Born in Athens, eucild accepted Greek classical mathematics and various scientific cultures, and became a famous scholar at the age of 30. At the invitation of the king of Egypt, he stayed in Alexandria to teach and do research.

Mathematics research in ancient Greece has a very long history, and there have been some works on geometry, but all of them discuss a certain aspect and the content is not systematic enough. Euclid collected predecessors' achievements and adopted an unprecedented and unique writing method. First, he put forward definitions, axioms and postulates, then proved a series of theorems from simple to complex, and discussed plane figures and three-dimensional figures, as well as integers, fractions and proportions. , finally completed the masterpiece "Geometry".

After the publication of the original, its manuscript has been circulated for 1800 years. After 1482 was printed and published, it was reprinted about 1000 times, and it was also translated into major languages in the world. /kloc-was introduced to China in the 3rd century and soon lost. The first six volumes were retranslated in 1607, and the last nine volumes were retranslated in 1857.

Euclid was good at solving complex problems with simple methods. He measured the length of the shadow of the pyramid at the moment when the figure of a person was just equal to the height, and solved the big problem of the height of the pyramid that no one could solve at that time. He said: "At this time, the length of the tower shadow is the height of the pyramid."

Euclid was a gentle and honest educator. Euclid was also a rigorous scholar. He opposes opportunism and the pursuit of fame and fortune in his studies, and the style of opportunism and quick success. Although Euclid simplified his geometry, the king (Ptolemy) still didn't understand and wanted to find a shortcut to learn geometry. Euclid said: "In geometry, everyone can only take one road, and there is no paved road for the king." This sentence has become an eternal learning motto. Once, one of his students asked him, what are the benefits of studying geometry? He said humorously to his servant, "Give him three coins because he wants to get real benefits from his study."

Euclid also wrote the known number and division of numbers.

Hua

Hua, a mathematician, is an academician of China Academy of Sciences. 191010 65438 was born in Jintan, Jiangsu province, and 1985 12 died in Tokyo, Japan.

1924 graduated from Jintan middle school and studied hard. 1930, taught in Tsinghua University. 1936 Visiting study at Cambridge University, UK. 1938 became a professor in The National SouthWest Associated University after returning to China. From 65438 to 0946, he went to the United States and served as a researcher at Princeton Institute of Mathematics, a professor at Princeton University and the University of Illinois, and returned to China from 65438 to 0950. He has served as Professor Tsinghua University, director and honorary director of Institute of Mathematics and Institute of Applied Mathematics of China Academy of Sciences, chairman and honorary chairman of Chinese Mathematical Society, director of National Mathematical Competition Committee, foreign academician of American National Academy of Sciences, academician of Third World Academy of Sciences, academician of Bavarian Academy of Sciences of the Federal Republic of Germany, deputy director, vice president and presidium member of physics department, mathematics and chemistry of China Academy of Sciences, director and vice president of mathematics department of China University of Science and Technology, vice chairman of China Association for Science and Technology, and member of the State Council Academic Degree Committee. He was a member of the first to sixth the NPC Standing Committee and vice-chairman of the sixth China People's Political Consultative Conference. He was awarded honorary doctorates by Nancy University in France, The Chinese University of Hong Kong and the University of Illinois in the United States. Mainly engaged in the research and teaching of analytic number theory, matrix geometry, typical groups, automorphic function theory, multiple complex variable function theory, partial differential equations, high-dimensional numerical integration and other fields, and has made outstanding achievements. In the 1940s, the historical problem of Gaussian complete trigonometric sum estimation was solved, and the best error order estimation was obtained (this result is widely used in number theory). The results of G.H. Hardy and J.E. Littlewood on the Welling problem and E. Wright on the Tully problem have been greatly improved and are still the best records.

In algebra, the basic theorem of one-dimensional projective geometry left over from history for a long time is proved. This paper gives a simple and direct proof that the normal child of an object must be contained in its center, which is Hua theorem. His monograph "On Prime Numbers of Pile Foundations" systematically summarizes, develops and perfects Hardy and Littlewood's circle method, vinogradov's triangle sum estimation method and his own method. Its main achievements still occupy the leading position in the world after more than 40 years of publication, and have been translated into Russian, Hungarian, Japanese, German and English, becoming one of the classic works of number theory in the 20th century. His monograph "Harmonic Analysis on Typical Fields of Multiple Complex Variables" gives the complete orthogonal system of typical fields with accurate analysis and matrix skills, combined with group representation theory, and thus gives the expressions of Cauchy and Poisson kernel. This work has a wide and deep influence on harmonic analysis, complex analysis and differential equations, and won the first prize of China Natural Science Award. Advocating the development of applied mathematics and computer, he has published many works such as Master Planning Method and Optimization Research, which have been popularized in China. In cooperation with Professor Wang Yuan, he has made important achievements in the application research of modern number theory methods, which is called "Hua Wang Fa". He made great contributions to the development of mathematics education and the popularization of science. He has published more than 200 research papers and dozens of monographs and popular science works.

