In China, the origin of mathematics can also be traced back to ancient times. By the Western Zhou Dynasty (BC 1 1 century to the 8th century), "number", as one of the "six arts" that noble disciples must learn (ritual, music, shooting, calligraphy and number), had formed specialized knowledge, and some knowledge later became the first two mathematical works handed down from generation to generation in China-Zhouyi suan.
Zhou Shu suan Jing is also an astronomical work with unknown author, and it was written no later than the 2nd century BC. The most important mathematical aspects of Zhou Tao and Shu Jing are Pythagorean theorem, fractional operation and measurement.
There is no proof of Pythagorean Theorem in The Classic of Weekly Parallel Calculations, but the Pythagorean Square Theory in Zhao Shuang's Annotation in The Classic of Weekly Parallel Calculations contains the earliest proof of Pythagorean Theorem in ancient China. Zhao Shuang, whose real name is Jun Qing, was born and died in an unknown year, and lived in the Three Kingdoms period of the Later Han Dynasty. The Pythagorean Graph Theory is just over 500 words, which summarizes the main achievements of Pythagorean arithmetic in the whole Han Dynasty.
Nine Chapters Arithmetic is the most important classical mathematics in ancient China, which has a far-reaching influence on the development of ancient mathematics in China. Liu Hui's "Nine Chapters Arithmetic Preface" said that "Nine Chapters" was developed from the "Nine Numbers" of the Zhou Dynasty, and was deleted and supplemented by Zhang Cang and Geng Shouchang in the Western Han Dynasty. There are some contents similar to Jiusuan (unearthed in 1984) in the bamboo slips of the early Han Dynasty tomb in Zhangjiashan, Hubei, which were discovered in recent years. It can be considered that Nine Chapters Arithmetic started from the pre-Qin period, and was finally written in the middle of the Western Han Dynasty (the first century BC) after a long period of compilation and revision by many scholars.
"Nine Chapters Arithmetic" takes the form of examples of commands in art and literature. The book contains 246 math problems, which are divided into nine chapters (① Square Field, ② Millet, ③ Decreasing Score, ④ Less Generality, ⑤ Quotient Work, ⑤ Loss, ⑦ Profit and Loss, ⑧ Equation and ⑨ Pythagoras). The mathematical achievements contained in Nine Chapters Arithmetic are rich and varied, among which the most famous ones are fractional arithmetic, double-seeking method ("remainder"), open method, elimination method of linear equations ("equation") and introduction of negative numbers ("addition and subtraction"), which are of world significance.
China was the first country in the world to adopt decimal system for counting, which was widely used in the Spring and Autumn Period and the Warring States Period, that is, it strictly followed decimal system. Now the only information about counting methods is in the calculation of Sun Tzu's Art of War. Sun Tzu's Calculations is a three-volume book with unknown author's name, which was written in the 4th century. The first volume of this book is a systematic introduction to the calculation rules, and the second volume has the famous title of "I don't know how many things there are", also called "grandson problem".
Suan Qiujian Suanjing-Baijishu
According to Qian Baoyu's research, Zhang Qiujian, a native of Qinghe (now Linqing, Shandong Province) in the Northern Wei Dynasty, was written in 466 ~ 485 AD. The application of the least common multiple, the mutual summation of arithmetic progression elements and "Hundred Chicken Skills" are his main achievements. "Hundred Chickens Skill" is a world-famous indefinite equation problem. /kloc-Fibonacci calculation in Italy in the 3rd century, and/kloc-Alkasi in Arabia in the 5th century < < The Key to Arithmetic > and other works all have the same problems.
Jia Xian: Nine Chapters of the Yellow Emperor Calculate Fine Grass. "
China's classical mathematicians reached their peak in the Song and Yuan Dynasties, and the prelude of this development was the discovery of "Jiaxian Triangle" (binomial expansion coefficient table) and the establishment of higher-order open method ("increase, multiply and open method") closely related to it. Jia Xian, a native of Northern Song Dynasty, completed Nine Chapters of Fine Grass in Huangdi Neijing about 1050. The original book was lost, but the main contents were copied by Yang Hui's works (about13rd century), which can be handed down from generation to generation. Yang Hui's Detailed Explanation of Nine Chapters' Algorithms (126 1) has a picture of "Learning the Original Prescription", which means "Jia Xian used this technique". This is the famous "Jiaxian Triangle", or "Yang Hui Triangle". At the same time, it records Jia Xian's "method of increasing, multiplying and opening" to the root of higher order.
