Pauli wrote a summary paper on the theoretical and experimental results of general relativity at the age of 19. It was only three years before Einstein published his "General Theory of Relativity" (19 16). People thought that he was so young but had such original opinions, which shocked the whole physics circle and made him famous at one fell swoop.
There are many stories about Paulie. He is famous for his preciseness and erudition, and also for his sharpness and criticism. It is said that Pauli met Einstein at an international conference. After Einstein's speech, Pauli stood up and said, "I don't think Einstein is completely stupid."
Once, the Italian physicist segre, who later discovered antiprotons, finished his report and Pauli left the meeting room. Pauli said to him, "I have never heard such a bad report as yours." At that time, segre said nothing. Pauli thought for a moment, then turned to Brescher, a Swiss physical chemist who was traveling with them, and said, "If you give a report, the situation will be even worse. Of course, except for your opening remarks in Zurich last time. "
Another time Paulie wanted to go to a place, but she didn't know how to get there. A colleague told him. Later, this colleague asked him if he had found the place that day. Instead, he sarcastically said, "When you don't talk about physics, you should think clearly."
Paulie is rude to his students, too. Once a student wrote a paper for Paulie to read. Two days later, the student asked Paulie for advice. Paulie returned the paper to him and said, "Even mistakes are not enough."
But Pauli was called "the conscience of physics" by Bohr, because of his sensitivity and prudence, he had the ability to find mistakes at a glance. In physics, there is a "Pauli effect"-when Pauli appears, people there will make mistakes in both theoretical deduction and experimental operation.
And when Pauli says "Oh, there's nothing wrong with it", it usually means very high approval. There is a joke that Paulie went to see God after his death, and God showed him his own design plan for the world. Paulie shrugged after reading it and said, "You could have done better ..."
Sue's story.
At the invitation of famous mathematician Chen, the famous mathematician Su returned to China on March 193 1 and was employed by National Zhejiang University. He has served as an associate professor, professor, dean, provost and provost of the Department of Mathematics. Until June 1952, due to the adjustment of colleges and universities all over the country, he was a little reluctant to become a professor. He was the head of the Department of Mathematics at Fudan University in Shanghai, and later served as provost, vice president and principal. He has served many times as a member of the China People's Political Consultative Conference, a deputy to the National People's Congress, a vice-chairman of the 7th and 8th China People's Political Consultative Conference, and a vice-chairman of the NLD Central Committee.
Looking back on Su's life in the past century, it is also rugged and muddy, with many stories. Here are a few to comfort readers.
Story 1
September 23rd 1902 was an ordinary day, but it was a rare day for Su Zushan's family who fled from Tongan, Fujian to Daixi Village, Pingyang, Zhejiang. God knows, and God bless the people. Su Zushan's family added a ding, and the couple laughed from ear to ear, and finally had a "successor" who had been farming for generations. However, Su Zushan and his wife have never been to school, and they have had enough suffering from illiteracy. They are eager for success, so they choose "Qing Bu" as their son's name. The fortune teller also said some nice words, saying that in the name of "Qing Bu", he would be able to "climb high and look far, and worship his ancestors" in the future.
After all, a name is not a ladder of fame and fortune. Just as his peers were carrying schoolbags to school, Su Zushan gave his son a bullwhip. From then on, Sue wore a big bamboo hat made by her father and coarse cloth sewn by her mother. He rode barefoot on the back of the cow and came to the foot of Woniu Mountain with a wave of his whip. Sue's family is a big buffalo, fat and strong, and never takes the short cowherd seriously. Once, when the buffalo got angry, it ran and jumped, throwing Sue into a newly cut bamboo garden. Blessed by God, he fell into several bamboo roots and survived.
When herding cattle home, Sue walked through the gate of the village private school and was often attracted by the sound of books. Once, the teacher was reading aloud: "Sue, at the age of 27, began to read books on fire." After listening, he read it several times. From then on, he remembered the jingle and sang in the mountains when herding cattle.
