Liu Hui (born around 250 AD) is a very great mathematician in the history of Chinese mathematics, and also occupies a prominent position in the history of world mathematics. His representative works "Nine Chapters of Arithmetic Notes" and "Calculations on the Island" are the most precious mathematical heritages in China. Nine Chapters of Arithmetic was written in the early Eastern Han Dynasty, with a total of 246 volumes. Calculation of positive and negative numbers, calculation of volume and area of geometric figures, etc. It is advanced in the world. However, due to the primitive solution and the lack of necessary proof, Liu Hui made supplementary proof for them. These proofs show his creative contributions in many aspects. He was the first person in the world to put forward the concept of decimal, and used decimal to represent the cube root of irrational numbers. In algebra, he correctly put forward the concept of positive and negative numbers and the principles of addition and subtraction. The solution of linear equations is improved. In geometry, the secant method is put forward, that is, the method of finding the area and perimeter of a circle by using inscribed or circumscribed regular polygons. He scientifically obtained the result that pi = 3. 14 by using secant technology. Liu Hui put forward in the secant technique that "if you cut it carefully, the loss is not great, and then you can't cut it." This can be regarded as the representative work of China's ancient limit concept. In the book Calculation of the Island, Liu Hui carefully selected nine survey questions, all of which were noticed by the West at that time because of their creativity, complexity and representativeness. Liu Hui's thinking is agile and flexible, and he advocates both reasoning and intuition. He was the first person in China who explicitly advocated using logical reasoning to demonstrate mathematical propositions. Liu Hui's life is a life of hard exploration of mathematics. Although he is in a low position, he has a noble personality. He is not a mediocre man who seeks fame and fame, but a great man who never tires of learning. He left us a valuable fortune. Jia Xian and Jia Xian were outstanding mathematicians in the Northern Song Dynasty in ancient China. The Nine Chapters of Yellow Emperor's Arithmetic Fine Grass (nine volumes) and Arithmetic Ancient Collection (two volumes) have been lost. His main contribution is to create the "Jiaxian Triangle" and the method of multiplication and multiplication, which is the positive root method for finding the higher power. At present, the principle and procedure of mixed division in middle school mathematics are similar, while the multiplication and division method is more neat, simple and programmed than the traditional method, so it shows its superiority, especially when it comes to high power. This method was put forward more than 700 years before the conclusion of European mathematician Horner. Qin Jiushao (about 1202- 126 1) was born in Anyue, Sichuan. He was once an official in Hubei, Anhui, Jiangsu, Zhejiang and other places, and was demoted to Meizhou (now Meixian County, Guangdong Province) around 126 1, and soon died. He, Yang Hui and Zhu Shijie are also called the four great mathematicians in Song and Yuan Dynasties. In his early years in Hangzhou, he visited the Taishi and learned mathematics from a hermit. 1247, he wrote the famous Shu Shu Jiu Zhang. The book "Shu Shu Jiu Zhang" has a total of 18 volumes and 8 1 title, which is divided into nine categories. Its most important achievements in mathematics-"the sum of large calculations" (a solution of congruence group) and "the solution of positive and negative square roots" (a numerical solution of higher-order equations) made this Song Dynasty arithmetic classic occupy a prominent position in the history of medieval mathematics. Ye Li 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 lived in seclusion and was studied by Kublai Khan of Yuan Shizu. 1248 was written in "Circular Sea Mirror", the main purpose of which was to explain the method of arranging equations with astronomical elements. "Astrology" 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. Another mathematical work by Ye Li, Yi Gu Yan Duan (1259), also explains Heaven. Zhu Shijie (1300 or so), whose real name is Yanshan (near Beijing today), "traveled around the lake and sea with famous mathematicians for more than 20 years" and "gathered scholars by following the door" ("Mo Ruo and Zu Yi: Four Lessons"). 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. "Meeting with the source of thinking" 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 about the source" (formulation and elimination of multivariate higher-order equations), "superposition" (higher-order arithmetic progression summation) and "seeking differences" (higher-order interpolation). Zu Chongzhi (AD 429-500) was born in Hebei Province. He is not only a mathematician, but also familiar with astronomical calendar, machinery manufacturing, music and other fields, and is an astronomer. Zu Chongzhi's main achievement in mathematics is the calculation of pi. He calculated pi as 3. 14 159260, a >；; 0), the proof of "gravity difference technique" is given by using the area relation of geometric figures in the solar altitude map annotation. The method used by astronomers in the Han Dynasty to measure the height and distance of the sun is called gravity difference technique. Hua is a modern mathematician in China. 