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), "superposition 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, the most prominent of which is 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.
Liu Hui, an ancient mathematician in China, was born in Shandong in Wei and Jin Dynasties.
Personal profile
Shandong people in Wei and Jin Dynasties were born in the late 1920s. According to Sui Shu Law and Discipline, "Chen Wei and Wang Jingyuan lived together for four years (263), and Liu Hui wrote nine chapters". On the basis of studying Nine Chapters Arithmetic for a long time, he devoted himself to writing a highly theoretical and accurate annotation text for Nine Chapters. His annotations are detailed and rich, and some mistakes handed down from the original book are corrected. He also has many new ideas, created many mathematical principles and proved them strictly, and then applied them to various algorithms, becoming one of the founders of China's traditional mathematical theory system. For example, he said, "There are nine chapters in the West, so take a closer look. Observing the separation of yin and yang is the foundation of technology, exploring leisure time and realizing its significance. I dare to exhaust Lu's stubbornness, take what he sees and make a note for it. " He also said: "Analyze with words and disintegrate with pictures. You can also make an appointment, but you can't talk. People who browse think that more than half. " In addition to commenting on the Nine Chapters, he also wrote a volume of Heavy Difference, which was renamed Island Calculation in the Tang Dynasty. His main contribution lies in establishing secant and calculating the area and pi of a circle with the concept of limit; The idea of creating decimals, small unit numbers and micro fractions; Define many important mathematical concepts and emphasize the role of "rate"; Based on the properties of right triangle, the method of parallel deduction and wide weight difference is established, and a unique and accurate measurement method is formed. The theoretical system of linear solid volume algorithm based on "Liu Hui principle" is put forward. In terms of examples, he used models, graphs and examples to demonstrate or popularize relevant algorithms, which strengthened persuasiveness and application, and formed China's traditional mathematical style. With a serious, earnest and objective spirit, he made mistakes in the rough, made sense in the refined and convinced people by reasoning, which established a good style of study for later scholars. There are also some ideas and ideas in arithmetic and proportional sequence. The Nine Chapters Arithmetic annotated by him has influenced and dominated the development of ancient mathematics in China 1000 years. It is one of the models of oriental mathematics, and it supplements the ancient western mathematics represented by Greek Euclid (about 330-275 BC).
When Liu Hui was engaged in mathematical research, China's decimal numeration and calculation tool "Calculation and Compilation" had been used for more than 1000 years. Among all kinds of notation in the world, decimal notation is the most advanced and convenient. The crystallization of China's ancient mathematical knowledge "Nine Chapters Arithmetic" has been written for more than 300 years. "Nine Chapters Arithmetic" reflects the mathematical knowledge created by Chinese ancestors in practical activities such as productive labor, measuring land, measuring volume, etc., including nine chapters, such as square field, millet, mourning, small but wide, commercial merit, occasional loss, surplus and loss, equation, Pythagoras and so on. It is the basis of China's ancient algorithm, which contains hundreds of calculation formulas and 246 application problems, and has complete operation rules of four fractions, proportion and proportion distribution. Many of these achievements are in the leading position in the world. The year before the first year of A.D., the ancient Greek mathematics in its heyday declined, and the appearance of Nine Chapters Arithmetic marked the transfer of the world mathematics research center from the Mediterranean coast to China, creating a situation in which the East dominated the world mathematics stage with applied mathematics as the center for more than 1000 years. In the arrangement of "Nine Chapters Arithmetic", either a short essay (proposition) is put forward first and then a few examples are listed, or one or several examples are listed first and then a short essay is put forward. However, it does not define the concepts used, does not deduce and prove all the works, and some formulas are still inaccurate or wrong. Since the Eastern Han Dynasty, many scholars have studied Nine Chapters Arithmetic, but the theoretical results are not great. Liu Hui's Notes on Nine Chapters Arithmetic mainly explains and logically proves the technical text of Nine Chapters Arithmetic, and corrects some wrong formulas in it, so that future generations can know what it is and why. With Liu Hui's annotation, Nine Chapters Arithmetic can become a perfect ancient mathematics textbook.