Su Zushan often listens to his son recite three-character classics and hundreds of surnames, which is puzzling. Once, I happened to see my son "eavesdropping" at the gate of a private school. Father's heart finally moved. As soon as the couple got together, they decided to tighten their belts and send Sue to a private school.
Story 2
At the age of 9, Su's father took a cart of rice as tuition, walked 50 kilometers of mountain roads and sent Su to Pingyang County, where he became a high school placement student. From the mountainous area to the county seat, Sue is really an eye-opener, and everything is novel. The first time he saw the minced meat in the steamed bread, he often changed his meal ticket into money to buy "meat steamed bread" to eat. A month's meal ticket has been used up long ago, so I have to go hungry. When he saw the tiger stove boiling water, he felt very interesting. He threw the eggs he brought from home into the pot, and a pot of boiling water turned into a pot of egg drop soup. The boiler man was so angry that he grabbed him and hit him
Sue plays all day. He often comes out top in exams. At the end of the final exam, he came last in the class. However, his composition is not bad. "Eavesdropping" in the private school stimulated his interest in learning Chinese and laid a little foundation for his composition. However, the more Chinese teachers read it, the less they believe it. They always thought that Sue's composition was plagiarized. Therefore, he was awarded a low score. In this way, his stubbornness was even more aroused. The more the teacher says that he is not good, the less he studies hard. For three consecutive semesters, he was the last one. Both classmates and teachers say that he is a "fool".
Once, the geography teacher Chen Yufeng called Su to the office and told him a short story: "When Newton 12 years old, he transferred from a rural primary school to a city to study, and his grades were not good, so his classmates looked down on him. Once, a classmate bullied him rudely and kicked him in the stomach. He rolled in pain. That classmate is better than him in health and homework, and Newton is afraid of him at ordinary times. But at this moment, he couldn't bear it, jumped up and fought back, forcing the classmate into a corner and pressing it against the wall. This classmate saw that Newton was furious and had to give in. There are only so many reasons for Newton to learn from this incident: as long as he makes up his mind, he can subdue it. He worked hard and soon became the first in his class, and later became a great scientist. "
Sue is grateful to Mr. Chen for not criticizing him and telling him stories. Seeing his drooping head, Teacher Chen touched his head and said, "I think you are a clever boy. If you are willing to work hard, you will definitely get the first place in the exam. " He added, "Your parents have worked hard and saved money. I hope you can read this book well. As you are now, what will you repay them in the future? " Sue couldn't hold back her shock any longer. Tears rolled down his chest like broken pearls, and he felt that he had done something wrong for the first time. Since then, he has completely become a sensible child, stopped playing, studied hard and won the first place in the final exam.
Story 3
A math class in Zhejiang 10 Middle School in Wenzhou led Su to the road to the kingdom of mathematics. Teacher Yang, who returned to Wenzhou from studying in Japan, took a math class with a real feeling of worrying about the country and the people: "In today's world, the law of the jungle prevails. The world powers built cannons by ships, carved up China's beans and wolfed them down. The danger of national subjugation and extinction of the Chinese nation is imminent. In order to save the nation and survive, we must revitalize science. Mathematics is the pioneer of science. In order to develop science, we must learn math well. " Teacher Yang's words touched Sue's heart. Since then, his interest has shifted from literature to mathematics. Once, Sue proved a geometric theorem in 20 different ways. When the headmaster first learned, he called Sue to the office, patted him on the shoulder and said, "Study hard and send you abroad to study in the future." When he graduated from Suzhou University, President Hong had been transferred to the Ministry of Education in Beijing, but he still cared about Su's study and sent 200 yuan money to help Su study abroad.
