Modern mathematics is a studynumber、structure、change、spaceas well asinformationetc.conceptA subject of.In the 17th century, mathematics developed by leaps and bounds, realizing the transition from constant mathematics to variable mathematics.The study of modern mathematics in China began in 1919the May 4th MovementIt really started in the future.
1919the May 4th MovementLater, the study of modern Chinese mathematics began.The development period of modern mathematics is a period from the beginning of the 20th century to the present. It is often divided into two stages marked by the founding of New China in 1949.
Feng Zuxun, who studied in Japan for nearly three years, Zheng Zhifan, who studied in the United States in 1908, Hu Mingfu and Zhao Yuanren, who studied in the United States in 1910, Jiang Lifu, who studied in the United States in 1911, He Lu, who studied in France in 1912, Chen Jiangong, who studied in Japan in 1913, and Xiong Qinglai, who studied in Belgium (who transferred to France in 1915), Su Buqing, who studied in Japan in 1919, and others.Most of them became famous mathematicians and mathematical educators after returning home, making important contributions to the development of modern mathematics in China.Hu Mingfu obtained it in 1917Harvard UniversityHe became the first Chinese mathematician to obtain a doctor's degree.With the return of overseas students, mathematics education in universities around the country has improved.
At first, only the Department of Mathematics of Peking University was established in 1912. In 1920, Jiang Lifu established the Department of Mathematics of Nankai University in Tianjin. In 1921 and 1926, Xiong Qinglai established the Department of Mathematics of Southeast University (now Nanjing University) and Tsinghua University respectively. Soon, Wuhan University, Qilu University, Zhejiang University, and Sun Yat sen University successively established the Department of Mathematics,By 1932, 32 universities had established departments of mathematics or mathematics and physics.
In 1930, Xiong Qinglai initiated the Mathematics Research Department at Tsinghua University and began to recruit graduate students. Chen Shengshen and Wu Daren became the first mathematics graduate students in China.
In the 1930s, Jiang Zehan (1927), Chen Shengshen (1934), Hua Luogeng (1936), Xu Baoxuan (1936) and others went abroad to study mathematics. They all became the backbone of the development of modern mathematics in China.At the same time, foreign mathematicians also gave lectures in China, such as Russell (1920) of Britain, Berkhov (1934), Osgood (1934), Wiener (1935) of the United States, Adama (1936) of France, etc.
In 1935, the founding meeting of the Chinese Mathematical Society was held in Shanghai, and 33 representatives attended.
In 1936, the Journal of the Chinese Mathematical Society and the Journal of Mathematics were published one after another, which marked the further development of modern mathematical research in China.
Before liberation, mathematical research focused on pure mathematics, and more than 600 kinds of theories were published at home and abroad.
In terms of analysis, Chen Jiangong's trigonometric series theory, Xiong Qinglai's meromorphic function and whole function theory are representative works, as well as functional analysis, variational method, differential equation and integral equation;
In number theory and algebra,Hua Luogengbest-known Chinese mathematicianHis research on analytic number theory, geometric number theory, algebraic number theory and modern algebra has made remarkable achievements;
In geometry and topology, Su Buqing's differential geometry, Jiang Zehan's algebraic topology, Chen Xingshen'sFiber bundle theoryandIndicator class theoryAnd other researchers have done pioneering work:
In terms of probability theory and mathematical statistics, Xu Baoxuan has obtained many basic theorems and rigorous proofs in monistic and multivariate analysis.
In addition, Li Yan and Qian Baocong initiated the study of the history of Chinese mathematics, and they did a lot of groundbreaking work in the annotation, collation, textual research and analysis of ancient mathematical historical data, which madeNational cultural heritageLet it shine again.
The Chinese Academy of Sciences was established in November 1949.
In March 1951, the Journal of Chinese Mathematics was republished (changed to the Journal of Mathematics in 1952)
In October 1951, the Chinese Journal of Mathematics was republished (changed to Mathematics Bulletin in 1953).