Jiaxian Triangle is called Pascal Triangle in western literature and was rediscovered by French mathematician B Pascal in 1654.
Qin: Counting Books and Nine Chapters.
Qin (about 1202 ~ 126 1), a native of Anyue, Sichuan, once served as an official in Hubei, Anhui, Jiangsu, Zhejiang and other places, and was exiled to Meizhou (now Meixian County, Guangdong Province) around 126 1, and soon died. Qin, Yang Hui and Zhu Shijie are also called the four great mathematicians in Song and Yuan Dynasties. In his early years, he studied mathematics in seclusion in Hangzhou, and wrote the famous Shu Shu Jiu Zhang in 1247. The book "Shu Shu Jiu Zhang" 18, 8 1 title, is divided into nine categories (Wild Goose, Shi Tian, Tianjing, Prospecting, Foraging, Qian Gu, Architecture, Military Service, Market Changes). Its most important mathematical achievements —— "Dayan summation method" (one-time congruence group solution) and "positive and negative leveling method" (numerical solution of higher-order equations) made this Song Dynasty arithmetic classic occupy a prominent position in the history of medieval mathematics.
Ye Li: Circular Sea Mirror-Kaiyuan Art
With the development of numerical solution technology of higher-order equations, the sequential equation method came into being, which is called "Kaiyuan technique". Among the mathematical works handed down from Song Dynasty to Yuan Dynasty, Ye Li's "Measuring the Round Sea Mirror" is the first work that systematically expounds Kaiyuan.
Ye Li (1 192 ~ 1279), formerly known as Li Zhi, was born in Luancheng, Jin Dynasty. He used to be the governor of Zhou Jun (now Yuxian County, Henan Province). Zhou Jun was destroyed by the Mongolian army in 1232, so he studied in seclusion. He was hired by Kublai Khan of Yuan Shizu as a bachelor of Hanlin for only one year. 1248 was written into "Circle Survey Mirror", the main purpose of which was to explain the method of establishing equations by using Kaiyuan. "Kai Yuan Shu" is similar to the column equation method in modern algebra. "Let Tianyuan be so-and-so" is equivalent to "Let X be so-and-so", which can be said to be an attempt of symbolic algebra. Ye Li also has another mathematical work Yi Gu Yan Duan (1259), which also explains Kaiyuan.
Zhu Shijie: Four Yuan Jade Sword
Zhu Shijie (about 1300) was born in Songting, Han Qing, and lived in Yanshan (now near Beijing). He "traveled around the lake and sea for more than twenty years as a famous mathematician" and "gathered scholars by following the door". Zhu Shijie's representative works in mathematics include "Arithmetic Enlightenment" (1299) and "Meeting with the Source" (1303). "Arithmetic Enlightenment" is a well-known mathematical masterpiece, which spread overseas and influenced the development of mathematics in Korea and Japan. "Thinking of the source meets" is another symbol of the peak of China's mathematics in the Song and Yuan Dynasties, among which the most outstanding mathematical creations are "thinking of the source" (the formulation and elimination of multivariate higher-order equations), "overlapping method" (the summation of higher-order arithmetic progression) and "seeking difference method" (the high-order interpolation method).
Hua
"Mathematics, like music, is famous for its geniuses. These geniuses are smart even without formal education. Although Hua modestly avoids using the word "wizard", it appropriately describes the outstanding China mathematician-G B Kolata.
Hua is a legend and a self-taught mathematician.
He was born in Jintan County, Jiangsu Province,19101012. 1June, 985 102, Hua, a superstar in China's mathematics field, died of myocardial infarction while giving lectures in Japan.
Hua is a famous mathematician at home and abroad. He is the founder and pioneer of China's research on analytic number theory, canonical group, matrix geometry, automorphism, multiple complex functions and so on. His famous academic paper "On Functions of Multiple Complex Variables in Typical Fields" has done pioneering work in the field of mathematics because it has applied methods that have never been used before, and won the first prize of 1957 China Science. His research results were named "Fahrenheit Theorem" and "Brouwer-Gadang-Hua Theorem" by the international mathematical community. Hua worked tirelessly all his life, struggled ceaselessly, wrote books, set forth opinions and covered a wide range. He has published about 200 academic papers, including Heap Prime Theory, Introduction to Advanced Mathematics, Estimation of Exponential Sum and Its Application in Number Theory, Typical Groups, Analysis of Typical Fields in the Theory of Functions of Multiple Complex Variables, Introduction to Number Theory, Numerical Integral and Its Application, Starting from the Unit Circle and Optimization Method.
