During his college years, Poincaré became even more obsessed with mathematics. Being physically weak, he devoted himself to the wonderful and magical ocean of mathematics. Through diligent thinking and study, in 1878, he wrote an "unusual" paper on the general solution of differential equations. The following is the story of the mathematician I brought to you. I hope you like it.
Mathematician’s Story 1
After entering the Royal Artillery Academy in Turin, Lagrange began to study mathematics on his own in a planned way. Due to his hard work, he made rapid progress and took up the job of teaching mathematics in the school before graduating. At the age of 20, he was officially appointed as an associate professor of mathematics at the school. From this year, Lagrange began to study the problem of "maximum and minimum". He adopted a purely analytical approach. In August 1758, he wrote to Euler about his research methods, and Euler spoke highly of it. From then on, the two masters began to correspond frequently. During this exchange, a new branch of mathematics was born - the calculus of variations.
In 1759, on the recommendation of Euler, Lagrange was nominated as a corresponding academician of the Berlin Academy of Sciences. Then, he was elected as a foreign academician of the academy.
In 1762, the French Academy of Sciences offered a reward for solving the problem of why the moon rotates and why it always faces the earth with the same side. Lagrange wrote an excellent paper that successfully solved this problem and won a grand prize from the Academy of Sciences. Lagrange's name spread throughout Europe and attracted the attention of the world. Two years later, the French Academy of Sciences proposed the so-called "six-body problem" regarding the perturbations between Jupiter's four satellites and the sun. Faced with this problem, Lagrange was not afraid. After several sleepless nights, he finally found the answer using an approximate solution and won the award again. This award earned him worldwide reputation.
In 1766, Lagrange succeeded Euler as director of the Institute of Physics and Mathematics of the Berlin Academy of Sciences. During the 20 years he served as director, Lagrange published many papers and won many awards from the French Academy of Sciences: in 1722, his paper "On the Three-Body Problem" won the award; in 1773, his paper "On the Long-Term Evolution of the Moon" Equation" won the prize again; in 1779, Lagrange won double the prize for his paper "Study of the Perturbation Theory of Comet by Experiments of Planetary Activity".
While working at the Berlin Academy of Sciences, Lagrange conducted extensive and in-depth research on algebra, number theory, differential equations, calculus of variations and mechanics. One of his most valuable contributions was in the theory of equations. His conclusion that "it is impossible to use algebraic operations to solve general equations of degree n (n>4)" can be said to be the basis for Galois's establishment of group theory.
The most noteworthy thing is that Lagrange completed the greatest classic work since Newton-"On the Analysis of Indeterminacy". This book was written with 37 years of hard work. When it was published, he was already in his 50s. In this work, Lagrange composed the universe into a rhythmic melody composed of numbers and equations, developed dynamics to its peak, and unified the two branches of solid mechanics and fluid mechanics. He used the principle of variation to establish a beautiful and harmonious mechanical system, which can be said to be the foundation of the entire modern mechanics. The great scientist Hamilton hailed this masterpiece as "scientific poetry".
On April 10, 1813, Lagrange died of illness, completing his glorious scientific journey. His rigorous scientific attitude and work style of excellence influence every scientist. His academic achievements also provided rich nutrition for the growth of world-famous mathematicians such as Gauss and Abel. It can be said that in the following 100 years, many major discoveries in mathematics were almost all related to his research.
Mathematician’s Story 2
A Chinese international student applied for the famous Mathematics Department of Tohoku Imperial University in Sendai and was admitted with the first place. Imperial University is a well-known university in Japan. Su Bu won the first place in his youth and he also has some research projects in progress, so he has naturally become a celebrity in the school.
At this time, he developed a special concern for another celebrity in the school, Matsumoto Yoniko. Yonoko is the daughter of Professor Matsumoto of Imperial University. She is not only talented in appearance, but also proficient in flower arrangement, calligraphy and tea ceremony. She also loves music, especially playing the guzheng well.
After a party, Su Buqing and Mi Zi met. In fact, Mizi has always admired Su Buqing, and she was particularly moved by his wisdom and sincerity. Later, the two often spent time walking hand in hand.