In August 1951, the Chinese Mathematics Society held its first meeting since the founding of the People's Republic of ChinaNational CongressThe development direction of mathematics and the reform of mathematics teaching in various schools are discussed.In the early 1950s, he published Hua Luogeng's Theory of Stacked Prime Numbers (1953), Su Buqing's Introduction to Projective Curves (1954), Chen Jiangong's Sum of the Series of Right Angle Functions (1954), Li Yan's Essays on the History of Chinese Computing (5 series, 1954-1955) and other monographs. By 1966, he had published about 20000 mathematical papers.In addition to continuing to make new achievements in such disciplines as number theory, algebra, geometry, topology, function theory, probability theory and mathematical statistics, and mathematical history, breakthroughs have also been made in such branches as differential equations, computing technology, operations research, mathematical logic, and mathematical foundations. Many of the works have reached the world's advanced level, and a large number of outstanding mathematicians have been cultivated and grown up.
In the late 1960s, China's mathematical research basically stopped, education was paralyzed, personnel were lost, and foreign exchanges were interrupted. After many efforts, the situation changed slightly.
In 1973, Chen Jingrun published a paper entitled "A big even number is expressed as a prime number and the sum of the products of a prime number that does not exceed two prime numbers" in Science in China, which made outstanding achievements in the research of Goldbach conjecture.In addition, Chinese mathematicians in the field of function theorymarkov process , probability application, operational research, optimization method, etc.
In November 1978, the Chinese Mathematics Society held the third congress, marking the recovery of Chinese mathematics.
In 1978, the National Mathematical Competition was resumed, and in 1985, China began to participate in the International Mathematical Olympiad Mathematical Competition.
In 1981, Chen Jingrun and other mathematicians won the National Natural Science Award.In 1983, the country first awarded 18 young and middle-aged scholars with doctoral degrees, of which 2/3 were mathematics workers.
In 1986, China sent its first representative to the International Conference of Mathematicians and joined the International Mathematical Union. Wu Wenjun was invited to give a 45 minute speech on the history of ancient Chinese mathematics.In recent decades, mathematical research has yielded fruitful results. The number of published papers and monographs has doubled and the quality has been rising.
At the annual meeting to celebrate the 50th anniversary of the founding of the Chinese Mathematical Society in 1985, the long-term goal of the development of mathematics in China was set.The delegates are determined to make unremitting efforts to make China a new mathematical power in the world at an early date.
Discipline establishment
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Modern mathematics
1. In the 17th century, mathematics developed by leaps and bounds, realizing the transition from constant mathematics to variable mathematics.
2. French scholarsDescartes Analytic geometry was founded, and variables were introduced into mathematics, which became a turning point in mathematics.
3. British scientist Newton and German mathematicianLeibnizCalculus has been independently established, which makes it possible for precise measurement and variable calculation.
4. After the invention of analytic geometry, mathematics entered a new field with variables as the main research object, called "advanced mathematics".
Development difficulties
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Four colour conjecture
The four color conjecture came from Britain.In 1852, when Fernandes Guthrie, who graduated from London University, came to a scientific research unit to do map coloring work, he found an interesting phenomenon: "It seems that every map can be colored with four colors, making countries with common borders different colors." Can this conclusion be strictly proved mathematically?He and his brother Gris, who was studying in the university, decided to give it a try.The papers used by the brothers to prove this problem have piled up, but the research work has not progressed.
On October 23, 1852, his brother asked his teacher, the famous mathematician De Morgan, for the proof of this problem. Morgan could not find a way to solve this problem, so he wrote to his friend, the famous mathematician Sir Hamilton for advice.After receiving Morgan's letter, Hamilton demonstrated the four color problem.But until Hamilton died in 1865, the problem could not be solved.
