Gauss
I have heard a story in my mind: Gauss is a second-grade primary school student. One day, because his math teacher had handled more than half of the things, he still wanted to finish them even after class, so he planned to give the students a math problem to practice. His topic is:1+2+3+4+5+6+7+8+9+10. Because addition has just been taught for a long time, the teacher thinks it will take a long time for students to work it out, so that they can use this time to deal with unfinished things. But in the blink of an eye, Gauss had stopped writing and sat there doing nothing. The teacher was very angry and scolded Gauss, but Gauss said he had worked out the answer, which was 55. The teacher was shocked and asked how Gauss worked it out. I just found that the sum of 1 and 10 is the sum of1,2 and 9, 1 1, 3 and 8, 1 1, 4 and 7. And11+1+1+1+11= 55, which is how I calculated it. Gauss became a great mathematician when he grew up. When Gauss was young, he could turn difficult problems into simple ones. Of course, qualification is a big factor, but he knows how to observe, seek the law, simplify the complex, and is worth learning and emulating.
Hua, a "self-taught mathematician", was very talented in mathematics when he was a child, but his family changed, so he had to drop out of school to look after the shop and became a mathematician by self-study. ...
Gauss
I have heard a story in my mind: Gauss is a second-grade primary school student. One day, because his math teacher had handled more than half of the things, he still wanted to finish them even after class, so he planned to give the students a math problem to practice. His topic is:1+2+3+4+5+6+7+8+9+10. Because addition has just been taught for a long time, the teacher thinks it will take a long time for students to work it out, so that they can use this time to deal with unfinished things. But in the blink of an eye, Gauss had stopped writing and sat there doing nothing. The teacher was very angry and scolded Gauss, but Gauss said he had worked out the answer, which was 55. The teacher was shocked and asked how Gauss worked it out. I just found that the sum of 1 and 10 is the sum of1,2 and 9, 1 1, 3 and 8, 1 1, 4 and 7. And11+1+1+1+11= 55, which is how I calculated it. Gauss became a great mathematician when he grew up. When Gauss was young, he could turn difficult problems into simple ones. Of course, qualification is a big factor, but he knows how to observe, seek the law, simplify the complex, and is worth learning and emulating.
Hua has been struggling in the national disaster all his life. He often says that he has experienced three disasters in his life. Poor from a small family, out of school, seriously ill, and disabled in both legs. During the second disaster in War of Resistance against Japanese Aggression, it was isolated from the world and lacked reference books. The third disaster was the "Cultural Revolution". His home was searched, his hand was lost, he was forbidden to go to the library, and his assistants and students were assigned to other places. In such a harsh environment, you can imagine how much effort you have to make and how much you have achieved.
As early as 1940s, Hua was one of the leading mathematicians in the field of number theory. But he is not satisfied, he will not stop, he would rather start a new stove, leave number theory and learn algebra and complex analysis that he is not familiar with. How much perseverance and courage are needed!
Hua is good at telling profound truth in vivid language. These words are concise, philosophical and unforgettable. As early as the SO era, he proposed that "genius lies in accumulation, and cleverness lies in diligence". Although Hua is brilliant, he never mentions his own talent. Instead, he regards "diligence" and "accumulation", which are much more important than cleverness, as the key to success, and repeatedly educates young people to learn mathematics so that they can exercise themselves all the time. In the mid-1950s, in response to the problem that some young people in the Institute of Mathematics were complacent after making some achievements, or kept writing papers at the same level, Hua put forward in time: "There must be speed and acceleration." The so-called "speed" means producing results, and the so-called "acceleration" means constantly improving the quality of results. Just after the "Cultural Revolution", some people, especially young people, were influenced by bad social atmosphere, and some departments were eager for success, frequently demanding grades, evaluating bonuses and other practices that were not in line with scientific laws, which led to the corruption of the style of study. Performance for shoddy, fame and fortune, wanton boasting. 1978, he earnestly put forward at the Chengdu conference in chinese mathematical society: "Early publication, late evaluation." Later, it was further put forward: "Efforts are in me, and evaluation is in people." This actually puts forward the objective law of scientific development and scientific work evaluation, that is, scientific work can gradually determine its true value after historical test, which is an objective law that is independent of human subjective will. "
Hua never hides his weaknesses. As long as he can learn, he would rather expose them. When he visited Britain at the age of seventy, he changed the idiom "Don't teach others an axe" to "teach others an axe" to encourage himself. In fact, the previous sentence means that people should hide their shortcomings and not expose them. Did Hua go to college to get help by talking about other people's expertise, or did he turn his lectures into formalism because he was not specialized in others? Hua chose the former, that is, "wait a minute, and you will arrive at the door." As early as the 1950s, Hua compared mathematics to playing chess in the preface of Introduction to Number Theory, calling on everyone to find a master, that is, to compete with great mathematicians. There is a rule in chess in China, that is, "A gentleman does not regret watching chess without saying a word". 198 1 year, in a speech in Huainan coal mine, Hua pointed out: "Watching chess is not a gentleman, help each other; I regret the gentleman and change my shortcomings. " It means that if you see someone else's work problems, you must speak up. On the other hand, when you find something wrong with yourself, you must correct it. These are "gentlemen" and "husbands". In view of the fact that some people retreat when they encounter difficulties and lack the spirit of sticking to the end, Hua wrote on a banner for Jintan Middle School: "People cannot say that the Yellow River will not die, but I say that the Yellow River will be stronger."