Mentoring-Chen Shengsheng and Qiu Chengtong
There are two awards in the world today, which attract worldwide attention and are comparable to the Nobel Prize. One is the Fields Prize awarded by the International Congress of Mathematicians, which is only awarded to young mathematicians who are not over 40 years old. One is 1978 Wolf Prize awarded by Israel Wolf Foundation; Each prize is $ 654.38+ million (the number is close to the Nobel Prize at first), awarded to the greatest mathematician of our time.
1983, Professor Qiu Chengtong, a young mathematician from China living in the United States, won the Wolf Prize, while his teacher, Professor Chen Shengshen, an American mathematician from China, won the Wolf Prize.
Professor Chen Shengshen is an academician of American Academy of Sciences, winner of American National Science Award 65438-0975, one of the most influential mathematicians in the contemporary world, and the founder of modern differential geometry.
Chen Shengshen1911010 was born in Jiaxing County, Zhejiang Province on October 26th. Professor Chen Shengshen is a leading figure in the study of global differential geometry in the international mathematics field.
His first research paper published in Tsinghua at 193 1 was about "projective differential geometry".
His works on integral geometry pushed the work of integral geometry of Chirac School to a higher stage.
Chen Shengshen was very interested in the theory of deixis, which was little known in mathematics at that time. 1945, he discovered that there are invariants reflecting complex structural characteristics on complex flow, and later named Chen Shengshen's indicator class as the most important invariants in differential geometry, algebraic geometry and complex analytic geometry. Its application covers the whole mathematics and theoretical physics. Wei Yi said: "Chen's works have completely changed the concept of the demonstration class." Chen Shengshen established the connection between algebraic extension and differential geometry, which promoted the development of global geometry and shined brilliantly in the history of mathematics.
In the past half century, Professor Chen Shengshen has made a series of fruitful achievements in the study of differential geometry, among which the most prominent ones are: the decomposition theorem of the homology form of (1)Kahleian)G structure; (2) The total curvature and compact embedding theory of closed subflows in Euclidean space; (3) Uniqueness theorem of substreams satisfying geometric conditions; (4) Motion formula in integral geometry. (5) His and P. Griffith's work in network geometry has brought new life to this field and its recent development (I Gelfand, R mcpherson); (6) His and J. Mo Ze's work on CR- manifolds is the basis of recent progress in the theory of multiple complex variables; (7) The characteristic formula of him and J.Simons is the basic mathematical tool of abnormal phenomena in quantum mechanics; (8) His and J.Wolfson's work on harmonic mapping is a global differential geometry problem, which has important applications in theoretical physics. Differential Geometry, written by him at the University of Chicago in 1959, is a classic work.
Qiu Chengtong was born in Guangdong on April 4th, 1949, and his family moved to Hong Kong soon. 1976, at the age of 27, Qiu Chengtong solved a famous problem in differential geometry-"Calabi conjecture". The solution of Calabi's conjecture makes Qiu Chengtong a new star in the mathematical sky. In addition to solving Calabi's conjecture, he also solved many problems that have not progressed for many years, such as (1) positive prime conjecture, (2) real complex gaspard monge-Ampere equation. (3) A series of articles by Qiu Chengtong have made profound estimates on the first eigenvalue and other eigenvalues of Laplacian operators on some compact manifolds (or flow patterns with boundaries). (4) Qiu Chengtong and Xiao Yintang cooperated to give a beautiful proof of frankl's conjecture with minimal surface, that is to say, it was proved that a completely simply connected Keller flow with positive holomorphic cross-section curvature was equivalent to a double holomorphic space; (5) Qiu Chengtong and Meeske solved some old problems in classical minimal surface theory by using the continuation method of three-dimensional manifold. On the other hand, they obtained some results of three-dimensional continuation by using the minimal surface theory: Dean's Lemma, Equivariant Circle Theorem and Isosphere Theorem.
Because of Qiu Chengtong's outstanding achievements, he won the Van Buren Prize in American mathematics in 198 1, and he was well-deserved to win the Fields Prize in the international congress of mathematicians held in Warsaw in 1983.