In 1872, Kelly, the most famous mathematician in England at that time, formally raised this question to the London Mathematical Society, so the four color conjecture became a concern of the world's mathematical community.Many first-class mathematicians in the world have participated in the battle of four color conjecture.Between 1878 and 1880, the famous lawyer and mathematician Kemp and Taylor submitted papers respectively to prove the four-color conjecture and announced that they had proved the four-color theorem. Everyone believed that the four-color conjecture was solved from then on.
Eleven years later, in 1890, the mathematician Herwood pointed out that Kemp's proof was wrong with his accurate calculation.Soon, Taylor's proof was also denied.Later, more and more mathematicians have racked their brains, but nothing has been achieved.Thus, people began to realize that this seemingly easy question was actually a problem comparable to Fermat's conjecture: the efforts of the predecessors paved the way for future mathematicians to reveal the mystery of the four color conjecture.
Since the beginning of the 20th century, scientists have been basically following Kemp's ideas in proving the four-color conjecture.In 1913, Berkhov introduced some new techniques on the basis of Kemp. American mathematician Franklin proved in 1939 that maps under 22 countries can be colored in four colors.In 1950, some people promoted from 22 countries to 35 countries.In 1960, someone proved that maps under 39 countries can be colored with only four colors;Then it was promoted to 50 countries.It seems that this progress is still very slow.After the advent of electronic computers, the process of proving the four-color conjecture has been greatly accelerated due to the rapid increase of computing speed and the emergence of human-computer dialogue.In 1976, American mathematicians Apel and Haken completed the proof of the four color theorem after making 10 billion judgments in 1200 hours on two different computers at the University of Illinois.The computer proof of the four color conjecture has stirred the world.It not only solved a problem that lasted more than 100 years, but also may become the starting point of a series of new thinking in the history of mathematics.However, there are also many mathematicians who are not satisfied with the achievements of computers, and they are still looking for a simple and straightforward written proof method.
Fermat's big theorem
On June 24, 1993, the New York Times, recognized as the world's leading newspaper, published on its front page a piece of news about the solution of mathematical problems. The title of the news was "In the old mathematical dilemma, someone finally called 'I found it'".The opening article of the first page of the Times also attached a picture of a man with long hair and wearing a medieval European academic gown.This ancient man is Pierre de Fermat, a French mathematician (please refer to the appendix for his biography).Fermat was one of the most outstanding mathematicians in the seventeenth century. He made great contributions to many fields of mathematics because he was a professional lawyer. In order to commend his mathematical attainments, the world called him "amateur prince". One day more than 360 years ago, when Fermat was reading "The Arithmetic of Diophantus", he suddenly had a whim in the blank of the page,Write down a theorem that seems very simple: when the integer n ≥ 3, there is no satisfying xn+yn= znThe positive integer solution of.At that time, Fermat did not explain the reason, he just left this statement and said that he had found the magic method of proving the theorem, but the blank space on the page was not enough to write down.Fermat, the originator, also left an eternal problem. For more than 300 years, countless mathematicians have tried to solve this problem in vain.The Fermat's big theorem, which is known as the problem of the century, has become a major problem in the mathematical world, and is eager to solve it soon.
In the 19th century, the French Academy of Mathematics offered gold medals and three hundred francs to anyone who solved this problem twice in 1815 and 1860. Unfortunately, no one could receive a reward.In 1908, German mathematician Wolfsker provided 100000 marks to the person who can prove that Fermat's big theorem is correct. The validity period is 100 years.During this period, due to the Great Depression, the amount of this prize has been devalued to 7500 marks, which still attracts many "math enthusiasts".
