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.
Goldbach, the son of a priest, studied medicine and mathematics at the University of Konigsberg. 17 10 travel around Europe (this is a way that people with conditions often take to increase their experience). 1725 settled in Russia and became a professor of mathematics at the Royal Academy of Sciences in St. Petersburg. 1728 was a court teacher of Peter Alekseyevich Romanov (the grandson of Peter the Great), who died young.
Goldbach is famous in mathematics because he mentioned the so-called "Goldbach conjecture" in a letter to Euler from 65438 to 0742. (Goldbach often wrote letters to mathematicians at that time) This conjecture is that "any even number greater than 2 can be expressed as the sum of two prime numbers." For example, 4 = 2+2; six
=3+3; 8 = 3 15; 10=3+7: 12=5+7; Wait a minute. Mathematicians have actually verified some even numbers as large as 10.000 or even larger, and found that this conjecture is correct. No one expects to find exceptions. But the problem is that for more than two centuries, no mathematician has been able to prove this conjecture.
Why can't such a simple and obviously correct fact be proved? This is one of the setbacks suffered by mathematicians.
4. Hua (19 10~ 1985), mathematician, academician of China Academy of Sciences. 191010 65438 was born in Jintan, Jiangsu province, and 1985 12 died in Tokyo, Japan.
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.
Liu Hui (born around 250 AD) is a very great mathematician in the history of Chinese mathematics and occupies a prominent position in the history of world mathematics. His representative works "Nine Arithmetic Notes" and "Calculation on the Island" are the most precious mathematical heritages of China.
Zu Chongzhi (AD 429-500) was born in Laiyuan County, Hebei Province during the Northern and Southern Dynasties. He has read many books on astronomy and mathematics since he was a child, and he is diligent and eager to learn.
Practice finally made him an outstanding mathematician and astronomer in ancient China.
6. Zu Chongzhi's outstanding achievement in mathematics is about the calculation of pi. On the basis of predecessors' achievements, Zu Chongzhi worked hard and calculated repeatedly, and found that π was between 3. 14 15926 and 3. 14 15927.
The approximate value in the form of π fraction is obtained as the reduction rate and density rate, where the six decimal places are 3. 14 1929, which is the closest fraction to π value in the denominator of 1000.
7. Chen Jingrun (1933.5~ 1996.3) is a modern mathematician in China. 1933 was born in Fuzhou, Fujian on May 22nd. 1953 graduated from the Mathematics Department of Xiamen University. Because he is interested in Tali.
One result of the problem has been improved, which has attracted the attention of China. Transferred to Institute of Mathematics, Chinese Academy of Sciences, worked as an intern researcher and assistant researcher first, and then was promoted.
He was promoted to researcher and elected as a member of the Department of Mathematical Physics of China Academy of Sciences.
Chen Jingrun is one of the world famous analytic number theorists. In 1950s, he studied the predecessors' achievements of Gauss circle inner lattice point problem, sphere inner lattice point problem, Tali problem and Waring problem.
Important improvements have been made. After 1960s, he made extensive and in-depth research on screening methods and related important issues.
Newton (Newton 1643- 1727) Newton is one of the most influential scientists on earth.
1. Discovering binomial Theorem
1665, Newton, who was only 22 years old, discovered the binomial theorem, which is an essential step for the all-round development of calculus. The binomial theorem is based on energy.
The binomial series expansion found by calculation is a powerful tool for learning series theory, function theory, mathematical analysis and equation theory. Today we will find that this method only applies to.
When n is a positive integer, when n is a positive integer 1, 2, 3, ..., the series ends at n+ 1 If n is not a positive integer, the series will not end, which
This method is not applicable. But we should know that Leibniz introduced the word function in 1694, which was used to study transcendental functions in the early stage of calculus.
Their horizontal treatment is the most effective method.
2. Create calculus
Newton's most outstanding achievement in mathematics was the creation of calculus. His achievement beyond his predecessors is that he unified all kinds of special skills to solve infinitesimal problems since ancient Greece into two.
Differential and integral are commonly used algorithms, and the reciprocal relationship between these two operations is established. For example, area calculation can be regarded as the inverse process of tangent. At that time, Leibniz had just put forward the research report of calculus, which triggered the debate on the patent right of calculus invention until Leibniz's death. Future generations believe that
Differential products were invented by them at the same time.
In the method of calculus, Newton's extremely important contribution is that he not only clearly saw, but also greatly used the method provided by algebra which is much superior to geometry.
Open. He replaced the geometric methods of cavalieri, Gregory, Huygens and Barrow with algebraic method, and completed the algebra of integral. Since then, mathematics has gradually changed from studying feelings to studying feelings.
The subject turns to the subject of thinking. In the early days of micro-products, they were used by people with ulterior motives because they did not establish a solid theoretical foundation. What's more, it caused the famous
The second mathematical crisis. This problem was not solved until the limit theory was established in19th century.
3. Introduce polar coordinates and develop cubic curve theory.
Newton made a profound contribution to analytic geometry. He is the founder of polar coordinates. The first one studied the high-order plane curve extensively. Newton proved how
Generally, the curves expressed by cubic equations are all transformed into one of the following four forms through the transformation of scale axis: In the book Cubic Curves, Newton listed the possible cubic curves.
72 out of 78 forms. These are the most attractive;
The most difficult thing is: just as all curves can be projected as the center of a circle; All cubic curves can be used as curves:
The center of the projection. This theorem was a mystery until 1973 was proved.
Newton's cubic curve laid the foundation for studying higher plane straight lines, and expounded the importance of asymptotes, nodes and points. Newton's work on cubic curves inspired the study of cubic curves.
Many other research work on high-order plane curves.
4. Advance equation theory and develop variational method.
Newton also made a classical contribution to algebra, and his generalized arithmetic greatly promoted the theory of equations. He found that the imaginary roots of real polynomials must appear in pairs, so he required polynomials.
The upper bound rule of roots, he uses the coefficients of polynomials to express the sum formula of the n-th square roots of polynomials, and gives a Cartesian sign rule about the limitation of the number of imaginary roots of real polynomials.
Promotion.
Newton also designed a method to find the logarithm of the approximate values of the real roots of numerical equations and transcendental equations. The modification of this method is now called Newton method.