19101012 was born in Jintan county, Jiangsu province. 1June 1985 12 died in Tokyo, Japan. After graduating from junior high school, Hua 1924 studied in Shanghai China Vocational School for less than one year. He dropped out of school because of his poor family. He studies mathematics hard. 1930 He published an article on solving algebraic equations in Science, which attracted the attention of experts. He was invited to work in Tsinghua University and began to study number theory. 1934, became a researcher of China Education and Culture Foundation. 1936 went to Cambridge University as a visiting scholar. 1938 returned to China and was employed by Professor The National SouthWest Associated University. 1946 was invited by the Institute of Advanced Studies in Princeton, Soviet Union as a researcher and taught at Princeton University. From 65438 to 0948, he was a professor at the University of Illinois. Brief Introduction of Famous Mathematicians at Home and Abroad (Foreign Part) Blaise is a French mathematician and physicist. 1June 623 19 was born in clermont-ferrand, Overwien; 1662 died in Paris in August 0. Considering his short life and the last ten years of his life, he devoted himself completely to theology and inner reflection. Fortunately, Pascal has achieved a lot. He is a sick child. Once he is in infancy, people think that he will not live long. But he is a brain prodigy. His father is a government official, and I am also a mathematician. He personally supervised the children's education and decided to let them learn ancient languages first, so he was not allowed to touch any math books. Pascal asked questions about geometry and told him that geometry is the study of figures, so he independently discovered the first 32 theorems of Euclid, and the order was completely correct. This story was told by his sister. It seems too good to be true. So the awesome father gave in and let the children learn math. When Pascal was just sixteen years old, he published a book on the geometry of conic curves, which for the first time advanced the results obtained at Apolloni's Bird's Nest 19 centuries ago. Descartes firmly believed that a child of 16 years old could write such a book, while Pascal, in turn, did not accept the value of Descartes' analytic geometry. 1642 When he was just ten years old, Pascal invented a computer, which was made of gears and could do addition and subtraction. He obtained a patent and gave a model to Swedish female worker Christina, the royal academic protector. He hoped to profit from it, but he failed. Because it costs a lot of money to make a fully practical computer. However, it is the ancestor of the best mechanical device-the modern cash register. Pascal corresponded with Fermat, a lawyer and mathematician. Together, they solved the problem sent by an upper-class gambler and amateur philosopher. He can't figure out why gambling on three dice in a certain combination always loses. In the process of solving this problem, they laid the foundation of modern probability theory. This is of inestimable importance to the development of science, because it makes mathematics (and the whole world) require absolute affirmation. People begin to believe that useful and reliable knowledge can be obtained even from completely uncertain things. Under special circumstances, it is unpredictable whether the coin toss is heads or tails. However, after a large number of these unpredictable experiments, it is quite reliable to draw the conclusion that coin toss is a common phenomenon (the number of heads up is roughly equal to the number of tails up). Two centuries later, Maxwell and other mathematical physicists applied this idea to the theory of matter and drew important results from the blind, random and completely unpredictable motion of a single atom. Pascal is also engaged in the study of physics. When he studied fluid, he pointed out that the pressure acting on the fluid in a noisy container was transmitted to the whole fluid undiminished, and it acted vertically on all the interfaces it contacted. This is the so-called Pascal principle, which forms the basis of hydraulic press. Pascal once described the hydraulic press in theory. In the liquid container, if the small piston is pressed down; You can push the big piston upward in another part of the container. The ratio of the force pushing the big piston upward to the force pressing the small piston downward is equal to the ratio of the cross-sectional area of the big piston to the cross-sectional area of the small piston. The increase in force is due to the fact that the small piston moves a much larger distance than the large piston. Just like Archimedes' lever, the force multiplied by the distance on both sides is equal. In fact, the hydraulic press is also a lever. Pascal was also interested in Torricelli's new ideas about the atmosphere. If the atmosphere has weight, the weight will decrease with the increase of height, because the higher your position, the less air there is above you. The reduction of atmospheric weight can be measured by barometer. Pascal suffers from chronic diseases, indigestion, headache (autopsy proves that his skull is