After the development of computers in the 20th century, many mathematicians can prove this theorem when n is large by computer calculation. In 1983, computer expert Slovinsky proved that Fermat's theorem is correct when n is 286243-1 by computer running for 5782 seconds (note 286243-1 is an astronomical number, about 25960 digits).Nevertheless, mathematicians have not yet found a proof of universality.However, this 300 year old mathematical unsolved problem was finally solved by the British mathematician Andrew Wiles.In fact, Willis used the results of the development of abstract mathematics in the past three decades of the twentieth century to prove it.In the 1950s, Japanese mathematician Tanyama Feng first proposed a conjecture about the emergence of ellipses, which was later carried forward by another mathematician, Takero Shimura. At that time, no one thought that this conjecture had any connection with Fermat's big theorem.In the 1980s, the German mathematician Friedrich Friedrich Friedrich Friedrich combined Gushanfeng's conjecture with Fermat's theorem, and what Willis did was to prove that a form of Gushanfeng's conjecture was correct according to this association, and it was also correct to deduce Fermat's big theorem.This conclusion was officially published by Willis at the seminar of Newton Institute of Mathematics, Cambridge University, USA on June 21, 1993. This report immediately shocked the whole mathematical world, even the public outside the mathematical door also paid infinite attention to it.However, Willis' certificate was immediately found to have a few flaws, so Willis and his students spent another 14 months to correct it.On September 19, 1994, they finally handed over a complete and flawless solution, and the nightmare of the mathematical world finally ended.In June 1997, Willis received the Folfskell Prize at the University of Gottingen in Germany.The 100000 mark in that year was about two million dollars, but when Willis received it, it was only worth about 50000 dollars.But he has been listed in the history of history and will never die.To prove Fermat's big theorem is correct, we only need to prove xfour+ yfour=zfourAnd xp+ yp=zp(p is an odd prime number), there is no positive integer solution.
Goldbach conjecture
Goldbach was a middle school teacher in Germany and a famous mathematician. He was born in 1690 and was elected an academician of the Russian Petersburg Academy of Sciences in 1725.In 1742, Goldbach found in his teaching that every even number not less than 6 is the sum of two prime numbers (numbers that can only be divided by itself).For example, 6=3+3, 12=5+7, etc.On June 7, 1742, Goldbach wrote to Euler, an Italian mathematician, and asked him to help prove it.In his reply to him on June 30, Oula said that he believed that the conjecture was correct, but he could not prove it.Even Euler, a leading mathematician, could not prove such a simple problem. This conjecture has attracted the attention of many mathematicians.They began to check the even numbers one by one until they reached 330 million, which showed that the conjecture was correct.But for larger numbers, the conjecture should also be correct, but it cannot be proved.Euler could not prove it until his death.Since then, this famous mathematical problem has attracted the attention of thousands of mathematicians in the world.200 years later, no one succeeded.Goldbach conjecture thus became an unreachable "pearl" on the crown of mathematics.In the 1920s, people began to approach it.In 1920, the Norwegian mathematician Bujue proved with an ancient screening method and reached a conclusion that every even number with a greater ratio can be expressed as (99).This method of narrowing the encirclement circle worked very well, so scientists began from (9+9), gradually reducing the number of prime number factors contained in each number until finally making each number a prime number, thus proving "Goldbach".In 1924, mathematician Radmahal proved that (7+7);In 1932, mathematician Eisman proved that (6+6);In 1938, the mathematician Buhstab proved (55), and in 1940, he proved (4+4);In 1956, mathematician Vinogradov proved that (3+3);In 1958, Chinese mathematician Wang Yuan proved (23).Later, Chen Jingrun, a young mathematician in China, also devoted himself to the study of Goldbach conjecture. After 10 years of hard research, he finally made a major breakthrough on the basis of previous studies, and took the lead in proving (l2).So far, Goldbach's conjecture has only one last step (1+1) left.Chen Jingrun's paper was published in the 17th issue of the Science Bulletin of the Chinese Academy of Sciences in 1973. This achievement has attracted the attention of the international mathematical community, which has made China's number theory research take the lead in the world. Chen Jingrun's related theory is called "Chen's theorem".In late March 1996, when Chen Jingrun was about to take off the pearl on the crown of mathematics, "when he was only a few feet away from the glorious peak of Goldbach's conjecture (1+1), he collapsed..." Behind him, more people would climb the peak.
