nine-fold Agile Method" in his book The Origin of Multiplication and Division Transformation, and introduced various calculation methods of multiplication and division. In A.D. 1280, Wang Xun and Guo Shoujing listed the interpolation formula of triple difference when compiling the calendar method of the Yuan Dynasty. Guo Shoujing also found two formulas equivalent to the present spherical triangle by geometric method.
In A.D. 1303, Zhu Shijie of Yuan Dynasty (date of birth and death unknown) wrote a jade mirror with four elements. He extended "Tianshi skill" to "four-element skill" (four-element simultaneous equation) and put forward a solution to eliminate elements. It was not until A.D. 1775 that etienne bezout, a Frenchman in Europe, proposed the same solution. Zhu Shijie also studied the summation of finite series, and on this basis, obtained the interpolation formula of higher-order difference. Until 65438 to 1678, the Englishman James Gregory and the Englishman Isaac Newton put forward the general formula of European interpolation.
In the 4th century A.D./KLOC-,people in China already used abacus. Before modern computers appeared, abacus was a simple and effective computing tool in the world.
5. The decline of mathematics in China and the development of daily mathematics.
This period refers to 1582 from the establishment of the Ming Dynasty in the middle of the 4th century to the demise of the Ming Dynasty. In addition to abacus, mathematics is in a weak state as a whole, involving the limitations of abacus, the deletion of mathematics content in the examination system of13rd century, and the eight-stage examination system of Daxing in Ming Dynasty. Many Chinese and foreign historians of mathematics are still discussing the reasons involved.
The greatest achievement of the Ming Dynasty was the popularization of abacus, and many abacus readers appeared. It was not until Cheng Dawei's Command Arithmetic (1592) came out that the abacus theory became systematic, marking the completion of the transition from preparation to abacus. However, due to the popularity of abacus calculation, calculation almost disappeared, and ancient mathematics based on calculation gradually disappeared, and mathematics stagnated for a long time.
Six, the introduction of western elementary mathematics and the combination of Chinese and western.
/kloc-At the end of the 6th century, western missionaries began to emigrate to China. Because of the need of making astronomical calendars in Ming and Qing Dynasties, missionaries began to introduce western elementary mathematics knowledge related to astronomical calendars into China. Under the domination of China mathematician's thought of "Western learning spreading to the east", the integration of Chinese and western mathematics research appeared.
/kloc-At the end of the 6th century, western missionaries and China scholars jointly translated many western mathematical monographs. Among them, the first one is the first six volumes of Geometrical Elements translated by Italian missionaries Matteo Ricci and Xu Guangqi (1607), and its rigorous logical system and translation methods have been highly praised by Xu Guangqi. Xu Guangqi's "Measuring Similarities and Differences" and "The Meaning of Pythagoras" applied the logical reasoning method of "Elements of Geometry" and demonstrated China's Pythagorean observation. In addition, most of the nouns in the textbook "Elements of Geometry" are the first ones and are still in use today. In the imported western mathematics, trigonometry is second only to geometry. Before that, trigonometry had only sporadic knowledge, and then it developed rapidly. The works introducing western trigonometry include Days (Volume 2), 163 1, Table of Secant Circle and Eight Lines (Volume 6) and giacomo Rowe's Significance of Measurement (Volume 10). In Xu Guangqi's almanac of Chongzhen (Volume 137, Volume 1629- Volume 1633), the mathematical knowledge about conic curves is introduced.
After entering the Qing Dynasty, Mei Wending, an outstanding representative of Chinese and Western mathematics, firmly believed that China's traditional mathematics must be refined, made in-depth research on ancient classics, and treated western mathematics correctly, which made it take root in China and had a positive impact on the climax of mathematics research in the middle of Qing Dynasty. Contemporary mathematicians include Wang Xizhi and Xirao Nian. Emperor Kangxi of the Qing Dynasty loved scientific research, and his "Essentials of Mathematics in Yu Ding" (53 volumes, 1723) was a comprehensive elementary mathematics work, which had a certain influence on the mathematical research at that time.
Seven. Arrangement and revival of traditional mathematics
During the reign of Ganjia, the school of Ganjia, which was mainly based on textual research, compiled Sikuquanshu, in which the mathematical works included Ten Books of Calculating Classics and the works of Song and Yuan Dynasties, which made important contributions to the preservation of endangered mathematical classics.
In the research of traditional mathematics, many mathematicians have made inventions. For example, Jiao Xun, Wang Lai and Li Rui, who are called "three friends who talk about the sky", have done a lot of important work. In the stack ratio class, Li obtained the summation formula of triangular self-multiplying stacks (about 1859), which is now called Lie identity. These works are a step forward than the mathematics in Song and Yuan Dynasties. Ruan Yuan, Li Rui and others compiled 46 volumes (1795- 18 10) of Biography of Astronomers and Mathematicians, which was the first study of the history of mathematics.