deformed), and insomnia keeps tormenting him, so he thinks he can't climb the mountain by himself. But in 1646, he sent his strong in-laws with two barometers to climb the hillside of Dom Mountain, which is close to Pascal's birthplace. At a height of about a mile, the mercury column dropped by three inches. He repeated the experiment five times and confirmed that Torricelli's point of view was correct (though Descartes expressed doubts). It also shows that there is a vacuum above the atmosphere, which also denies Descartes' argument that there is a vacuum and the whole space is full of matter. Pascal also repeated Torricelli's original experiment, using red wine instead of mercury. Because red wine is lighter than water, Pascal used a 46-foot tube to hold enough liquid to balance the weight of the atmosphere. During his climbing years, Pascal was influenced by Ransen Sect (a Catholic Sect that strongly opposed the Jesuits). 1654, once his horse ran away and almost died. He interpreted it as evidence of God's displeasure, so he changed religion more resolutely, which prompted him to devote the rest of his short life suffering from illness to meditation, asceticism and religious works, including his famous Pensees. These works were brilliant and inspired Voltaire, but he studied for distraction except 1658 toothache for a week, and quickly solved a geometry neatly. In his later years, Pascal declared that reason was not enough to understand the material universe, and returned to Thales. Jean Baptiste Joseph Fourier (1768 ~1830) was born in a tailor's family in Oszer, central France. Orphaned at the age of 8, he studied in a local military academy. 1795 served as an assistant professor at the Paris Polytechnic University. 1798 went on an expedition to Egypt with Napoleon's army, which was highly valued by Napoleon. After returning to China, he was appointed as the governor of Grenoble Province. 18 17 was elected as an academician of the Paris Academy of Sciences, and 1822 became a lifelong secretary of the Academy of Sciences. Fourier Drought wrote a basic paper on heat conduction in 1807, but it was rejected by the Academy of Sciences after being reviewed by Lagrange, Laplace and Legendre. 18 1 1 submitted a revised paper and won the Academy Award, but it was not officially published. 1822, Fourier finally published the monograph "Analysis Theory of Heat" (Theorieana1YTIQUEDelacha1EUR, Didot, Paris, 1822). This classic book developed the trigonometric series method applied by Euler and Bernoulli in some special cases into a rich general theory, and trigonometric series was later named after Fourier. Fourier uses trigonometric series to solve the heat conduction equation, and in order to deal with the heat conduction problem in infinite region, the so-called "Fourier integral" is derived, which greatly promotes the study of boundary value problems of partial differential equations. But the significance of Fourier work goes far beyond this, which forces people to revise and popularize the concept of function, especially the discussion of discontinuous function; The convergence of trigonometric series stimulated the birth of set theory. Therefore, "thermal analysis theory" has influenced the process of analytical rigor in the whole19th century. Pythagoras Pythagoras (about 580 -500 BC) was an ancient Greek philosopher, mathematician and astronomer. He founded a secret society of politics, religion and mathematics-Pythagoras School in Crotone, southern Italy. They attach great importance to mathematics and try to explain everything with mathematics. Pythagoras himself is famous for discovering Pythagoras theorem (called Pythagoras theorem in the west). In fact, Babylonians and China knew this theorem for a long time, but the earliest proof can be attributed to Pythagoras school. The school also found that if it is odd, it constitutes three sides of a right triangle, which is actually what we call Pythagoras number. This school divides natural numbers into several categories: odd number, even number, perfect number (that is, the number equal to the sum of all its factors including 1 but excluding itself), relative number, triangular number (1, 3, 6, 10 ...) and square number (1, 4). They also discovered five regular polyhedrons, which made many contributions to astronomy and music theory. His thoughts and theories have a great influence on Greek culture. The 20th century is coming to an end, and the 2 1 century is coming. When we look back on the brilliant development of science and technology in the 20th century, we cannot but mention von Neumann, one of the most outstanding mathematicians in the 20th century. As we all know, the electronic computer invented by 1946 has greatly promoted the progress of science and technology. It greatly promoted the progress of social life. In view of von Neumann's key role in the invention of electronic computers, he is praised by westerners as "the father of computers". Johnvonnouma (1903-1957), a Hungarian American, was born on February 28th,1903. His family is very rich and attaches great importance to children's education. Von Neumann was brilliant since he was a child, with a wide range of interests, and he was obsessed with reading. It is said that he was able to chat with his father in ancient Greek at the age of 6 and mastered seven languages in his life. He is best at German, but when he thinks about ideas in German, he can translate them into English at the speed of reading. He can quickly repeat the contents of books and papers he has read word for word, and still do so a few years later. 