To those who like mathematics and those who do not like mathematics
To those who know mathematicians and those who do not understand mathematicians
To those promoters of civilization Deep respect
Inscription——
There are two kinds of beauty
One is the profound and touching equation
The other is your general Wearing a tired and faint smile
Euler stopped living and stopped calculating.
——de Condorcet
In a topology class, Minkowski proudly declared to the students: "The most important reason why this theorem has not been proven is that so far there are only some third-rate Mathematicians have spent time on this. Now I'm going to prove it..." So Minkowski started to pick up the chalk. At the end of this class, the certificate was not completed. During the next class, Minkowski continued to prove. Several weeks passed... One hazy morning, Minkowski entered the classroom. At that time, a bolt of lightning flashed across the sky. The thunder was deafening, and Minkowski said seriously: "God is angered by my pride, and my proof is incomplete..."
Hilbert once had a student who gave Hilbert was given a paper to prove the Riemann conjecture. Although there was an irreparable error in it, Hilbert was deeply attracted. The next year, the student died of unknown causes, and Hilbert asked to give a speech at the funeral. That day, it was stormy and the family members of this student were filled with grief. Hilbert began his speech and first pointed out that it was really sad for such a genius to leave us so early. Everyone felt the same and cried more and more fiercely. Next, Hilbert said that although this person's proof was wrong, if we follow this path, it should be possible to prove the Riemann conjecture. Next, Hilbert continued to speak enthusiastically in the rain: "In fact, let us consider a Complex function of a single variable..." Everyone fell down.
Proof is an idol before which mathematicians torture themselves.
——A. Eddington
There was a man named Paul Wolfskehl, who studied mathematics in college and was obsessed with a beautiful girl, which made him frustrated. He was rejected countless times and felt helpless, so he set a date for suicide and decided to bid farewell to this world when the clock struck midnight and never care about the world again. Wolfskehl still worked hard in the remaining days, not in mathematics of course, but in some business matters. On the last day, he wrote his will and wrote letters to all his friends and relatives. Because of his relatively high efficiency, he finished everything before midnight. In the remaining few hours, he ran to the library and flipped through mathematics books. Soon, I was attracted by a paper by Kummer explaining why Cauchy and other predecessors failed to do Fermat's last theorem. It was a great paper, suitable for a suicidal mathematician to read in his last moments. Wolfskehl actually discovered a bug in Kummer, and it was not until dawn that he made this proof. He was so proud that everything went up in smoke... So he made a new will, set a large part of his property as a prize, and gave 100,000 marks to the first person to prove Fermat's theorem... This is The origin of the Wolfskehl Prize.
The wall on the ground floor of Gottingen City Hall is bluntly engraved:
"There is no life outside Gottingen."
In 1854, Riemann wanted to work in Gottingen (Brother). Tingen (a famous German university that was the center of mathematics and physics before World War II) received a lectureship and delivered his epoch-making speech on geometry. Since many of the people who listened to this speech were school administrators and did not understand mathematics at all, Riemann only used a mathematical formula in his speech. Weber recalled that after the speech, Gauss excitedly praised Riemann's idea with a rare expression. If you read Riemann's lecture notes, you will find that it is almost philosophy. Despite this, there was only one person in the audience who could understand Riemann, and that was Gauss. The entire mathematical community has spent nearly 100 years perfecting and digesting Riemann's ideas.
Some people say that Riemann's work is closer to philosophy than mathematics. Even at the beginning, many mathematicians in Europe thought that Riemann's work was a kind of family publication, closer to the view of physicists. Nothing to do with mathematicians. Once, Helmholz and Weiestrass went on vacation together. Weiestrass took a doctoral thesis of Riemann with him so that he could study it quietly in a beautiful environment. It is complex and magnificent work.
But Helmholz was puzzled. He thought that Riemann's article couldn't be more clear. Why did Weiestrass, as a mathematician, spend so much effort?
Let’s start talking about D. Hilbert
David Hilbert did not graduate from Gottingen. In the 1880s, the doctoral thesis defense at the University of Berlin required two students as opponents, who kept asking you questions. One of Hilbert's opponents was Emil Wiechert, who later became the most famous seismologist. At that time, there were very few university professors in Germany (perhaps called Prussia). Berlin only has three mathematics professors, while the average university has at most two.