When people get old, their energy will decline, which is a natural law. Hua knows that time waits for no man. 1979 when he was in England, he pointed out: "The village is old and easy to empty, and people are old and easy to disperse. The scientific approach is to abstain from empty and scattered. I am willing to stick to it all my life. " This can also be said to be his "determination book" to fight against his aging with the greatest determination, so as to spur himself. The patient with the second myocardial infarction in Hualuosuo still insisted on working in the hospital. He pointed out: "My philosophy is not to prolong life as much as possible, but to do more work during the day." If you are ill, you should listen to the doctor and have a good rest. But his indomitable spirit is still valuable.
In a word, all of Hua's expositions are permeated with a general spirit, that is, constant struggle and continuous progress.
Zu Chongzhi (429-500) had a grandfather named Zuchang, who was an official in charge of royal architecture in Song Dynasty. Zu Chongzhi grew up in such a family and learned a lot from childhood. People all praise him as a knowledgeable young man. He especially likes studying mathematics, and he also likes studying astronomical calendars. He often observes the movements of the sun and planets and makes detailed records.
When Emperor Xiaowu of Song heard of his fame, he sent him to work in a government office specializing in academic research in Hualin Province. He is not interested in being an official, but he can concentrate more on mathematics and astronomy there.
There have been officials who studied astronomy in all previous dynasties in our country. They made calendars according to the results of astronomical research. By the Song Dynasty, the calendar had made great progress, but Zu Chongzhi thought it was not accurate enough. Based on his long-term observation, he created a new calendar called "Daming Calendar" ("Daming" is the title of Emperor Xiaowu of Song Dynasty). The number of days in each tropical year measured by this calendar (that is, the time between winter and sun in two years) is only 50 seconds different from that measured by modern science; It takes less than one second to measure the number of days for the moon to make one revolution, which shows its accuracy. In 462 AD, Zu Chongzhi requested Emperor Xiaowu of Song Dynasty to issue a new calendar, and Emperor Xiaowu called ministers to discuss it. At that time, Dai Faxing, one of the emperor's minions, stood out against it and thought that it was deviant for Zu Chongzhi to change the ancient calendar without authorization. Zu Chongzhi refuted Defarge on the spot with his own research data. Relying on the emperor's favor, Dai Faxing said arrogantly: "The calendar was formulated by the ancients and cannot be changed by future generations." Zu Chongzhi is not afraid at all. He said very seriously, "If you have a solid basis, argue it out. Don't scare people with empty talk. " Emperor Xiaowu of Song wanted to help Dai Faxing, and found some people who knew the calendar to argue with Zu Chongzhi, but Zu Chongzhi refuted them one by one. However, Emperor Xiaowu of Song still refused to issue a new calendar. It was not until ten years after Zu Chongzhi's death that his Da Ming Li was put into practice.
Although the society was very turbulent at that time, Zu Chongzhi studied science tirelessly. His greater achievement is in mathematics. He once annotated the ancient mathematics book Nine Chapters Arithmetic and wrote a book Composition. His most outstanding contribution is to get quite accurate pi. After a long and arduous study, he calculated pi between 3. 14 15926 and 3. 14 15927, becoming the first scientist in the world to calculate pi to more than seven digits.
Zu Chongzhi is a generalist in scientific inventions. He built a kind of compass, and the copper man in the car always pointed south. He also built a "Thousand-Li Ship" and tried it in Xinting River (now southwest of Nanjing). It can sail 100 Li a day. He also used hydraulic power to rotate the stone mill, pounding rice and grinding millet, which was called "water hammer mill".
In Zu Chongzhi's later years, Xiao Daocheng, who mastered the Song Guards, wiped out the Song Dynasty.
During the Northern Song Dynasty in China, there was an outstanding scientist who read widely. He was Shen Kuo (103 1 ~ 1095).