1911-1921von Neumann made his mark when he was studying in Lu Se Lun Middle School in Budapest, and was highly valued by teachers. Under the individual guidance of Mr Fichte, he co-published his first mathematical paper. At this time, von Neumann was less than 18 years old. 192 1- 1923, he studied at the University of Zurich. Soon after, he got a doctorate in mathematics from Budapest University with 1926. Von Neumann was only 22 years old at this time .30438+0927. 1930, he accepted the position of visiting professor at Princeton University and went to the United States. 193 1 became a tenured professor of the school. 1933 transferred to the Institute of Advanced Studies of our school and became one of the first six professors. He has worked there all his life. Von Neumann is an honorary doctor of Princeton University, University of Pennsylvania, Harvard University, Istanbul University, University of Maryland, Columbia University and Munich Institute of Advanced Technology. He is a member of the National Academy of Sciences of the United States, the National Academy of Natural Sciences of Peru and the National Forestry Institute of Italy. From 1938 to 0954, he was a member of the American Atomic Energy Commission. From 195 1 to 1953, he was the president of the American Mathematical Society. 1954 In the summer, von Neumann was diagnosed with cancer and died in Washington on February 8, 1957 at the age of 54. Von Neumann has done pioneering work in many fields of mathematics. Mainly engaged in operator theory, nose theory, set theory and other aspects of research. 1923' s paper on over-limit ordinal number in set theory shows von Neumann's unique way and style of dealing with set theory. He axiomatized set theory, and his axiomatic system laid the foundation of axiomatic set theory. Starting from axioms, many important concepts, basic operations and important theorems in set theory are derived by algebraic methods. Especially in a paper in 1925, von Neumann pointed out that there are undecidable propositions in any axiomatic system. 1933, von Neumann solved Hilbert's fifth problem. It is proved that local Euclidean compact groups are Lie groups. 1934, he unified the compact group theory and Bohr's almost periodic function theory. He also has a deep understanding of the structure of general topological groups, and clearly points out that its algebraic structure and topological structure are consistent with real numbers. He did pioneering work in his subalgebra, but he didn't define its theoretical basis. Thus, a new branch of mathematics, operator algebra, is established. This branch is called von Neumann algebra in contemporary mathematical literature. This is a natural extension of matrix algebra in finite dimensional space. Von Neumann also founded another important branch of modern mathematics-game theory. 1948+0944 published a fundamental and important paper Game Theory and Economic Behavior. This paper includes the explanation and practice of pure mathematical form of game theory. This paper also contains teaching ideas such as statistical theory. Von Neumann has done important work in lattice theory, continuous geometry, theoretical physics, dynamics, continuum mechanics, meteorological calculation, atomic energy and economics. Von Neumann's greatest contribution to mankind is his pioneering work in computer science, computer technology and numerical analysis. Now it is generally believed that ENIAC is the first electronic computer in the world, which was developed by American scientists. February 1946 started operation in Philadelphia. In fact, the "Crosas" computer developed by British scientists Tommy and Fei Rauls is more than two years earlier than ENIAC computer. It started running in blakely Park on February1944+1October 10. ENIAC computer proves that electronic vacuum technology can be used. (2) It is controlled by the wiring board, and even needs a meeting day, so the calculation speed is offset by this work. Moakley and eckert of ENIAC Machine Development Group obviously felt this, and they also wanted to start developing another computer as soon as possible, so as to improve it. After von Neumann was introduced by Captain Golds Ding of ENIAC Machine Development Group to join ENIAC Machine Development Group, he led this group of innovative young scientific and technological personnel. March towards a higher goal. 1945, on the basis of discussion, they published a brand-new "stored program general electronic computer scheme"-edvac (abbreviation of electronic discrete variable automatic computer). In this process, von Neumann showed his rich basic knowledge of mathematics and physics, and gave full play to his advisory role and his ability to explore problems and analyze comprehensively. The EDVAC scheme clearly establishes that the new machine consists of five parts: arithmetic unit, logic control device, memory and input and output equipment, and describes the functions and relationships of these five parts. There are two remarkable improvements to the EDVAC machine, namely, (65438+) (2) When establishing a stored program, instructions and data can be put together in the memory and processed in the same way, which simplifies the structure of the computer and greatly improves the speed of the computer. 