In Notes on Arithmetic in Nine Chapters, Liu Hui developed China's ancient thought of "rate" and the principle of "complementary entry and exit". Most of the algorithms and problems in "Nine Chapters Arithmetic" are proved by "rate", and Pythagorean theorem and some formulas for calculating area and volume are proved by the principle of "complementary access". In order to prove the garden area formula and calculate the garden rate, Liu Hui founded the garden cutting technique. People tried to prove it before this emblem, but it was not strict. Liu Hui put forward the garden cutting technology based on limit thought, and strictly proved the garden area formula. He also proved some cone volume formulas with the idea of infinitesimal division. When calculating the girth ratio, Liu Hui applied the cutting technology, starting from the regular hexagon in the garden, calculating the regular hexagon, regular hexagon and regular hexagon area in turn until the regular hexagon in the garden is 192, and then using the so-called "extrapolation method" to get the approximate value of girth ratio of 3.65438+. Extrapolation is an important method of modern approximate computing technology, which was discovered in Liu Hui far ahead of the west. Liu Hui's garden cutting technology is the correct method to calculate the garden cycle rate, which has laid the foundation for China to be in the forefront of the world for a long time. It is said that Zu Chongzhi used Liu Hui's method to make the effective figure of garden rate accurate to seven places. Pythagorean theorem and square root should be used repeatedly in the process of garden cutting. In order to make a prescription, Liu Hui put forward the idea of finding "decimal number", which is exactly the same as the decimal number of irrational numbers today. The difference ensures the accuracy of girth ratio calculation. At the same time, Liu Hui's micro-fraction also created a precedent for decimals.
Liu Hui's serious attitude towards academics set an example for future generations. When calculating the garden area formula, the square root reached 12 effective figure when the calculation tool was very simple at that time. When he annotated the problem 18 in the chapter "Equation", * * used more than 500 words of/kloc-0, and repeated elimination operations reached 124 times. Yes, the answer is correct, even as an answer sheet for today's college algebra class. Liu Hui was only about 30 years old when she wrote Nine Chapters of Arithmetic. In the third year of Daguan in the Northern Song Dynasty (1 109), Liu Hui was made Xiangzigong.
Von Neumann (1903- 1957) is an American mathematician. Born in Hungary. In his early years, he was famous for his work in set theory and mathematical foundation. During World War II, he participated in various scientific projects related to the anti-fascist war and served as a consultant for the manufacture of atomic bombs. His scientific footprint covers pure mathematics, applied mathematics, mechanics, economics, meteorology, theoretical physics, computer science and brain science, and his achievements are equivalent to a summary of the 30-year history of scientific development. He focuses on pure mathematics, involving axiomatic system of set theory, meta-mathematics, operator ring of von Neumann algebra and so on. , solved Hilbert's fifth problem and axiomatized quantum mechanics. 1940, he changed from a pure mathematician to an applied mathematician, and was called to participate in many important military scientific plans and engineering projects to help design the optimal structure of atomic bombs, study aerodynamics and turn to aviation technology. At the end of World War II, he began computer research, introduced codes into the logic system of electronic computers, compiled various programs, and put brand-new scientific ideas into practice. He was the midwife of the first electronic computer, ANIAC. Many basic designs and designs of modern computers are branded with his thoughts. Von Neumann also founded the game theory, which abandoned the traditional classical mechanical methods to deal with economic problems and replaced them with novel strategic ideas and combined tools. In his later years, he devoted himself to automata theory and realized some similarities between computer and human brain, which laid the foundation for the research of artificial intelligence.
British mathematician Turing. In his early years, his interest focused on "computable numbers", and his theory laid the foundation of computer science theory. During World War II, Turing was called to the Cryptography School under the Communication Department of the British Foreign Office to engage in deciphering. Mathematicians, linguists and calculators led by Turing have developed a fast computer that can analyze passwords at high speed-all possible combinations. Turing's ideal computer thought led to the successful development of the world's first digital "giant" electronic computer, and also made immortal contributions to the final victory of World War II. After the war, Turing devoted himself to the development of large electronic computers, and compiled the overall design scheme of the computer, including simulation system, subroutine and subroutine library, error self-checking system, automatic machine compiler and so on. Turing has done a lot of pioneering work in machine intelligence. This paper discusses the possibility of intelligent machines, and strictly classifies all machines including intelligent computers with his unique theoretical thoroughness, and divides mathematical computers into "organized" and "unorganized" categories. Turing's life work covers several important fields: mathematical logic, group theory, code breaker, computer and machine intelligence, and has made great contributions. He also made a valuable exploration on the theory of morphogenesis which is closely related to the origin of life. His originality and foresight are more and more admired by people.