Eight, western mathematics once again eastward.
After the crow war of 1840, the closed-door policy was forced to stop. The second climax of translation and introduction began with the addition of "Arithmetic" in Wentong Pavilion and the addition of a translation pavilion in Shanghai Jiangnan Manufacturing Bureau. The main translators and works are: the last nine volumes of The Elements of Geometry (1857) jointly translated by Li and British missionary William Greer, which gave China a complete Chinese translation of The Elements of Geometry; Algebra13 (1859); The generation of micro products, volume 18 (1859). Li and the British missionary Ai He translated 3 volumes of the Theory of Conic Curves, and Hua and the British missionary John Flair translated 25 volumes of Algebra (1872), 8 volumes of Tracing the Source of Differential Products (1874), and 64 18 of Suspicious Mathematics. In these translations, many mathematical terms and terms were created, which are still used today. 1898, Shi Jing University Hall was established and Wentong Museum was merged. 1905, the imperial examination was abolished and western-style school education was established. The textbooks used were similar to those of other western countries.
Nine, the establishment of modern mathematics in China
This period is a period from the beginning of the 20th century to the present, which is often divided into two stages marked by the establishment of 1949 New China.
Modern mathematics in China started from studying abroad in the late Qing Dynasty and the early Republic of China. 1903 Feng Zuxun who studied mathematics earlier, 1908 Zheng who studied in America, 19 10 Hu Mingfu who studied in America,191/kloc-0. Chen 19 13 studied in Japan; 19 15 Xiong Qinglai studying in Belgium; Su et al. study in Japan 19 19. Most of them became famous mathematicians and mathematicians after returning to China, and made important contributions to the development of modern mathematics in China. Among them, Hu Mingfu received his doctorate from Harvard University in the United States on 19 17, becoming the first mathematician in China to receive his doctorate. With the return of foreign students, mathematics education in universities all over the world has improved. At first, only Peking University 19 12 established the Department of Mathematics, Jiang Lifu 1920 established the Department of Mathematics in Tianjin Nankai University, and Xiong Qinglai established the Department of Mathematics in Southeast University (now Nanjing University) and Tsinghua University 1926 respectively. 1930, Xiong Qinglai initiated the establishment of the Mathematics Research Department in Tsinghua University, and began to recruit graduate students. Chen Shengshen and Wu Daren became the earliest mathematics graduate students in China. In 1930s,,, Hua, 1936 and Xu Baozhen went abroad to study mathematics. At the same time, foreign mathematicians also come to China to give lectures, such as British Russell (1920), boekhoff (1934), osgood (1934) and Wiener (USA). 1935 the inaugural meeting of chinese mathematical society was held in Shanghai, attended by 33 delegates. The publication of 1936 annals of chinese mathematical society and Journal of Mathematics marks the further development of modern mathematics research in China. Before liberation, mathematical research focused on the field of pure mathematics, and more than 600 theories were published at home and abroad. In terms of analysis, Chen's trigonometric series theory and Xiong Qinglai's research on meromorphic functions and whole functions are representative works, as well as functional analysis, variational methods, differential equations and integral equations; In the field of number theory and algebra, Hua's analytical number theory, geometric number theory, algebraic number theory and modern algebra have achieved remarkable results; In geometry and topology, Su's differential geometry, his algebraic topology, his fiber bundle theory and indicator theory have all done pioneering work. In probability theory and mathematical statistics, Xu Baozhen obtained many basic theorems and strict proofs in univariate and multivariate analysis. In addition, Li Yan and Qian Baoyu initiated the study of the history of Chinese mathematics, and they did a lot of basic work in the annotation and textual research of ancient historical materials, which made our national cultural heritage shine again.
China Academy of Sciences was established in June 1949 1 1. 1951March China Mathematics Newspaper (1952) was changed to Mathematics Newspaper (1951March China Mathematics Newspaper (10). 1951August, the Chinese Mathematical Society held its first national congress after the founding of the People's Republic of China to discuss the development direction of mathematics and the reform of mathematics teaching in various schools.
Since the founding of People's Republic of China (PRC), great progress has been made in mathematical research. In the early 1950s, Hua's Heap Prime Theory (1953), Su's Introduction to Projective Curves (1954) and Chen's Series Sum of Rectangular Functions (1954) were published. In addition to continuing to make new achievements in number theory, algebra, geometry, topology, function theory, probability theory and mathematical statistics, history of mathematics and other disciplines, they have also made breakthroughs in differential equations, computing technology, operational research, mathematical logic, mathematical foundation and so on. Many of them have reached the world advanced level, and at the same time, they have trained and grown a large number of outstanding mathematicians.