In 1927, the Department of Mathematics of Northeastern Imperial University hired Su Buqing, who was studying for graduate school, as an algebra lecturer, making him the first foreign student to hold a concurrent lectureship in the history of the school. The love affair between the two people became an open secret in the school, and many people blessed them; but those who usually pursued Mi Zi had a kind of jealousy and said to Mi Zi: "Su Buqing is a Chinese country bumpkin, his family is very poor, and he is good at studying. People may not be successful in the future. You won't have a good life if you follow him." But Yonzi was unmoved. Su Buqing couldn't stand the hostility of some boys, and he didn't want Mi Zi to be entangled by others anymore. After discussion, they decided to get married as soon as possible.
Yoniko’s mother is a kind-hearted Japanese housewife. She believes that Su Buqing is a person who can be entrusted to her for life. Although Professor Matsumoto also likes Su Buqing very much, he feels that he is Chinese after all and has a humble background, so he has always disapproved of this marriage. At Yoniko's insistence, Professor Matsumoto finally compromised. In 1928, this foreign young couple finally came together and got married in Sendai City. Matsumoto Yoniko has since changed her husband's surname to Sumiko.
Yoniko devoted herself to being a housewife. In order not to affect Su Buqing, she even gave up her talents such as guzheng and calligraphy, leaving only tea ceremony and flower arrangement, because these two hobbies were beneficial to Su Buqing's body and spirit. One year after their marriage, in 1929, Yoniko gave birth to a girl. By the beginning of 1931, Su Buqing had 41 research papers on affine differential geometry and related aspects appearing in mathematical journals in Japan, the United States, Italy and other countries, becoming a well-known figure in Japan and even the international mathematics community. The Matsumoto family all hoped that Su Buqing would stay and work in Japan, and Tohoku Imperial University also issued a letter of appointment to him. Su Buqing has his own difficulties. Before going abroad, he had made an appointment with his senior student Chen Jiangong and returned to China after completing his studies to build a first-class mathematics department in his hometown. Now that Chen Jiangong has completed his studies and returned to China, whether he should go or stay has become a problem that troubles his mind.
The attentive Mi Zi has long discovered that he sighs all day long and does not think about food or tea. One day after dinner, Su Buqing, who had never smoked, was smoking a cigarette, so Mi Zi asked him what was on his mind. Su Buqing told the truth. He didn't want to stay in Japan for his own selfish reasons. What he didn't expect was that Yonzi heard his plan and did not stop it. Instead, he encouraged: "Qing, I support your decision. First of all, I love you, and you love China, so I also love China. I support you to return to the place we both love, and I will follow you wherever you go." Su Buqing was particularly moved by these few words: Mizi is a woman who understands the general situation! With the support of his wife, Su Buqing can take the lead alone. Return to Hangzhou. The conditions at Zhejiang University were far worse than he had imagined. Not only was the monthly salary stated in the appointment letter far less than what he would have received if he was hired as a professor at Yanjing University, but due to the school's tight funding, although he was named an associate professor, he had no job for four consecutive months. Get a penny. Fortunately, his brother, who was an engineer at the Shanghai Arsenal, provided timely help, otherwise Su Buqing would have to rely on pawns to make a living. In order to support his family, Su Buqing plans to return to Japan.
Mathematician’s Story 3
Sophie Kovalevskaya has had a special affection for mathematics since she was a child, and has great curiosity and strong pursuit of knowledge. desire. When she was 8 years old, the family moved to Polibino Grange. Since the wallpaper they brought was not enough, her parents used calculus lectures written by the famous mathematician Ostrogradsky to paper the walls in her room. At that time, Sophie Kovalevskaya often sat alone in front of the wall of her bedroom, staring at the wonderful numbers and mysterious symbols on the wallpaper for hours. Later, Sophie Kovalevskaya wrote in her autobiography: "I often sat in front of the mysterious wall, trying to explain certain words and phrases and find the correct order of these pages. Through repeated reading, the words on the pages Strange formulas and even some literal expressions left a deep impression on my mind, even though I knew nothing about them at the time. ”
Sophie Kovalevskaya’s. Her grandfather and maternal grandfather were both excellent mathematicians, which may have contributed to her mathematical talent, but her success was mainly due to her unremitting hard work.