Shen Kuo, Chinese character, was born in Qiantang, Zhejiang (now Hangzhou, Zhejiang) in the ninth year of Tiansheng in Song Renzong (A.D. 103 1). His father Shen Zhou worked as a local official in Quanzhou, Kaifeng and Jiangning. Mother Xu Shi is a well-educated woman.
Shen Kuo studied hard since childhood. Under the guidance of his mother, he finished reading at home at the age of fourteen. Later, he followed his father to Quanzhou, Fujian, Runzhou, Jiangsu (now Zhenjiang), Jianzhou, Sichuan (now Jianyang) and Kaifeng, the capital of China. He had the opportunity to get in touch with the society, understand the life and production of the people at that time, increase his knowledge and show his superhuman intelligence.
Shen Kuo is proficient in astronomy, mathematics, physics, chemistry, biology, geography, agriculture and medicine; He is also an outstanding engineer, excellent strategist, diplomat and politician. At the same time, he is knowledgeable, good at writing and proficient in other people's calendars, music, medicine, divination and so on. Meng Qian Bi Tan, written in his later years, recorded in detail the outstanding contributions of working people in science and technology and their own research results, reflecting the brilliant achievements of natural science in ancient China, especially in the Northern Song Dynasty. Meng Qian's pen talk is not only an academic treasure house in ancient China, but also occupies an important position in the history of world culture.
Japanese mathematician Kazuo Sanshi once said: People like Shen Kuo can't be found in the history of mathematics all over the world. Only China has such people. Dr Joseph Needham, a famous British expert on the history of science, said that Shen Kuo's Meng Xi Talk is the coordinate of the history of Chinese science.
Gauss is a German mathematician, astronomer and physicist. He is regarded as one of the greatest mathematicians in history, as well as Archimedes and Newton.
Gauss 1977 was born in a craftsman's family in Brunswick on April 30th, and 1955 died in G? ttingen on February 23rd. When I was a child, my family was poor, but I was extremely smart. I was educated by a noble. From 1795 to 1798, I studied at the University of G? ttingen, and 1798 transferred to Helmstadter University. The following year, he received his doctorate for proving the basic theorem of algebra. From 1807, he served as a professor at the University of G? ttingen and director of the G? ttingen Observatory until his death.
Gauss's achievements cover all fields of mathematics, and he has made pioneering contributions in number theory, non-Euclidean geometry, differential geometry, hypergeometric series, complex variable function theory, elliptic function theory and so on. He attached great importance to the application of mathematics, and emphasized the use of mathematical methods in the research of astronomy, geodesy and magnetism.
Euler, a Swiss mathematician, received a good theological education in his early years and served in the Russian court after becoming a mathematician.
Once, the Russian queen invited the French philosopher Diderot to visit her court. Diderot tried to prove himself worthy of being invited by converting courtiers to atheism. Tired, the queen ordered Euler to shut the philosopher up. So Diderot was told that a learned mathematician had proved the existence of God by algebra, and if he wanted to listen, the mathematician would give this proof in front of all courtiers. Diderot accepted the challenge happily.
The next day, in court, Euler found Diderot and said solemnly in a very positive tone: "Sir, therefore God exists. Please answer! " For Diderot, this sounds reasonable. He was confused and didn't know what to say. The people around him laughed loudly, which made the poor man feel ashamed. He asked the queen to allow him to return to France immediately, and the queen agreed very calmly.
In this way, a great mathematician "defeated" a great philosopher by cheating.
Laplace and Lagrange were two French mathematicians in the early19th century. Laplace is great at math, but he is a total villain in politics. Every time the regime changes, he can go to have it both ways without any political integrity. Laplace once dedicated his masterpiece "Celestial Mechanics" to Napoleon. Napoleon wanted to annoy Laplace and accused him of an obvious negligence: "You wrote a book about the world system, but never mentioned the creator of the universe-God."
Laplace retorted, "Your Majesty, I don't need such an assumption."
When Napoleon repeated this sentence to Lagrange, Lagrange said, "Ah, but this hypothesis is very good and explains many problems."
Two prodigies/kloc-at the beginning of the 9th century, two prodigies appeared on both sides of the Atlantic: a British boy Hamilton and an American boy Colborn Hamilton, whose genius was manifested in linguistics. By the age of eight, he had mastered English, Latin, Greek and Hebrew. /kloc-At the age of 0/2, he had mastered Persian, Arabic, Malay and Bengali, but he didn't learn Chinese because he didn't have a textbook. Colborn showed a magical genius in mathematics. When I was a child, someone asked him if 4294967297 was a prime number, and he immediately replied no, because it had 64 1 as a divisor. There are countless similar examples, but he can't explain how he came to the correct conclusion.
