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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 notes 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 the establishment of secant and the calculation of circular area and pi 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, American mathematician. Born in Hungary.
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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.
Turing (19 12- 1954) was a British mathematician.
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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. Gauss (1777- 1855) is a German mathematician, physicist and astronomer. Gauss showed extraordinary mathematical genius in his childhood. He began to learn arithmetic at the age of three, and won the admiration of teachers and classmates at the age of eight because he discovered the summation formula of arithmetic series. In his sophomore year, he obtained the ruler drawing method of regular heptagon, and gave the conditions for drawing regular polygon with ruler.
Gauss's achievements in mathematics cover all fields, and his contributions in many aspects of mathematics are of epoch-making significance, and he has made outstanding contributions to the research of astronomy, geodesy and magnetism. Arithmetic Research, published in +080 1, is one of the few classic works in the history of mathematics, which opened up a new era of number theory research.
Non-Euclidean geometry is another important discovery of Gauss, and his legacy shows that he is one of the founders of non-Euclidean geometry. Gauss has devoted himself to astronomical research for about 20 years. His masterpiece in this field is The Theory of Celestial Motion published in 1809. Gauss also made outstanding contributions to physics, and Maxwell said that his magnetic research transformed the whole science. Gauss also trained many outstanding mathematicians in his life.
Lagrange [[Lagrange, Joseph Lewis,1736-1813]]
Lagrange, a French mathematician, mechanic and astronomer, 17361was born in Turin, northwest Italy on October 25th. When I was a teenager, I read Harley's paper on Newton's calculus, so I became interested in analysis. He also often corresponded with Euler. When he was only 65,438+08 years old, he developed the variational method initiated by Euler by pure analysis, which laid the theoretical foundation for the variational method. Later, he entered the University of Turin.
1755, 19 years old, became a professor of mathematics at the Royal Artillery School in Turin. He soon became an academician of the School of Communication of the Berlin Academy of Sciences. Two years later, he participated in the establishment of the Turin Science Association, and published a large number of papers on variational methods, probability theory, differential equations, string vibration and minimum action principle in scientific journals published by the Association. These works made him recognized as a first-class mathematician in Europe at that time.
1764, he won an award from the Paris Academy of Sciences for explaining the gravity balance of the moon. 1766, he successfully studied a complex six-body problem [the motion of four satellites of Jupiter] proposed by the Academy of Sciences with the theory of differential equations and approximate solutions, and won another prize.
In the same year, Frederick, king of Prussia, Germany, invited him to work in the Berlin Academy of Sciences, saying that "the biggest king in Europe should have the biggest mathematician in Europe", so he was invited to work in the Berlin Academy of Sciences and lived there for 20 years. In the meantime, he wrote another important classic mechanical work, Analytical Mechanics, after Newton [1788]. In this book, a complete and harmonious mechanical system is established by variational principle and analytical method, which makes mechanics analytical. In his preface, he even claimed that mechanics has become a branch of analysis.
Frederick the Prussian king died in 1786 and settled in Paris in 1787 at the invitation of King Louis XVI of France. In the meantime, he served as the director of the French Metrology Committee, and successively served as a professor of mathematics at the Paris Teachers College and the Paris Institute of Technology. Finally, he died in April 18 13.
Lagrange not only made great contributions to equation theory, but also promoted the development of algebra. In his two famous papers submitted to the Berlin Academy of Sciences: On the Solution of Numerical Equations [1767] and Research on Algebraic Solutions of Equations [177 1], he investigated a general solution of quadratic, cubic and quartic equations, that is, turning the equations into low-order equations [auxiliary equations or resolvent] But this does not apply to quintic equations. In his research on the conditions of solving equations, the germination of group theory has been included, which makes him a pioneer in Galois' establishment of group theory.
In addition, he is also excellent in number theory. Many questions raised by Fermat were answered by him, such as: a positive integer is not greater than the sum of four squares; The problem of finding all integer solutions of equation X2-AY2 = 1 [A is a non-square number] and so on. He also proved the irrational number of π. These research results enrich the content of number theory.
In addition, he also wrote two analytical masterpieces, Analytic Function Theory [1797] and Lecture Notes on Function Calculation [180 1], summarizing his series of research work during that period.
In Analytic Function Theory and a paper he included in this book [1772], he tried to reduce the differential operation to algebraic operation, thus abandoning the infinitesimal that has been puzzling since Newton and making a unique attempt to lay the theoretical foundation of calculus. He also defined the derivative of the function f(x) as the coefficient of the h term in Taylor expansion of f(x+h), and thus established all the analyses. However, he did not consider the convergence of infinite series. He thinks that he got rid of the concept of limit, but avoided it in essence, so he didn't reach the algebraic and rigorous calculus thought. However, he adopted a new differential symbol and expressed functions by power series, which influenced the development of analysis and became the starting point of the theory of real variable functions.
Moreover, in the theory of differential equations, he made a geometric explanation that the singular solution is the envelope of the integral curve family, and put forward the concept of linear substitution eigenvalue.
Many achievements in mathematics in the last hundred years can be directly or simply traced back to Lagrange's work. Therefore, he is considered to be one of the mathematicians who have a comprehensive influence on the development of analytical mathematics in the history of mathematics.