When she is studying mathematics, she always pays very close attention and can quickly understand and master what the teacher says. Once, the math teacher asked Sophie Kovalevskaya to repeat what she said in the last class. Sophie Kovalevskaya did not follow the teacher's method of teaching, but changed to own way of thinking. When she finished speaking, the teacher immediately gave her a thumbs up and praised her for being great. It can be seen that Sophie Kovalevskaya is good at thinking about problems independently and is good at actively looking for her own thinking methods so that her thinking is not limited to a specific way, which is very important for her future mathematics research.
After graduating from high school, Sophie Kovalevskaya wanted to continue learning advanced mathematics. However, there was a general trend of contempt for women in Russia at that time, and women did not have the right to receive higher education. For Sophie Kovalevskaya, the only way to further her education was to study abroad. When Sophie Kovalevskaya told her family about her desire to study abroad, she encountered strong opposition from her family. In order to fight for the right to go to university, Sophie Kovalevskaya broke through all kinds of resistance and finally got her wish and came to study at Heidelberg University in Germany. She lived an intense and simple study life in a strange foreign city.
While studying at Heidelberg University, in order to make greater progress, Sophie Kovalevskaya went to the mathematics master Weierstra, who is known as the "father of modern analysis". I went to Professor Si's home to ask for advice. The mathematics master was moved by Sophie Kovalevskaya's sincere attitude. After many tests, he accepted the diligent and studious female student with satisfaction. Under the careful guidance of Weierstrass, Sophie Kovalevskaya studied mathematics harder. After a period of study and practice, Sophie Kovalevskaya wrote three important academic papers on mathematics. Soon, she successfully solved the "mathematical water monster" that has troubled mathematicians for more than a hundred years. problem, and thus received the famous "Botting Prize".
Sophie Kovalevskaya received many honors throughout her life and made great contributions to the development of mathematics, but she was never complacent. Unfortunately, she contracted a cold during a trip and was bedridden because she could not rest in time. She died soon after at the age of 41.
Mathematician’s Story 4
Doblin carried his research papers and the theorem he was about to complete with him to the front line and stationed at the Maginot Line. In the early months of the war, his superiors authorized him to use all his spare time to continue his mathematical research. In the summer of 1940, the German army crushed the French resistance, and Doblin's infantry regiment was also facing annihilation. While other soldiers retreated, Doblin volunteered to stay with two comrades to resist the incoming German troops. On June 21, when the German army was about to occupy the position, Dobrin shot himself, preferring to die as a prisoner. He was only 25 years old. His brother Claude recalled: "Fortunately, Dobrin burned all the research papers on him before the Germans captured the position to avoid falling into the hands of the Germans. He could not tolerate the Germans plagiarizing his ideas."
After the war, Doblin's name was quickly forgotten. However, half a century after his heroic death, an official from the French Academy of Sciences accidentally discovered that as early as February 1940, Dobrin had carefully classified his research results according to a secret rule dating back to the Louis XIV period. Saved. He sealed the manuscript of his mathematical theory in an envelope and hid it in the basement of the Academy of Sciences. According to the secret storage rules, the envelope must be opened with the author's permission. In the event of the author's death, it must be opened 100 years from the date of collection. In this way, the manuscript of Doblin's paper will not be made public until 2040. But after years of lobbying by academicians of the French Academy of Sciences and mathematicians from around the world, his brother Claude finally agreed to break this rule in the summer of 2000.
As a result, the mathematical manuscripts written by Dobrin while fighting in the Ardennes came to light. This established the young soldier as one of the most important figures in modern mathematics and the founder of contemporary probability theory. This caused a stir in French intellectual circles. The French Academy of Sciences published a special issue for this purpose, publishing the full text of Dobrin's manuscript "as a tribute to the genius."
