Su Yu 1902 was born in a mountain village in Pingyang County, Zhejiang Province in September. Although the family is poor, his parents scrimp and save, and they have to work hard to pay for his education. When he was in junior high school, he was not interested in mathematics. He thinks mathematics is too simple, and he will understand it as soon as he learns it. It can be measured that a later math class influenced his life.
That was when Su was in the third grade. He was studying in No.60 Middle School in Zhejiang Province. Teacher Yang teaches mathematics. He has just returned from studying in Tokyo. In the first class, Mr. Yang didn't talk about math, but told stories. He said: "In today's world, the law of the jungle, the world powers rely on their ships to build guns and gain benefits, and all want to eat and carve up China. The danger of China's national subjugation and extinction is imminent, so we must revitalize science, develop industry and save the nation. Every student here has a responsibility to' rise and fall in the world'. " He quoted and described the great role of mathematics in the development of modern science and technology. The last sentence of this class is: "In order to save the country and survive, we must revitalize science. Mathematics is the pioneer of science. In order to develop science, we must learn math well. "I don't know how many lessons Sue took in her life, but this lesson will never be forgotten.
Teacher Yang's class deeply touched him and injected new stimulants into his mind. Reading is not only to get rid of personal difficulties, but to save the suffering people in China; Reading is not only to find a way out for individuals, but to seek a new life for the Chinese nation. That night, Sue tossed and turned and stayed up all night. Under the influence of Teacher Yang, Su's interest shifted from literature to mathematics, and since then, she has set the motto "Never forget to save the country when reading, and never forget to save the country when reading". I am fascinated by mathematics. No matter it is the heat of winter or the snowy night in first frost, Sue only knows reading, thinking, solving problems and calculating, and has worked out tens of thousands of math exercises in four years. Now Wenzhou No.1 Middle School (that is, the provincial No.10 Middle School at that time) still treasures a Su's geometry exercise book, which is written with a brush and has fine workmanship. When I graduated from high school, my grades in all subjects were above 90.
/kloc-At the age of 0/7, Su went to Japan to study, and won the first place in Tokyo Technical School, where she studied eagerly. The belief of winning glory for our country drove Su to enter the field of mathematics research earlier. At the same time, he has written more than 30 papers, and made great achievements in differential geometry, and obtained the doctor of science degree in 193 1. Before receiving her doctorate, Su was a lecturer in the Department of Mathematics of Imperial University of Japan. Just as a Japanese university was preparing to hire him as an associate professor with a high salary, Su decided to return to China to teach with his ancestors. After the professor of Zhejiang University returned to Suzhou, his life was very hard. In the face of difficulties, Su's answer is, "Suffering is nothing, I am willing, because I have chosen the right road, which is a patriotic and bright road!" "
This is the patriotism of the older generation of mathematicians.
The epitaph of a mathematician
Some mathematicians devoted themselves to mathematics before their death, and after their death, they carved symbols representing their life achievements on tombstones.
Archimedes, an ancient Greek scholar, died at the hands of Roman enemy soldiers who attacked Sicily. ), people carved the figure of the ball in the cylinder on his tombstone to commemorate his discovery that the volume and surface area of the ball are two-thirds of that of the circumscribed cylinder. After discovering the regular practice of regular heptagon, German mathematician Gauss gave up the original intention of studying literature, devoted himself to mathematics, and even made many great contributions to mathematics. Even in his will, he suggested building a tombstone with a regular 17 prism as the base.
/kloc-Rudolph, a German mathematician in the 6th century, spent his whole life calculating pi to 35 decimal places, which was later called Rudolph number. After his death, someone else carved this number on his tombstone. Jacques Bernoulli, a Swiss mathematician, studied the spiral (known as the thread of life) before his death. After his death, a logarithmic spiral was carved on the tombstone, and the inscription also read: "Although I have changed, I am the same as before." This is a pun, which not only describes the spiral nature, but also symbolizes his love for mathematics.
Zu Chongzhi (AD 429-500) was born in Laiyuan County, Hebei Province during the Northern and Southern Dynasties. He read many books on astronomy and mathematics since childhood, studied hard and practiced hard, and finally made him an outstanding mathematician and astronomer in ancient China.