19 19, 17-year-old Sue bought a boat ticket to Japan, and the rest 170 yuan could hardly support him for three months. He can only eat two meals a day and has no money to hire a Japanese teacher, so he has to learn from the landlord. Finally, he answered the examiner's questions in fluent Japanese, and entered the famous school-tokyo institute of technology Electrical Engineering Department with the first place. 1924 was admitted to the Department of Mathematics of Imperial University in Tohoku, Japan with the first place, and studied under the famous geometer Professor Tadashian. 1927, after graduating from college, I sold newspapers, delivered milk, proofread magazines and tutor after school, and paid tuition with the money I earned, so I was promoted to the graduate school of our school without an exam. With a strong will, he studied hard and published 4 1 research papers on affine differential geometry and projective differential geometry, which opened up a new field of differential geometry research and was called "a brilliant mathematical star rising from the East" by the mathematical community. 193 1 in March, 2008, he obtained the doctor of science degree with excellent results, becoming the second foreigner to receive this degree after Chen. Since then, invitations from home and abroad have flown in like snowflakes, and Sue refused them one by one. Because two years ago, when Chen got his doctor of science degree, he sent Su to Zhejiang University, where the conditions were very poor. Sue said, "Go home first, and I'll come back after graduation. Let's make the Department of Mathematics of Zhejiang University a world-class department in 20 years ... "This may be the reason why Su did not want to leave Zhejiang University when the departments of colleges and universities in China were adjusted.
After Su took office, except for the quartic (cubic) algebraic cone discovered in graduate school, which was called Su cone in academic circles, he later made brilliant scientific research and teaching achievements in the fields of projective curve theory, projective surface theory, high-dimensional projective space yoke network theory, general spatial differential geometry, computational geometry and so on. He also proved that the closed Laplace sequence and structure (T4) are called "Su (Qing Bu) chain" by the world academic circles. Therefore, the famous German mathematician Brasuke called Su "the first geometer in the East", and mathematicians in Europe, America and Japan called him and his colleagues "Zhejiang University School". Indeed, during the period from 193 1 to 1952, the Soviet Union trained nearly 100 students, of whom 25 served as deans and vice-deans in more than 10 famous universities nationwide, 5 were elected academicians of the Chinese Academy of Sciences, and even 3 academicians trained after liberation. In Fudan University of Mathematics, there are Gu Chaohao, Hu, Hu and Su, which is a rare and gratifying phenomenon.
Story 4
After the July 7th Incident, Zhejiang University was forced to move westward. At the head of this national disaster, Su received an urgent telegram: Mr. Matsumoto, his father-in-law, was critically ill and asked the Su couple to go to Sendai for the last time. Sue handed the telegram to her wife and said ... you go, I want to stay in my own country. Sue's wife Su Songben said, "I'll follow you." However, because his wife just gave birth to a baby and couldn't live with him, Sue sent her to Pingyang for refuge in the countryside. It was not until the summer vacation of 1940 that President Zhu Kezhen approved the special passage fee for his wife and daughter to Meitan.
During the days in Meitan, the life of teachers and students was extremely difficult, and it was difficult for university professors to make a living by salary. Sue bought a hoe, and every day when she came home from work or had a rest day, she opened up wasteland to grow vegetables. Once, the restaurant in Meitan Hotel was not available, so he had to buy several baskets of cauliflower from Su's vegetable field. Another night, President Zhu came to the ruined temple where he lived and saw Su carrying water to grow vegetables, while Su Songben was cooking with his son on his back. Careful President Zhu saw that the pot was full of radishes and dried sweet potatoes, so he asked Sue. Sue explained: "My family has many children, and my salary is not enough to buy rice. Dried sweet potatoes have been dipped in salt for several months. " Zhu Kezhen was amazed. So, he chartered Sue's two middle school sons to make an exception and eat and live at home in middle school (because Sue's family couldn't come up with bedding).
The difficulties in life go from bad to worse. One of Sue's youngest sons died soon after his birth due to malnutrition. Su Qing Bu buried him in Meitan Mountain and engraved the words "Su Ying's Tomb" on the small stone tablet. However, the difficulties in life can't scare people with will and perseverance, and the teaching and scientific research of Zhejiang University is still proceeding in an orderly way. Sue also stepped onto the podium with difficulties. When he turns to draw geometric figures on the blackboard, the students will talk about the "triangle, trapezoid ..." patches on Teacher Su's clothes and the "spiral curve" on his ass! In the evening, Su put the tung oil lamp on the incense table of the ruined temple to write a textbook, and finally finished the book Introduction to Projective Curves with her perseverance. 1in the summer of 994, the author was lucky enough to see the small temple where Su lived during his migration in Qingyan, and a feeling of reverence came to mind and was unforgettable.