1In July and August, 1946, when von Neumann, Goldstein and Boxes developed IAS computers for the Institute of Advanced Studies of Princeton University on the basis of the EDVAC scheme, they also put forward a more perfect design report and made a preliminary study on the logical design of electronic computers. The above two documents with both theory and concrete design set off a "computer craze" all over the world for the first time. Their comprehensive design idea is the famous "von Neumann Machine", and its center is the principle of stored programs-instructions and data are stored together. This concept is called "a milestone in the history of computer development". It marks the real beginning of the electronic computer era and guides the future computer design. Naturally, everything is always developing. With the progress of science and technology, today people realize that the deficiency of "von Neumann Machine" hinders the further improvement of computer speed, and put forward the idea of "non-von Neumann Machine". Von Neumann also actively participated in the popularization and application of computers, and made outstanding contributions to how to write programs and engage in numerical calculation. Von Neumann was awarded to the United States on 1937. 1947 won the US Presidential Medal of Meritorious Service and the US Navy Outstanding Citizen Service Award; 1956 was awarded the Medal of Freedom, Einstein Memorial Award and Fermi Award by the President of the United States. After von Neumann's death, his unfinished manuscript was published in the name of computer and human brain in 1958. His major works were included in the Complete Works of von Neumann in six volumes and published in 19 1. Thales disdained the family's political status and the prosperity of economic life, but devoted all his energy to the study of philosophy and science. When he was young, he traveled around the world and went to the country of pyramids, where he learned astronomical observation and geometric measurement. I have also been to Babylon in the two river basins and learned a lot about the splendid culture of the East. After returning to his hometown of Miletus, he founded the Austrian School, which became the first of the seven famous schools in ancient Greece. Thales is known as "the father of science". Thales famously said, "Water is the source of all things, and all things eventually return to water." He denied the view that God created everything and created a correct way to know the world from the world itself. In science, he advocates rationality, is not satisfied with intuitive and perceptual expertise, and advocates abstract and rational general knowledge. For example, two isosceles triangles with equal base angles do not refer to a single isosceles triangle we can draw, but to "all" isosceles triangles. This requires argumentation and reasoning to ensure the correctness of mathematical propositions, so that mathematics is rigorous in theory and widely used. Thales' active advocacy laid the foundation for Pythagoras to establish rational mathematics. Thales found many theorems of plane geometry in mathematics, such as "the diameter bisects the circle", "the angles between two sides of a triangle are equal", "two straight lines intersect and the vertex angles are equal", "the two angles and their sides of a triangle are known, and the triangle is completely determined", and "the angle of the circle opposite to a semicircle is a right angle" and so on. Although these theorems are simple, the ancient Egyptians and Babylonians may have known them for a long time, Thales adopted them. It is said that he can use a benchmark to measure and calculate the height of the pyramid. Thales also made extraordinary achievements in astronomy. It is said that he detected a total solar eclipse on May 28th, 585 BC. At that time, during the war, Thales announced to the world that if there was no truce, the gods would be angry! By that afternoon, the two factions of soldiers were still fighting fiercely. In an instant, the sun disappeared in the sky, the stars flashed and the earth was dark. When the soldiers of both sides saw this scene, they were really furious and wanted to punish mankind, so they immediately stopped fighting, forged swords into plowshares and lived in harmony. According to another legend, Thales is obsessed with studying philosophy and science. He is poor and conservative, so he is laughed at by the public. He said disapprovingly that a gentleman loves money and takes it wisely. On the basis of climate prediction, he estimated that there would be a bumper harvest of oil crops in the coming year, so he monopolized all oil mills in Miletus and Caius and rented them at high prices in the current season. With money, scientific research can be done better. If these two legends are true, Thales really deserves the eulogy engraved on his tombstone: "He is a saint and an astronomer. In the kingdom of the sun, the moon and the stars, he is indomitable and immortal. " However, this is also a legend, because Thales lives too far away from us and has no exact and reliable information.