Zu Chongzhi's outstanding achievement in mathematics is about the calculation of pi. Before the Qin and Han Dynasties, people used "the diameter of three weeks a week" as pi, which was called "Gubi". Later, it was found that the error of Gubi was too large, and the pi should be "the diameter of a circle is greater than the diameter of three weeks". However, there are different opinions on how much is left. Until the Three Kingdoms period, Liu Hui put forward a scientific method to calculate pi-"secant" which approximated the circumference of a circle with the circumference inscribed by a regular polygon. Liu Hui calculated the circle inscribed with a 96-sided polygon and got π=3. 14, and pointed out that the more sides inscribed with a regular polygon, the more accurate the π value obtained. On the basis of predecessors' achievements, Zu Chongzhi devoted himself to research and repeated calculations. It is found that π is between 3. 14 15926 and 3. 14 15927, and the approximate value in the form of π fraction is obtained as the reduction rate and density rate, where the six decimal places are 3. 14 1929. There's no way to check now. If he tries to find it according to Liu Hui's secant method, he must work out 16384 polygons inscribed in the circle. How much time and labor it takes! It is obvious that his perseverance and wisdom in academic research are admirable. It has been more than 1000 years since foreign mathematicians obtained the same result in the secrecy rate calculated by Zu Chongzhi. In order to commemorate Zu Chongzhi's outstanding contribution, some mathematicians abroad suggested that π = be called "ancestral rate".
Zu Chongzhi exhibited famous works at that time and insisted on seeking truth from facts. He compared and analyzed a large number of materials calculated by himself, found serious mistakes in the past calendars, and dared to improve them. At the age of 33, he successfully compiled the Daming Calendar, which opened a new era in calendar history.
Zu Chongzhi and his son Zuxuan (also a famous mathematician in China) solved the calculation of the volume of a sphere with ingenious methods. They adopted a principle at that time: "If the power supply potential is the same, the products should not be different." That is to say, two solids located between two parallel planes are cut by any plane parallel to these two planes. If the areas of two sections are always equal, then the volumes of two solids are equal. This principle is based on the following points. But it was discovered by Karl Marx more than 1000 years after Zu's father. In order to commemorate the great contribution of grandfather and son in discovering this principle, everyone also called it the "ancestor principle". The works of Italian scientist Maria Gaetana Agnesi (17 18 ~ 1799) in natural science and philosophy have opened up a complete academic world.
Born in 17 18, Aniezer was regarded as a genius since he was a child. In her family gatherings, she always talks about a wide range of topics such as logic, machinery, chemistry, botany, zoology, mineralogy and analytic geometry. At the age of 9, she published a long speech convincingly advocating women's right to receive higher education. Although she spoke in Latin, she answered the audience in the local dialect. 1 1 years old, she is proficient in Latin, French, Greek, German, Hebrew and Spanish, including her native language Italian.
Hannuzet is modest and introverted by nature. After 1738, she didn't want to attend the party at home, but joined the monastery and devoted her life to the poor. Agnezer's father persuaded her to continue her research. Since then, she has lived an isolated life and devoted herself to the study of mathematics.
In the next fourteen years, Hannuzet focused on the field of mathematics and wrote some admirable works. Her lecture on analysis is a classic work with more than 1000 pages, including the original discoveries from algebra to calculus and differential equations. Because of her works, Hannuzet's name is often put together with the bell curve (also called "Hannuzet Witch", the equation is). Because of its mathematical properties and its application in physics, this curve has aroused the interest of mathematicians.
Hannuzet's book was called "the best and most complete work in this field" by French Academy of Sciences, and Pope Benedict XIV awarded her a gold medal in recognition of her outstanding contribution in mathematics. 1750, Agnez was appointed as the head of the Department of Mathematics and Natural Philosophy at the University of Bologna. However, she only accepted their honorary title.
175 1 year, Agnes was at the peak of her mathematics career, but she suddenly stopped all research in mathematics and science. She took care of her father until he died on 1752, and then took care of and educated her twenty brothers and sisters. After that, she devoted the rest of her life to charity and became the director of 177 1
Euler was born in the Swiss city of Basel in 1707. At the age of 13, he went to university of basel to study under the careful guidance of the most famous mathematician at that time (John johann bernoulli, 1667- 1748).