Descartes (rene descartes 1596 ~ 1650) was born in France. His father is a juror in the French district court, equivalent to a lawyer and a judge now. When his mother died at the age of one, Descartes left a legacy, which provided a reliable financial guarantee for him to engage in his favorite work in the future. At the age of eight, I entered a Jesuit school, where I studied for eight years, received traditional culture education, and read classical literature, history, theology, philosophy, law, medicine, mathematics and other natural sciences. When studying at school, the principal chartered Descartes to read and think in bed every morning, and formed the habit of "thinking in the morning" until his later years. Descartes later recalled that this school was "one of the most famous schools in Europe", but he was quite disappointed with what he had learned. Because in his view, the subtle arguments in the textbook are actually just ambiguous or even inconsistent theories, which can only make him doubt and unable to obtain conclusive knowledge. The only thing that comforted him was math. At the end of his studies, he made up his mind not to learn from books, but to ask for advice from "world books". So 16 12 went to the University of Poitiers in Paris to study law, and received his doctorate four years later. 16 18 joined the army and has been to Holland, Denmark and Germany. /kloc-returned to China in 0/621year, traveled to Holland, Switzerland and Italy during the civil strife in France, and returned to Paris in 0/625. Descartes made many friends in the field of science. Because he solved several publicly answered math problems independently, he was full of confidence in his ability in math and science, so he decided to avoid war, stay away from cities with frequent social activities and find an environment suitable for research. From 65438 to 0628, he moved from Paris to the Netherlands, where he began his 20-year devoted research and writing career and published many works that had a great influence on mathematics and philosophy. 1649 winter, invited to give a lecture to Christina (1626- 1689) in Queen Christina. She died of pneumonia a few months later because her living habits were destroyed. (16 years later, the body was transported back to Paris). His works were criticized by the church before his death and banned by the Vatican Pope after his death, but this did not stop the spread of his thoughts.
Descartes is one of the founders of modern European philosophy. Hegel called him "the father of modern philosophy" and Engels called him "the outstanding representative of dialectics". At the same time, Descartes is a scientist who dares to explore, and he has commendable innovations in physics, physiology and other fields, especially in mathematics. He founded analytic geometry, which opened the door to modern mathematics and has epoch-making significance in the history of science.
Before Descartes, geometry and algebra were two different research fields in mathematics. Descartes stands on the height of methodology and natural philosophy, and thinks that Greek geometry relies too much on graphics, which limits people's imagination. For algebra, which was popular at that time, he felt that it was completely subordinate to laws and formulas and could not be a science to improve intelligence. So he must combine the advantages of geometry and algebra to establish a kind of "real mathematics". The core of Descartes' thought is to simplify geometric problems into algebraic problems, calculate and prove them by algebraic methods, and finally solve geometric problems. According to this idea, he founded what we now call analytic geometry. Descartes' concrete methods are: introducing the concept of coordinates and establishing the corresponding relationship between points and number pairs on the plane; Starting with solving the problem of geometric drawing, this paper puts forward a method of representing geometric curves with algebraic equations. Solve the problem of geometric drawing by solving the roots of algebraic equations. In this way, Descartes easily solved the problems that classical geometricians did not solve by pure geometric methods. In the process of studying geometric canon with algebraic equations, Descartes also obtained a series of novel ideas and achievements. The most valuable thing is that Descartes regards a curve as the trajectory of a point from the viewpoint of motion, which not only establishes the corresponding relationship between a point and a real number, but also unifies the two opposing objects of shape (including point, line and surface) and number, and establishes the corresponding relationship between canon and equation. The establishment of this correspondence not only marks the germination of the concept of function, but also marks that variables have entered mathematics, which has made a great turning point in mathematics-the period from constant mathematics to variable mathematics. Descartes' achievements paved the way for Newton and Leibniz to discover calculus, and also paved the way for a large number of mathematicians to make new discoveries. Descartes' main mathematical achievements are concentrated in his Geometry. It is worth pointing out that in Geometry, Descartes chose his own coordinate system according to the characteristics of the problem, which is an oblique coordinate system. There is no standard Cartesian coordinate system, which was put forward by the outstanding German philosopher and mathematician G.W. Leibniz.