According to Bernard Blue, an outstanding French mathematical historian, Dobrin's paper made up for the "Mathematical Analysis" before World War II and the Japanese progress in probability theory in the 1950s. The white space left.
Doblin's research touched on one of the most important areas of applied mathematics, and he foresaw the laws of motion of things susceptible to irregular disturbances, such as the movement of particles in fluids such as water.
Professor Joel was the first person to see Doblin's manuscript. He said; "I believe Doblin knew that he would be doomed in this war. You will notice that he left as little writing as possible. He clearly knew that what he was engaged in was the most promising of his era. His mathematical research work was short-lived, but he recorded the results of his thoughts on mathematics that were not yet fully formed. ”
Mathematician’s Story 5
Poincaré was born in France in April 1854. His childhood was extremely unfortunate, and his father, who was skilled in medicine, could not bring him good health. He has suffered from a strange motor nervous system disease since he was a child, making it difficult to write and draw. At the age of 5, he suffered from severe diphtheria, which slowed the development of his language skills and severely damaged his vision. Fortunately, he had a talented and educated mother who gave him a good family education since childhood. From this, Poincaré's talent began to be revealed through family education and self-training. During class, he couldn't clearly see the teacher's writing on the blackboard and couldn't take notes, so he listened with all his concentration and memorized it in his mind. The following short story can fully reflect the learning characteristics of this legendary figure:
In the autumn of 1864, in a classroom of a middle school in France, a well-known local astronomer Tell students about the movement of planets. Most of the students who lacked interest in astronomy were distracted, either expressionless or yawning profusely, which obviously annoyed the thankless teacher. At this time, he once again discovered that a small boy in the back row had his head lowered and never looked at the blackboard. He seemed to be deserting, so he strode over.
"Classmate, what are you doing? Why are you not looking at the blackboard? Do you understand everything?" the teacher asked angrily. "I'm used to listening with my ears, and I understand, thank you!" the little boy stood up and replied respectfully. "Is it true? Then please tell everyone!" The teacher who didn't really believe it was deliberately trying to make things difficult. "The movement of the planets..." The little boy repeated completely what the teacher just said. "Oh my god! It's amazing that you can remember what you have heard!" The teacher was dumbfounded and felt incredible: "Then why don't you read the content on the blackboard? It will be easier to understand!" The teacher was still a little puzzled.
"Teacher, he is severely short-sighted and cannot see the words on the blackboard clearly." The classmate next to him hurriedly explained. "Oh, that's right. It seems that God is fair. Your concentration has made up for your shortcomings in vision. You already have the best pair of 'inner eyes'!"
This one has extraordinary memory. The young man was Poincaré, the later mathematics master. Due to visual impairment, Poincaré could only listen and memorize his lectures, which meant that he had to put in more effort and hardship than ordinary people, but what he gained at the same time was that his brain was surprisingly developed, especially his ability to understand and remember. Super capable. His memory of things is fast, accurate, and long-lasting, and he is highly focused when thinking about problems, especially in mathematics. He can complete complex operations and reasoning in his mind. That kind of highly concentrated attention, no matter how great the external interference is, cannot interrupt his thinking, and these characteristics are exactly what a mathematician must possess. At that time, senior students often tested him on mathematics questions. As a result, Poincaré almost always gave the answer instantly, but the person who tested him took a long time to verify the answer he gave. Therefore, he obtained A nickname for "Mathematical Monster".
In 1873, 19-year-old Poincaré took the entrance examination to the Ecole Polytechnique in Paris, a school known throughout the world for its rigid examinations. At this time, Poincaré's mathematical talent had emerged. In order to test his ability, the examiners deliberately postponed the exam for 45 minutes. They used this time to carefully design several mathematical problems for him. This is not surprising. The young man easily completed the calculation in his head without writing. When he reported the answer, the time was short and the method was so clever that the examiners were stunned and ecstatic. Although Poincaré's painting ability was very poor and he got zero points on the geometric drawing question, the examiners who were interested in Xicai finally broke the convention and admitted him by giving him the first place after intense discussion.
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