Euler's profound knowledge, endless creative energy and unprecedented rich works are amazing! He published papers from the age of 19 to the age of 76, and has written countless books and papers for more than half a century. Up to now, Euler's name can be seen in almost every mathematical field, from Euler line of elementary geometry, euler theorem of polyhedron, Euler transformation formula of solid analytic geometry, Euler solution of quartic equation to Euler function in number theory, Euler equation of differential equation, Euler constant of series theory and Euler equation of variational method. Euler formula of complex variable function, etc. , is countless. His contribution to mathematical analysis is even more original. Introduction to infinitesimal analysis is his epoch-making masterpiece, and mathematicians call him "the embodiment of analysis" at that time.
Euler is the most prolific outstanding mathematician in the history of science. According to statistics, * * * has written 886 books and papers in his tireless life, of which 40% is analysis, algebra and number theory, 18% is geometry, 28% is physics and mechanics, 1 1% is astronomy, as well as ballistics and navigation.
The amazing productivity of Euler's works is not accidental. He can work in any harsh environment. He often holds his children on his knees to finish his papers, regardless of their noise. His indomitable perseverance and tireless academic spirit made him blind, and he didn't stop studying mathematics. During the 17 years after his blindness, he also dictated several books and about 400 papers. Gauss (1777- 1855), a great mathematician in the 9th century, once said, "Studying Euler's works is always the best way to understand mathematics."
Euler's father Paul Euler is also a mathematician. He wants little Euler to study theology and teach him a little at the same time. Because of his talent and extremely diligent spirit, he got johann bernoulli's appreciation and special guidance. When he was 19 years old, he wrote a paper on the mast and won a prize from the Paris Academy of Sciences. His father no longer opposed him to study mathematics.
Johann bernoulli's son daniel bernoulli went to Russia on 1725 and recommended Euler to czar Cadling I. In this way, Euler came to Petersburg on 17 and 1733. At the age of 26, Euler became a professor of mathematics at the Academy of Sciences in Petersburg. 1735, Euler solved a problem. It took several famous mathematicians several months to solve this problem, but Euler finished it in three days with his own invented method. However, due to overwork, he got an eye disease and unfortunately lost his right eye. At this time, he was only 28 years old. At the invitation of Prussian frederick the great, Euler went to Berlin as the director of the Institute of Physics and Mathematics of the Chinese Academy of Sciences until 1768. Later, at the sincere urging of Tsar Cadling II, he returned to Petersburg. Unexpectedly, not long after, his left eye vision decreased and he was completely blind. Unfortunately, the fire in Petersburg in 177 1 affected Euler's residence. 64-year-old Euler was blinded by illness and was trapped in the fire. Although he was saved from the fire by others, his research and a lot of research results were reduced to ashes.
The heavy blow still didn't knock Euler down. He vowed to recover the loss. Before he was completely blind, he could still see vaguely. He seized this last moment, scribbled down the formula he found on a big blackboard, and then dictated its contents, which were recorded by his students, especially his eldest son A. Euler (mathematician and physicist). After Euler was completely blind, he still struggled with the darkness with amazing perseverance and studied it with memory and mental arithmetic.
Euler's memory and mental arithmetic are rare. He can retell the contents of his notes when he was young. Mental arithmetic is not limited to simple operations, and advanced mathematics can also be done by heart. An example is enough to illustrate his skill. Two students of Euler added the term 17 of a complex convergence series to the 50th place, and the difference between them was one unit. In order to determine who is right, Euler calculated all the errors in his mind and finally put them into the errors. It also solved Newton's headache-the problem of starting from the moon and many complicated analysis problems.
Euler has a high style. Lagrange is a great mathematician after Euler. Since the age of 19, he has been communicating with Euler to discuss the general solution of isoperimetric problems, from which the variational method was born. The isoperimetric problem is a problem that Euler has painstakingly considered for many years. Lagrange's solution won warm praise from Euler. 1February 2, 759, Euler praised Lagrange's achievements in his reply. He modestly suppressed his immature works in this respect from being published for the time being, so that the works of young Lagrange could be published and circulated, and won great reputation. In his later years, all mathematicians in Europe regarded him as a teacher. The famous mathematician Laplace once said, "Euler is our mentor." Euler's energy was maintained until the last moment, in the afternoon of September 1783. In order to celebrate his successful calculation of the law of balloon rising, Euler invited friends to dinner. Soon after Uranus was discovered, Euler wrote the essentials of calculating Uranus' orbit and made fun of his grandson. After drinking tea, he suddenly fell ill, and his pipe fell out of his hand, muttering "I'm dead". Finally, Euler "stopped living and calculating".