Story 5
197265438+On February 7th, Zhang Su, a famous mathematician and a student of Soviet Union, became the second issue of Mathematics Magazine and visited mathematicians all over the world. He should have visited Mr. Su in Shanghai. Unexpectedly, in the book Introduction to Projective Geometry (English version) presented by Teacher Su, he wrote a poem on the title page:
Thirty years ago in Guizhou,
I'm worried about singularity,
Now I am old enough to go to Shenjiang Day.
It's nice to see old friends fighting for the upper reaches.
This not only breaks the stereotype of ordinary people's inscriptions, but also tells the whole picture of teachers' and students' feelings, which shows that Su Lao's poetic skills are superb and his writing is profound.
Many people know that Sue is a master of mathematics, but they don't know that he is also a master of literature, a writer and a poet. He loved ancient poetry since he was a child, and learned to write poetry at the age of 13. When I was a child, I used to ride on the back of an ox and read Poems of a Thousand Families. For decades, he has been accompanied by poetry and walked with poetry books. Every time he goes on a business trip, he always puts one or two poems in his bag, such as Selected Poems of Du Fu. Sue not only reads poems, but also is interested in writing them. He has been writing for decades and has written nearly a thousand poems. When he was 96 years old, Su's Amateur Poetry was published by the publishing house. * * * Received 444 modern poems with 60 words, copied by Su Lao, in which 193 1 ~ 1949 early works 19 1 40 words. From this, we can appreciate the light reflected by Su Lao's academic career and poetry and calligraphy skills in the past 60 years, which is full of the breath of the times and gives people a lot of inspiration.
Looking back at the time when Zhejiang University moved to Meitan, he and Qian Baoyu, a master of mathematics, founded Meitan Printing Society. Under extremely difficult circumstances, he published the first Poem Collection of Meitan Press at his own expense, which included about 65,438+000 poems of various schools. In the days of national disaster, poets often drink tea and recite poems, or talk about the road, or comment on the current situation, and their feelings of worrying about the country and homesickness are often revealed in their works.
1944, Sue wrote a poem entitled "You Ting":
Climb the path with a single coat, and lean on a stick to pass the light.
Road protection tree, Linjiang Qiqi Pavilion.
Guests are always traveling far away, and their hometown is green.
Looking north without tears, blood shed in the Central Plains.
This is Su Bu's expression of affection for things, nostalgia for the fall of his hometown and the broken mountains and rivers of the motherland, and praise for the people's rise to the war of resistance. Patriotism and concern for the world welled up from his heart.
Su's poetic skills are superb and breathtaking. His poems are lofty in artistic conception, fresh in style and full of allusions and philosophies.
Reading many of Su's poems not only makes people feel that Su Lao often instills the importance of the "pyramid" foundation for later learning, but also makes people feel that the arts and sciences are interlinked. For decades, he skillfully used what he called "odd odds and ends" (odd odds and ends of time) to study and study. Aren't these immortal poems the fragmentary evidence that Sue made full use of time?
A Mathematical Genius —— Leibniz
Gott's friend William Leibniz (1646- 17 16) is the most important mathematician, physicist and philosopher in Germany at the turn of 17 and 18 centuries, and he is a rare scientific genius in the world. He read widely and dabbled in encyclopedias, making indelible contributions to enriching the treasure house of human scientific knowledge.