Miletus is the most prosperous city in Ionia, located at the crossroads of east-west traffic. It is also the hometown of Thales, the first world-renowned scholar in ancient Greece (about 640-546 BC). Thales was a businessman in his early years, and later traveled to Babylon, Egypt and other places, and soon learned astronomy and geometry.

In the early stage of the development of natural science, it has not been separated from philosophy. So every mathematician is a philosopher, just as every mathematician in China is a historian. To understand the relationship between man and nature and man's position in the universe, we must first learn mathematics, because mathematics can help people find order in chaos and draw laws according to logical reasoning.

Thales is recognized as the originator of Greek philosophers. He founded the philosophy of Ionian school, got rid of religion, sought truth from natural phenomena, and denied that God was the master of the world. He believes that there is life and movement everywhere, and water is the source of all things. Thales has a high reputation and is considered to be the first of the seven sages of Greece.

Thales' epoch-making contribution to mathematics began to prove the proposition. The advice he got was simple. For example, a circle is equally divided by any diameter; The two base angles of an isosceles triangle are equal; Two straight lines intersect and the vertex angles are equal; Similar triangles are proportional to the corresponding sides; The circumferential angle on the semicircle is a right angle; If two angles of two triangles correspond to one side, the two triangles are congruent, and these propositions are proved.

Thales has been to many places. When he was in Egypt, he used similar triangles's principle to measure the height of the pyramids, which surprised Egyptian Pharaoh Amhersis (Pharaoh of the 26th dynasty of Amhersis). Thales is also very proficient in astronomy. It is said that there are two countries near his hometown: Medea and Lydia. There was a fierce war one year. There was no victory or defeat for five consecutive years, and the bodies were everywhere. Thales knew in advance that there would be a solar eclipse, so he threatened that God would oppose the war, and one day he would be furious and the sun would disappear. On that day, the two armies fought fiercely, and suddenly the sun lost its luster, the birds returned to their nests, the stars flashed, and the day turned into night. The soldiers and generals of both sides were frightened, so they stopped fighting and made up. Later, the two countries exchanged marriages. According to textual research, this solar eclipse occurred on May 25th, 585 BC.

Thales is a well-deserved father of mathematics, astronomy and philosophy in ancient Greece.

Fibonacci (about 1 170- about 1250)

Italian mathematician, 12 and 13 representative figures of European mathematics. Born in Pisa, he followed his father, who was a businessman in his early years, to Buziyi (a small port in eastern Algeria) in North Africa, where he received education. Later, I traveled to Egypt, Syria, Greece, Sicily, France and other places and became familiar with the business arithmetic systems of various countries. He returned to Pisa around 1200 and devoted himself to writing.

There are five kinds of * * * in his book. The most important book is the abacus calculation book (completed by 1202 and revised by 1228). Abacus refers not only to Roman abacus or sand table, but also to general calculation.

Among them, the most intriguing thing is that the solution of indefinite equation in China's Sunzi Suanjing appeared in this book. The topic is that a number not exceeding 105 is divided by 3, 5 and 7 respectively, and the remainder is 2, 3 and 4. Find this number. The solution is the same as Sun Tzu's calculation. Another "rabbit problem" has also aroused great interest of future generations. The topic assumes that a pair of big rabbits can give birth to a pair of small rabbits every month, and the small rabbits will have reproductive ability two months after birth. How many pairs of rabbits can a pair of big rabbits breed in a year? This leads to the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 2 1, …, and its law is that each term (starting from the third term) is the sum of the first two terms. This series is closely related to the later "optimization method".

Lagrange [[Lagrange, Joseph Lewis,1736-1813]]

French mathematician.

He dabbled in mechanics and wrote analytical mechanics.

For a hundred years, mathematics is still influenced by its theory.

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 resolvents] 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 analytic masterpieces, Analytic Function Theory [1797] and Lecture Notes on Function Calculation [180 1], summarizing his series of research work in 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 thought he got rid of the concept of limit, but actually avoided it, so he didn't reach the idea of algebraic rigorous calculus. However, he adopted a new differential symbol and expressed the function as a power series, which had an impact on 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 transformation 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.

Lagrange [[Lagrange, Joseph Lewis,1736-1813]]

French mathematician.

He dabbled in mechanics and wrote analytical mechanics.

For a hundred years, mathematics is still influenced by its theory.

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 resolvents] 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 analytic masterpieces, Analytic Function Theory [1797] and Lecture Notes on Function Calculation [180 1], summarizing his series of research work in 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 thought he got rid of the concept of limit, but actually avoided it, so he didn't reach the idea of algebraic rigorous calculus. However, he adopted a new differential symbol and expressed the function as a power series, which had an impact on 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 transformation 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.