Euler's life is a life of struggle for the development of mathematics. His outstanding wisdom, tenacious perseverance, tireless spirit of struggle and noble scientific ethics are always worth learning. Euler has made many achievements in mathematics, and the solution of the famous problem of the Seven Bridges in Konigsberg initiated the research of graph theory. Euler also found that no matter what shape of convex polyhedron, there is always a relationship between the number of vertices V, the number of edges E and the number of faces F, that is, v-e+f=2. V-e+f, which is called Euler characteristic, has become the basic concept of topology. In number theory, Euler first introduced the important Euler function φ(n), and proved Fermat's theorem in many ways. Mathematical formulas and theorems named after Euler can be found everywhere in mathematics books. At the same time, he has made brilliant achievements in physics, astronomy, architecture, music and philosophy. Euler also created many mathematical symbols, such as π( 1736), i( 1777), e( 1748), sin and cos( 1748), tg( 1753).
German mathematician david hilbert (1862 ~ 1943) is one of the greatest mathematicians in the 20th century. His contribution to mathematics is enormous and multifaceted, and his research fields involve algebraic invariants, algebraic number fields, geometric foundations, variational methods, integral equations, infinite dimensional spaces, physics and mathematical foundations. He published it in 1899. And thus promoted the formation of "Mathematical Axiomatic Chemistry School". It can be said that Hilbert is the founder of modern axiomatic school. 1900, 38-year-old Hilbert delivered a famous speech entitled "Mathematical Problems" at the Second International Congress of Mathematicians held in Paris. In the speech, according to the achievements and development trend of mathematics research in19th century, with outstanding foresight and extraordinary insight, 23 problems faced in the new century were put forward. These 23 questions involve the most important fields of modern mathematics (the famous Goldbach conjecture is part of the eighth question), and the study of these questions has strongly promoted the development of various branches of mathematics in the 20th century.
This paper introduces two short stories about Hilbert's youth.
First, the teacher wants to push the class now.
1In the autumn of 880, 18-year-old Hilbert entered his hometown University of Konigsberg. Despite his father's desire to study law, he did not hesitate to enter the philosophy department to study mathematics (the university at that time, the mathematics department was still located in the philosophy department). Hilbert discovered how free college life was at that time. Unexpected freedom, many young people spend their precious first year of college on traditional activities of the student union, such as drinking and fighting swords. However, for Hilbert, the more fascinating thing about college life is that he can finally devote all his energy to mathematics freely.
In the first semester of college, Hilbert took three courses: integral calculus, matrix theory and surface curvature theory. You can transfer to another university in the second semester. Hilbert chose Heidelberg University, which was the most attractive and romantic school among all universities in Germany at that time. Hilbert took lazarus fuchs's course at the University of Heidelberg. Fuchs is a different person. Take it remotely? Toes are dizzy. 1. Address craftsman carbon negative flash? Is the department stable and fat? Say ∠??? Kiss eight? Are you in a hurry? Smash? Refute what? Are you tired? Humble 37 [5]? Hey? That kind of danger? Why don't you play with me? Hey? What's the matter with you? What's wrong with more money and slower eyebrows? What's the matter with you? What's the matter with you? What's the matter with you? Hey? Worm overseas Chinese comfort ZUk? The bag is lying and the plaque is smashed. Dangerous? What's the matter with you? Curtains? What's wrong with the sulfur spectrum? Nyoka? Neon guide? Kick? What is the charm? Park Ji-yi left? There are six gaps in the dark south. What are you doing? ъъъъъъъъъъъъъъъъъъъъъъъъъъ Do you want to pour milk into the industry? What's wrong with cutting charcoal? Neon guide to eunuch Jia's badger? Tao Zhizhi? Hey? Hey? 8 strokes of flattery. What's wrong? At night? Neon? х Chili? Hey? By stew? What do you mean? Hey, hey, hey? Are you pretty? What's wrong with ants? I'll call you? I've been fishing for badgers. I'm looking forward to it What's the story? /P & gt；
Second, the routine steps under the apple tree
Hilbert stayed in Heidelberg for one semester, and could have been allowed to give lectures in Berlin next semester, but he was reluctant to part with his hometown, so he returned to the University of Konigsberg. Next semester, in the spring of1882, Hilbert decided to stay in Konigsberg.