I. Life story
Leibniz was born in a scholarly family in Leipzig, eastern Germany. His father is a professor of moral philosophy at Leipzig University, and his mother was born in a professor's family. Leibniz's father died when he was only 6 years old, leaving him a rich collection of books. Leibniz got extensive contact with ancient Greek and Roman culture and read the works of many famous scholars, thus gaining a solid cultural foundation and clear academic goals. /kloc-He entered the University of Leipzig to study law at the age of 0/5. As soon as he entered the school, he took a standard humanities course in his sophomore year. He also extensively read the works of Bacon, Kepler, Galileo and others, and deeply thought and evaluated their works. After listening to Euclid's "Elements of Geometry", Leibniz became interested in mathematics. /kloc-at the age of 0/7, he studied mathematics for a short time at the University of Jena and obtained a master's degree in philosophy.
At the age of 20, Leibniz transferred to Altdorf University. This year, he published his first mathematical paper "On the Art of Combination". This is an article about mathematical logic, and its basic idea is to reduce the theoretical truth argument to a calculation result. Although this paper is not mature enough, it shines with innovative wisdom and mathematical talent. Leibniz joined the diplomatic community after receiving his Ph.D. from Altdorf University. Since 167 1, he has developed extensive contacts with the outside world through diplomatic activities, especially communication has become the main way for him to obtain outside information and exchange ideas with people. During his visit to Paris, Leibniz was deeply inspired by Pascal's deeds and determined to study advanced mathematics, and studied the works of Descartes, Fermat, Pascal and others. 1673, Leibniz was recommended as a member of the Royal Society. At this time, his interest obviously turned to mathematics and natural science, and he began to study infinitesimal algorithms, independently established the basic concepts and algorithms of calculus, and laid the foundation of calculus together with Newton. 1676 went to the Duke of Hanover's house as a legal adviser and librarian. 1700 was elected as an academician of the Paris Academy of Sciences, which contributed to the establishment of the Berlin Academy of Sciences and served as the first president.
1716165438+10/0/4, Leibniz died in hanover at the age of 70.
Second, the original calculus
/kloc-in the second half of the 0/7th century, European science and technology developed rapidly. Due to the improvement of productivity and the urgent needs of all aspects of society, through the efforts of scientists from all over the world and the accumulation of history, calculus theory based on function and limit concept came into being. The idea of calculus can be traced back to the method of calculating area and volume proposed by Archimedes and others in Greece. Newton founded calculus in 1665, and Leibniz also published works on calculus in 1673~ 1676. In the past, differential and integral were studied as two mathematical operations and two mathematical problems respectively. Cavalieri, Barrow, Wallis and others have obtained a series of important results of finding area (integral) and tangent slope (derivative), but these results are isolated and incoherent. Only Leibniz and Newton really communicated integral and differential, and clearly found the internal direct relationship between them: differential and integral are two reciprocal operations. And this is the key to the establishment of calculus. Only by establishing this basic relationship can we establish systematic calculus. And from the differential and quadrature formulas of various functions, the algorithm program of * * * is summarized, which makes the calculus method universal and develops into a symbolic calculus algorithm. Therefore, calculus "was mostly done by Newton and Leibniz, not invented by them" (Engels: Dialectics of Nature).
However, there has been a heated debate in the field of mathematics about the order of the creation of calculus. In fact, Newton's research on calculus was earlier than Leibniz's, but Leibniz's results were published earlier than Newton's. Leibniz's paper "Finding a Wonderful Computing Type of Minimax" published in Teacher's Magazine on June 1684+00 is considered as the earliest published calculus document in the history of mathematics. Newton also wrote in the first and second editions of Mathematical Principles of Natural Philosophy published in 1687: "Ten years ago, in my correspondence with the most outstanding geometricians G and W Leibniz, I indicated that I already knew the method of determining the maximum and minimum, tangent method and so on, but I concealed this method in my correspondence ... The most outstanding scientists wrote back. He also described his method, which is almost no different from mine, except for his wording and symbols. " (But in the third edition and later editions, this passage was deleted. So it was later recognized that Newton and Leibniz created calculus independently. Newton started from physics and studied calculus by set method. His application is more combined with kinematics, and his accomplishments are higher than Leibniz's. Leibniz, on the other hand, started from geometric problems, introduced the concept of calculus by analytical method, and got an algorithm, which was more rigorous and systematic than Newton's algorithm. Leibniz realized that good mathematical symbols can save thinking labor, and the skill of using symbols is one of the keys to the success of mathematics. So he invented a set of applicable symbol systems, such as introducing dx to represent the differential of X, ∫ to represent the integral, dnx to represent the n-order differential and so on. These symbols further promoted the development of calculus. 17 13, Leibniz published the article "History and Origin of Calculus", summed up his own thought of establishing calculus, and expounded the independence of his own achievements.