Wentsun Wu
Mathematician191May 09 12 was born in Shanghai. 1940 graduated from Shanghai Jiaotong University. 1947 to study in France. He studied mathematics at the French National Centre for Scientific Research in Paris, and received the French National Doctor of Science degree at 1949. 195 1 year. 1957 was elected as a member of China Academy of Sciences. Professor of Mathematics Department of Peking University, researcher and deputy director of Institute of Mathematics of China Academy of Sciences, researcher and deputy director of Institute of System Science of Chinese Academy of Sciences, honorary director and director of Research Center of Mathematical Mechanization. He used to be the chairman and honorary chairman of chinese mathematical society, and the deputy director and director of the Department of Mathematical Physics of China Academy of Sciences. Wu Wenjun is mainly engaged in the research of topology and machine proof, and has made many outstanding achievements. He is the founder of China's mathematical mechanization research and has made important contributions to China's mathematical research and scientific development. 1952 published the doctoral thesis "spherical fiber indicators", which is an important contribution to the theoretical basis of spherical fibers. Since the 1940s, the research on demonstrative and embedded classes has made a series of outstanding achievements, and they have many important applications. They are called "Wu Wenjun Formula" and "Wu Wenjun Instruction Class" by international mathematicians, and have been compiled into many masterpieces. This achievement won the first prize of National Natural Science Award 1956 (Natural Science Award of China Academy of Sciences). In 1960s, we continued to study embedding classes and creatively discovered new topological invariants, among which the achievements on polyhedron embedding and immersion still occupy the leading position in the world. The achievement of Pontryagin's characteristic class is the basic theoretical research of topological fiber bundle theory and differential manifold geometry, which has profound theoretical significance. In recent years, the principle of machine proof of Wu Wenjun's theorem (internationally known as "Folin-Wu method") has been established, and the machine proof of elementary geometry and differential geometry theorems has been realized, occupying a leading position in the world. This important innovation has changed the face of automatic reasoning research, had a great influence in the field of theorem machine proof, and has important application value, which will lead to the reform of mathematical research methods. The research achievements in this field have won the 1978 National Mathematics Congress Major Achievement Award, and the 1980 China Academy of Sciences First Prize for Scientific and Technological Progress. He has also made important contributions to the research of machine discovery and creation theorem, algebraic geometry, the history of Chinese mathematics and game theory.
Lege Yang
Mathematician1939165438+10 was born in Nantong, Jiangsu. 1956 was admitted to the Department of Mathematics of Peking University, and 1962 graduated. In the same year, he was admitted to the Institute of Mathematics, Chinese Academy of Sciences, and stayed in the Institute after graduation. He used to be director of the Institute of Mathematics of China Academy of Sciences, secretary-general and chairman of the Chinese Mathematical Society. Currently, he is a researcher and director of academic committee of Institute of Mathematics, China Academy of Sciences. 1980 was elected as an academician of China Academy of Sciences. Yang Le has been at the forefront of the world for 20 years, and has made many creative and important contributions in the fields of function module distribution theory, radiation angle distribution theory, normal family, etc. He is one of the world's leading mathematicians. 1. The deficient values and functions of whole functions and meromorphic functions are deeply studied. In cooperation with Zhang Guanghou, the close relationship between the number of deficient values of meromorphic functions and the Borel direction number is established for the first time. After introducing defect function, the total defect estimation of horizontal meromorphic function under finite condition is given, which proves that its defect function is countable. In this paper, the estimation of the total deficiency of meromorphic functions combined with derivatives is given, and three problems raised by the famous scholar D.Drasin70 in the 1970 s are completely solved. Secondly, the normal family is studied systematically, and some new important normal rules are obtained. Yang Le established the connection between normal family and fixed point, and between normal family and differential polynomial, and solved a problem of normal family put forward by famous scholar W.K.Hayman. Thirdly, the angular distribution of integral functions and meromorphic functions is systematically and deeply studied. Yang Le obtained a new singular direction when he studied the angular distribution of derivatives involved in meromorphic functions. The relationship between radial angle distribution and multiple values is obtained. The distribution law of Borel direction of meromorphic functions is completely characterized. Cooperate with Hyman to solve a conjecture of Littlewood. Yang Le's above-mentioned important research achievements have been highly praised and cited by domestic and foreign peers, and its deficit-deficit relationship is called "Yang Le deficit-deficit relationship" by foreign scholars.