At this time, Herman Jokowski returned to the University of Konigsberg after studying in Berlin for three semesters. Minkowski has been excellent in mathematics since he was a child. It is said that once in a math class, the teacher "hung up the blackboard" because he misunderstood the question, and the students shouted in unison: "Shut up and help!" When he was studying in Berlin, he won an award for his excellent math work. At this time, Jokowski, who was only 17 years old, was immersed in a very profound research-solving a problem that the Paris Academy of Sciences had to solve: summing a table into five squares. One year later, in the spring of 1883, 18-year-old Yuekovsky and the famous British mathematician Smith * * * won the grand prize of the Paris Academy of Sciences. This incident caused a sensation throughout Konigsberg. Hilbert's father warned his son not to make friends with "such a famous person" rashly. But because of their love of mathematics and their faith in * * *, Hilbert and Minkowski, two years younger than him, soon became good friends.
1884 In the spring, Adolf leonid hurwicz, a young mathematician, came to Koenigsberg from G? ttingen as an associate professor. He is less than 25 years old and has made outstanding research results in function theory. Hilbert and Minkowski soon established a close relationship with their new teacher. They three young people must meet at 5 o'clock every afternoon and go for a walk under the apple tree. Hilbert later recalled: "In the day-to-day walk, we were all immersed in discussion." Exchange our newly acquired understanding of the problem with each other, and exchange ideas and research plans with each other. "Among them, leonid hurwicz has a wide range of" solid basic knowledge, which has been well organized ",so he is a natural leader and persuaded the other two. At that time, Hilbert found that this learning method was many times better than boring in a dark classroom or library. This routine walk lasted for eight and a half years. In this leisurely and interesting way of learning, they explored "every corner" of mathematics and inspected every kingdom in the mathematical world. Hilbert later recalled: "At that time, I never thought that we would take ourselves so far!" " In this way, the three people "formed a lifelong friendship." "
As Professor Xu Lizhi pointed out, discussions between tutors and friends also played a very important role in Hilbert's growth and development. It is conceivable that that period was an important stage for Hilbert's rapid growth in talent, knowledge and knowledge. Without this experience, Hilbert could have raised so many famous questions in so many important fields at once in 1900. It is hard to imagine. This short story about Hilbert's walk tells us that in addition to classroom activities, extracurricular communication between teachers and students and between classmates is also an important way of learning, which is very beneficial to mathematics learning. Moreover, because there are no books, papers and pens for communication and no complicated deduction and calculation, we can only say something that can be "said" in words, that is, to understand and analyze problems and tap the soul of the commander-in-chief in the form of deduction ... and these are very important for learning mathematics well. Students might as well often invite a few good students to walk and chat together, which will definitely be fun.
(Wang) According to
He was the greatest algebraic geometer in the19th century, but he retaken the college entrance examination five times and failed every time because of his poor math test. He barely graduated from college, and every time he failed in the exam, it was for math subjects. After graduating from college, he couldn't get into any graduate students because the subject he didn't do well in was mathematics. Mathematics is the love of his life, but the math exam is a nightmare of his life. However, this does not change his greatness: he first put forward the "* * * yoke matrix" in textbooks, and he solved the "general solution of quintic equation" for more than 1000 years. He is the first person in the world to prove the transcendence of natural logarithm. His life has proved that "a person who fails the exam can still win?" Quot and what is even more wonderful is that failing the exam has become a blessing in his life. How did this happen? Well (expressing hesitation, etc.) ... maybe you can find the answer in this article! Open the map of Europe, there is a small map embedded in the northeast corner of France, named Lorraine.