People brought two prodigies together. This meeting is wonderful. Now it is impossible to know exactly what they talked about, but the result was completely unexpected: Colborn's mathematical talent was completely "transplanted" to Hamilton; Hamilton gave up linguistics and devoted himself to mathematics, becoming the greatest mathematician in Irish history.
As for Colborn, his genius gradually disappeared.
The Death of Mathematicians Abel, a Norwegian mathematician, made great contributions to the development of mathematics at the age of 22, but it was not accepted by the mathematics community at that time. He lived a poor life, which seriously affected his health. He got tuberculosis, which was terminal at that time. In the past few weeks, he has been thinking about the future of his unmarried sister. He wrote to his best friend Kilo: "She is not beautiful, with red hair and freckles, but she is a lovely woman." Although Kilo and Kemp have never met, Abel hopes they can get married.
Miss Kemp took care of Abel at the last moment of her life. At the funeral, she met Kilho who came here specially. Kilo helped her overcome her grief. They fell in love and got married. As Abel hoped, Kilo and Kemp were very happy after their marriage, and they often went to Abel's grave to miss him. As the years passed, they found that more and more people came from all over the world to pay their belated tribute to Abel's contribution to mathematics, and they were just a pair of ordinary pilgrims in this pilgrimage team.
1832 On May 29th, French youth Galois decided to duel with another man for so-called "love and honor". He knows that his opponent's marksmanship is very good, and his hope of winning is very small, and he is likely to die. He asked himself, how did he spend this last night? Before that, he had written two mathematical papers, but both of them were contemptuously rejected by the authorities: one was by Cauchy, a great mathematician; The other time was the sacred French Academy of Sciences, and what was in his mind was valuable. All night, he was in a hurry to write his last words in Science in a fleeting time. Write it as soon as possible before he dies, and try to write out the major events in his rich thoughts. He interrupted from time to time, wrote "I don't have time, I don't have time" in the margin, and then went on to write an extremely scribbled outline.
What he wrote in the last few hours before dawn once and for all found the real answer to a problem that has puzzled mathematicians for centuries, and created an extremely important branch of mathematics-group theory.
The next morning, in a duel, he was shot in the intestines. Before he died, he said to his brother who was crying beside him, "Don't cry, I need enough courage to die at the age of 20." He was buried in the ordinary trench of the cemetery, so today his grave is nowhere to be found. His immortal monument is his work, which consists of two rejected papers and a scribbled manuscript he wrote on the sleepless night before his death.
The mathematician's problem Fermat was a member of parliament in Toulouse, France in the17th century. He was an honest and diligent man and the most outstanding amateur in mathematics in history. In his life, he left many wonderful theorems to future generations; At the same time, due to temporary negligence, it also posed a severe challenge to later mathematicians.
Fermat has a habit. When he reads, he likes to keep his thoughts short. Once, while reading, he wrote the following words: "... it is impossible to divide a power higher than twice into two powers of the same degree." In this regard, I am sure that I have found a wonderful proof, but unfortunately the space here is too small to write down. " This theorem is now named "Fermat's Last Theorem", that is, it is impossible to satisfy xn+yn = Zn, which is Fermat's challenge to future generations. In order to find the proof of this theorem, countless mathematicians in later generations launched a charge again and again, but all failed. 1908, a German rich man offered a reward of 65,438+million marks for the first person to prove Fermat's last theorem completely. Since this theorem was put forward, mathematicians have struggled for more than 300 years and still have not proved it. But this theorem must exist, and Fermat knows it.
Mathematically, Fermat's Last Theorem has become a higher mountain than Mount Everest. Human's mathematical wisdom has only reached such a height once, and has never reached it since. Hua, 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.
After returning to China from 65438 to 0950, he successively served as Professor Tsinghua University, Head and Vice President of the Department of Mathematics of China University of Science and Technology, Director of the Institute of Mathematics of China Academy of Sciences, Director of the Institute of Applied Mathematics of China Academy of Sciences and Vice President of China Academy of Sciences. Hua is also a member of the first, second, third, fourth and fifth sessions of the NPC Standing Committee and vice chairman of the National Committee of the Sixth China People's Political Consultative Conference.
Hua is an internationally famous mathematician. He has made outstanding contributions in a wide range of mathematical fields, such as analytic number theory, matrix geometry, theory of multiple complex variables and partial differential equations. Because of his contribution, many theorems, lemmas, inequalities and methods are named after him. In order to promote the optimization method, Hua personally led a small team to 27 provinces to promote the application of mathematical methods for more than 20 years, which achieved obvious economic and social benefits and made great contributions to China's economic construction.