Hilbert’s doctoral oath ceremony, the principal presided over: “I solemnly ask you to answer whether the oath can enable you to bear the following promises and guarantees with a sincere conscience: you will bravely defend true science, Develop it and add luster to it; neither be driven by rich salary nor false fame, but only hope that the light of God’s truth will shine on the earth and be carried forward.” I would like to know if there are similar words in Tsinghua’s doctorate awarding ceremony. .
When Hilbert was old, he once heard a group of young people talking about a mathematician he knew. At that time, many of the people he knew well, such as Minkowski, were deceased. He was particularly concerned about the person being talked about. After everyone finished talking about how many children this person had, he asked: "...Does he still 'exist'..."
< p>Once in Hilbert's seminar, a young man reported a very beautiful theorem. Hilbert said: "This is really a wunderbaschon theorem. Who discovered it?" The young man said He stood blankly for a long time and said to Hilbert: "It's you...".A widely circulated story about Minkowski in Gottingen is that he was walking on the street and found a young man silently thinking about a very important question, so Minkowski patted him gently. Shoulders, telling him "Convergence is for sure", the young man smiled gratefully.
The chairman of the mathematics department from 1909 to 1934 was Edmund Landau. Landau's working habits are very strange. He works for 6 hours and takes a rest for 6 hours, alternating in this way. He received endless letters about proving Fermat's last theorem. Later, he really didn't have the energy to deal with it, so he printed a batch of cards, which probably looked like this
--------- ----------------------------------------
Dear _____
Thank you for sending me the proof of Fermat’s last theorem.
The first error is on page ______, line ______
This invalidates the proof.
E.M.Landau
---------------------------------- -----------------------
Although many manuscripts have been rejected, it is said that the remaining ones are still more than 3 meters high.
The most incomprehensible thing about this universe is that it can be understood.
——Albert Einstein
When Einstein conceived the general theory of relativity, although his mathematician friends taught him a lot of Riemann geometry, his mathematics was still not satisfactory. Later, he went to Gottingen once and gave several reports to Hilbert and many other mathematicians. Not long after he left, Hilbert calculated the famous field equation. Hilbert's mathematics was of course much better than Einstein's. Soon, Einstein also came out. Someone suggested that Hilbert consider the issue of authorship of this thing. Hilbert said frankly: "Every child on the road in Gottingen knows more about four-dimensional geometry than Einstein. However, despite this, the man who invented the theory of relativity It's still Einstein and not a mathematician. "
The first spherically symmetric solution of Einstein's field equation, which is the Schwarzschild (Schwarzschild) solution, was given by the man of the same name. Given in the trenches of battle. Schwarzschild is Professor of Astronomy at Gottingen.
Edditngton is a great astrophysicist. The following story is about how he bragged. Not long after Albert Einstein's general theory of relativity was published, a reporter went to interview Eddington and said that he heard that there were only three people in the world who understood this profound theory. Who were these three people? Eddington lowered his head in thought and didn't answer for a long time. The reporter couldn’t help but ask again, and Eddington said: “I was wondering who the third person was….
”
The mathematics used by Einstein to describe general relativity is the geometry of curved space. The Italian mathematician Levi-Civita has made outstanding contributions to this geometry. Therefore, someone asked Einstein what he What did he like most about Italy? He answered that it was Italian spaghetti and Levi-Civita.
Einstein was Minkowski’s student and missed countless classes. As for many years later, Minkowski learned about Einstein’s theory. At that time, he sighed: "Oh, Einstein always doesn't come to class - I really didn't expect him to do such a thing. ”
A. Coble was an American academician in the last century. He did algebraic geometry and was very influential for a time. It is said that he has infinite number of doctoral thesis topics: When you prove a 2-dimensional situation At that time, he asked the next doctoral student to prove the 3-dimensional case, and then asked the next doctoral student to do the 4-dimensional case. Later, there was a doctor named Gerald Huff, who not only did the 5-dimensional case, but also performed general research on the 5-dimensional case. n is also solved. This leaves Coble's infinite future doctors with nothing to do.
Archimedes is more imaginative than Homer.