This place has been a battleground for military strategists since ancient times, because the Rhine River estuary in the north and the Marne River in the south can go straight to Paris; The Ardennes on the verge are the military commanding heights; This stratum contains the largest iron ore in Europe. As early as the Holy Roman Empire, the Lorraine grassland was covered with the blood of knights; 187 1 After the bloody German soldiers ravaged France, the land that France was asked to cede was Lorraine.
The lineage of a revolutionary.
After a hundred years of war, Lorraine left behind a group of hardworking and philosophical French who were able to face the hardships of the environment. Charles Hermite (1822 12) was born in Diyug, a small village in Lorraine. His parents and grandparents both participated in the French Revolution. His grandfather was arrested by extremist political groups after the Revolution and later died in prison. Some relatives died on the guillotine; His father was an outstanding metallurgical engineer. Because he was wanted by the commune, he fled to the small village of Lorraine on the French border and worked incognito as a miner in an iron mine.
The owner of the iron mine is Lallemand, a standard and tenacious Lorraine. He has a stronger daughter, Madeleine. In that conservative era, Madeleine was famous for "daring to wear pants without skirts outdoors" and her management of miners was fierce. But as soon as she met this engineer from Paris, she softened up, knew whether the other person was killed or married to him, and gave birth to seven children for him. Hermite ranks fifth among seven children. He was born with a disability in his right foot and needed to walk with crutches. Half of him has the blood of his father's excellent intelligence and ideal struggle, and the other half has the strong blood of Lorraine, whose mother dares to do things and loves and hates each other. This is the first sign of his extraordinary career.
Understanding the beauty of mathematics from the master
Hermite was a problem student since he was a child. He always likes to argue with the teacher in class, especially some basic questions. He especially hates exams; Later, I wrote: "Learning is like the sea, and exams are like hooks. The teacher always hangs the fish on the hook, so how can the fish learn to swim freely and balance in the sea? " Seeing that he didn't do well in the exam, the teacher hit him on the foot with a wooden stick. He hates it. Later? Quot The purpose of education is to use the brain, not the feet. What's the use of kicking? Can kicking make people smart? "He did badly in the math exam, mainly because he was particularly good at math; What he said even made the math teacher mad. He said: "Math class is a pool of smelly water and a pile of rubbish. Those who do well in math are second-rate people, because they only know how to move garbage. "He pretended to be a first-class scientific madman. However, what he said is true. Most of the greatest mathematicians in history came from literature, diplomacy, engineering, military and other fields. They have nothing to do with mathematics. Hermite spent a lot of time reading the original works of mathematicians, such as Newton and Gauss. He believes that only there can we discover the beauty of mathematics, and only there can we return to the basic point of argument and get the source of mathematics excitement. " In his later years, he recalled the frivolity of his youth and wrote: "Traditional mathematics education requires students to learn step by step and cultivate them to apply mathematics to engineering or business, so it has not stimulated students' creativity. But mathematics has its own beauty of abstract logic. For example, in the program of solving multiple squares, the existence of roots is itself a kind of beauty. The value of mathematics is not only for the application in life, but also should not be reduced to a tool for engineering and commercial applications. The breakthrough of mathematics still needs to constantly break through the existing pattern. "
Filial piety genius
Hermite's performance worried his parents. They sent him to "Louis-le-Grande" in Paris, but begged him to study hard and was willing to pay more money. Because of his outstanding talent in mathematics, he can't put himself into the mold of mathematics education, but in order to comply with his parents' wishes, he has to face those subtle and complicated calculations every day, which makes him extremely painful. This filial genius seems destined to torture himself all his life. The entrance examination of Paris Institute of Technology is held twice a year. He/kloc-began to take the exam at the age of 0/8, and only passed the fifth exam with the score of Hewei. In the meantime, when he almost gave up, he met a math teacher, Richard. Teacher Richard said to Hermite, "I believe you are the second mathematical genius after Lagrange." Lagrange is known as Beethoven in mathematics, and his approximate root solution is known as "the poem of mathematics". But Hermite's talent is not enough. Teacher Richard said, "You need God's grace and persistence to complete your studies, so that you won't be sacrificed by the traditional education that you think is rubbish." So, he failed again and again, but continued to take the exam.