Third, many achievements in advanced mathematics.
Leibniz has made great achievements in mathematics, and his research and achievements have penetrated into many fields of higher mathematics. His series of important mathematical theories laid the foundation for later mathematical theories.
Leibniz once discussed the properties of negative numbers and complex numbers, and concluded that the logarithm of complex numbers does not exist, and the sum of * * * conjugate complex numbers is a real number. In later research, Leibniz proved that his conclusion was correct. He also studied linear equations, discussed the elimination method in theory, introduced the concept of determinant for the first time, and put forward some theories of determinant. In addition, Leibniz also founded the basic concept of symbolic logic, and invented computers and binary systems that can perform addition, subtraction, multiplication, division and square root operations, which laid a solid foundation for the modern development of computers.
Fourth, the fruitful results of physics.
Leibniz's achievements in physics are also extraordinary. He published the "New Hypothesis of Physics", and put forward concrete and abstract principles of motion, arguing that a moving object, no matter how small, will move with a part of an object in a completely static state. He also seriously discussed the principle of conservation of momentum proposed by Descartes, put forward the rudiment of the principle of conservation of energy, and published a brief proof of Descartes and others' obvious mistakes in the laws of nature in Teacher's Magazine, put forward the problem of the quantity of motion, proved that momentum cannot be used as the unit of measurement of motion, and introduced the concept of kinetic energy, which was considered as a universal physical principle for the first time. He also fully proved that perpetual motion machine is impossible. He also opposed Newton's absolute view of time and space, arguing that "there is no space without matter, and space itself is not an absolute reality." The difference between space and matter is just like the difference between time and movement, but although these things are different, they are inseparable. " In optics, Leibniz has also made some achievements. He deduced the law of refraction by using the extreme value method in calculus, and tried to explain the basic laws of optics by using the extreme value method. It can be said that Leibniz's research on physics has been moving towards the goal of establishing an axiomatic system similar to Euclidean geometry for physics.
Verb (abbreviation of verb) is an advocate of cultural exchange between China and the West.
Leibniz attached great importance to China's scientific, cultural and philosophical thoughts, and was the first German to study China culture and China philosophy. He learned a lot about China from Grimal Di, a Jesuit missionary in China, including sericulture, textile, papermaking, printing and dyeing, metallurgy and minerals, astronomy and geography, mathematics and writing, and edited and published these materials. He believes that a new relationship should be established between China and the West. Leibniz wrote in the introduction of China: "The greatest culture and the most developed civilization of all mankind seem to gather at the two ends of our continent today, that is, Europe and Eastern Europe-China on the other side of the globe." "Compared with Europe, China, an ancient civilization, has a similar area and a population of more than." "We are neck and neck in our daily life and our skills in dealing with nature. We all have the skills to benefit each other through mutual communication. Obviously, we should be slightly better at careful thinking and rational thinking, but "in the philosophy of time, that is, in the ethics of life and human reality and the theory of governing the country, we are really dwarfed." Here, Leibniz not only shows the spirit of being open-minded and eager to learn without the color of "Eurocentrism", but also depicts the grand blueprint for the two-way exchange between Chinese and Western cultures, which has effectively promoted the in-depth development of this exchange. People in the East and the West should learn from each other, learn from each other's strengths and make progress together.
Leibniz devoted his life to promoting cultural exchanges between China and the West, which had a wide and far-reaching influence. He is open-minded and eager to learn, treats China culture equally, and his spirit of not containing the prejudice of Eurocentrism is particularly commendable, which is worthy of eternal admiration and imitation by future generations.
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