Ertai
After talking about Einstein, it should be reasonable to continue with John von Neumann. This mathematician who built computers should talk about it every time we use the computer Game. Neumann expressed the highest respect.
von Neumann once encountered someone asking him a question that is probably familiar to Chinese primary school students. That is, two people are walking towards each other, and there is a dog running around in the middle. How far did the dog go after two people met? You should first find the time of encounter, and then take the dog's speed. If I remember correctly, I heard about Mr. Su Buqing's car in Germany when I was a child. When someone asked him this question, he certainly didn't find it difficult. Von Neumann also gave the answer instantly. The person who asked the question was very disappointed and said that you must have heard of this trick before. What he meant was This approach above. von Neumann said: "What's the trick? What I did was count every time the dog ran, and then calculate the infinite series... ”
When Banach (Banach, a talented Polish mathematician) attended a mathematics party in 1927, he and many mathematicians poured Neumann with vodka. In the end, Neumann was too drunk and went to the toilet. Probably vomiting. But Bananch recalled that when he returned to continue discussing mathematics, he did not interrupt his train of thought at all.
Mathematicians are born, not made. ——H.Poincare
Mathematics is harmful to health. It is better not to read books during the holidays.
The following are the existence of some of the most genius mathematicians in history on this timeline. Length:
Pascal is 39 years old; Ramanujan is 31 years old; Abel is 27 years old; Galois is 21 years old; Riemann is 39 years old. When de Moivre was 21 years old, he was already teaching mathematics. By chance, he was a guest at a Duke's house, and Newton sent him his "Principia". He turned over it and was surprised to find that mathematics is so. Such a profound and beautiful knowledge. In this way, he bought the book, even though he had to travel around to teach it, and he had to tear out the pages so that he could carry it in his pocket and study it at his leisure.
Let’s talk about the careers of several mathematicians as teachers. Most of the famous people’s lectures were not very good, or they occasionally failed. For example, Newton often spoke to empty lecture halls, and he was not very clear in his lectures. , the second is too difficult, so no Cambridge students like his class.
Let’s start with some people who are not very familiar with it.
Mondelbrot. ) is famous for drawing fractals. In fact, his uncle, Mandelbrojt, was a more outstanding mathematician and was once one of the earliest members of Bourbaki. When he was a student, he came all the way from. Poland went to France to study mathematics, and he suffered serious mental damage after going there because he chose Goursat's analysis class. However, Goursat always used the same tone in class, talking about old things that were twenty or thirty years ago. After listening to it for three After about a week of class, Mandelbrojt felt that it was so far from his dream class that he actually cried. However, a few years later, Bernstein came to Paris and comforted Mandelbrojt by saying that Goursat taught like this more than 20 years ago. People are very passionate.
Thinking back to how innocent Mandelbrojt’s passion for knowledge was, it seems that it no longer belongs to our era.
Lindemann, the person who proved the transcendence of π, is said to be one of the worst lecturers in history. Here are two stories about him, one is about his lectures, and the other is about his memories of studying in Paris, which is quite cute.
It is said that Lindemann could not hear clearly most of his lectures, and the words he heard clearly were incomprehensible and unintelligible words. However, in a few cases, what he said was clear and understandable. That is Wrong words.
When Lindemann went to Paris to study, he attended the classes of Bertrand and Jordan. There were too few people studying mathematics at that time. Although Jordan was considered a leading mathematician in France, only three people attended his classes. , occasionally up to 4, but one of them was because it was warm in the classroom.
There are also some words from mathematicians, recorded below -
All mathematicians live in two different worlds. One is a crystal clear world of perfect ideal forms, a palace of ice. But they still live in the ordinary world, where things are fleeting or obscure because of their development. Mathematicians shuttle between these two worlds. In the transparent world, they are adults, and in the real world, they are babies.
——S.Cappel
When I was 11 years old, I started to study Euclid’s books and asked my brother to be my teacher. This is a big event in my life, as charming as first love.
There is a path that leads through the fields to New South Gate, where I often go alone to watch the sunset and think of committing suicide. However, I finally refrained from committing suicide because I wanted to know more about mathematics.
——B. Russell
I don’t know what the world thinks of me; but I think to myself, I seem to be just a child playing at the beach, picking up smoother things from time to time. I rejoiced in pebbles or more beautiful shells, and before me lay a sea of ??truth which was entirely unexplored.
——Issac Newton
In an interview, Thom, a mathematician, discussed issues with two paleoanthropologists. When talking about why ancient people preserved fire, one anthropologist said that it was because preservation of fire could keep them warm and cold; another anthropologist said that preservation of fire could produce delicious meat. And Thom said, because when night falls, the firelight is swaying charmingly, brilliant and colorful, and it is the most beautiful.
Beauty is the eternal pursuit of our mathematician heroes.