Abel was the greatest mathematician who appeared in Norway in the19th century. He struggled in a poor environment all his life. On the day he was born, he hoped to have a regular job so that he could settle down and do research. He hoped to marry a girl he loved. But fate seems to be against him, and all his expectations have come to nothing. Finally, lung disease took his life, and he died at the age of 26!

Noun (abbreviation of noun) H.Abel was born in a big family with seven brothers and sisters. His father was a poor priest in a small village in Fendo, Norway. Abel is the second child in the family. When I was a child, my brother was taught literacy by his father, and primary education was basically taught by his father, because they didn't have the money to hire a tutor like others.

At the age of 13, he and his brother were sent to a Catholic school in Christianity (later Oslo, Norway). This is an ancient school. Some officials send their children here to study, and some scholarships are given to those who can't afford tuition. Abel also got a little scholarship.

When Abel entered the school, the standards of the school had been lowered, because a new university had just been established here, and most of the good teachers and experienced teachers had been transferred to the university to teach, leaving only poor teachers and new teachers in the school. A year or two ago, their brothers got good grades and won a book award. But later, the teacher's boring teaching methods and high-pressure means made my brother's grades decline, and what's worse, my brother became nervous. In the end, he couldn't study and had to be sent home. Then he became bad and could do nothing all his life.

18 17 What happened can be said to be a turning point in Abel's life. The math teacher is a rude guy and drinks like a bottle of wine. He often laughs at students with poor grades and often punishes them. A student was seriously injured and finally fell ill and died. After many people protested to the school authorities, the teacher was fired and replaced by a very young teacher, Berndt Michael Holm-Boyi, who was seven years older than Abel.

Hong Boyi studied some pure mathematics and worked as a teaching assistant for Chrisoffer Hansteen, a famous Norwegian astronomer. He is very familiar with middle school math classes. Different from previous teachers, he adopted a novel and inflexible teaching method: he adopted a teaching method that allowed students to exert their independent working ability and encouraged them to solve some math problems that suited them.

Abel likes the new teacher very much. He found that mathematics was not as boring as before, and he was glad that he could solve some problems that his classmates could not. At the end of the first year, Hong Boyi criticized Abel as "an excellent mathematical genius" in his student report.

Abel is more and more enthusiastic about mathematics. Humboldt encouraged him, gave him some special questions and lent him the textbooks he had learned in college. Hong Boyi later recalled: "From then on, Abel was fascinated by mathematics, and he marched into this science with amazing enthusiasm and speed. In a short time, he learned most of the elementary mathematics. At his request, I taught him advanced mathematics in private. Soon after, he read the works of French mathematician Poisson and German mathematician Gauss, especially Lagrange. He has begun to study several branches of mathematics. "

For a child of 16 years old, novels and poems can no longer attract his interest. He only went to the library to find books on pure mathematics and applied mathematics: Newton's books, astronomy's books, and D'Alembert's books on mechanics. He wrote down some of his research in a big book. At this time, he found that Euler only proved the exponent of rational number for binomial theorem, so he gave all general proofs.

He gets along well with his classmates at school, and he is not arrogant because of his teacher's praise. Because of his poor health, pale face and shabby clothes, his classmates nicknamed him "tailor Abel".

Dare to start solving problems

In his last year of middle school, he began to consider the general solution of the famous mathematical problem quintic equation at that time.

The formula for finding the root of quartic equation with one variable is a hot issue in16th century, which was solved by Italian mathematicians Ferro, tartaglia, Cadinot and Ferrari.

However, in the next few hundred years, mathematicians worked out a general formula for finding the roots of quintic or higher equations. The condition is that this formula is expressed by several algebraic operations of addition, subtraction, multiplication, division and division and the coefficients of the equation. But no one can succeed.

Abel thought for a while. He thought he got the answer, but Humboldt, the teacher, didn't understand, and he didn't know what went wrong. He took it to the university to meet his professor, and no one in Norway could understand his things. At that time, only Denmark in Northern Europe had a higher level of mathematics, so Professor Hanstin sent his manuscript to Degen, a famous Danish mathematician, hoping that it would be published by Danish Academy of Sciences.

Professor Duggan can't see anything wrong with Abel's argument, but from his experience, he knows that some great mathematicians couldn't solve this problem in the past, and it won't be so easy to solve. He asked Abel to illustrate his method with some practical examples. In his reply to Professor Hans Christian, he said that even if Abel's results were proved to be wrong, it showed that he was a talented person in mathematics. He suggested: "focusing on a mathematics that will have a great influence on analysis and mechanics, I suggest learning elliptic integral." A diligent and talented researcher will not be limited to functions with beautiful nature, but will find strait of magellan and enter the vast ocean of analysis. "

Duggan suggested that Abel study the properties of the following functions.

The former appears in solving the differential equation of motion of a simple pendulum, and the latter appears in finding the arc length of an ellipse. Duggan's suggestion is sincere and constructive. Abel later verified the actual example and proved that his discovery was wrong.

However, Mr. Humboldt criticized Abel in his report at the end of the study: "A mathematical genius ... if he were alive, he might become a great mathematician."

Humboldt himself made no achievements in mathematics, but his contribution to science was to discover Abel's talent in mathematics. And become his loyal friend and give him a lot of help. After Abel's death, Hong also collected and published his research results.

No money for college.

1820 he 18 years old, his father died. There is no property at home, and my mother has only a little pension to raise several children. The youngest brother is only 6 years old, but the eldest brother is mentally abnormal and can't work, so he can only rely on his mother to take care of him. His thin shoulders bear the burden of the family. He loves his brothers and sisters and hopes that they can read some books. But what can such a teenager find in poor Norway at that time?

Hong Boyi hopes that he can go to college and find some of his former professors, hoping to help this "promising young mathematician". At that time, there were no scholarships and grants in the university, but only one or two free rooms were provided to the poorer people in the dormitory. Abel wrote to the university authorities and asked, "My father died, and besides me, my mother had to take care of five other children. In that case, she can't give me any help. " I hope to get a free dormitory. Professor friends raise money for his study, and the economy has some sources. He was also lucky enough to get a free dormitory, and he allowed his younger brother to live with him.

Abel is very grateful to those professors who spend part of their salary on his life and study. He often goes to their home, especially Professor Hansen's wife, who cares about him as much as her mother and sister.

In college, he must first get a junior degree, and then he can study what he is interested in freely. He will get this degree in a year. At that time, there was no advanced mathematics in the university. Later, in retrospect, it was also good for him. He can read his favorite math by himself without restraint.

Abel is famous in both the university and the town. People know: "A genius, the professor pays for his reading." However, he is very modest and never boasts his talents among his friends. He is immature in some aspects, but he is not completely ignorant of the world. He is a very friendly person and is willing to help his friends.

1823, Professor Hans Christian founded a new scientific magazine. Abel wrote an article about functional equations in Norwegian. His second article is to consider mechanical problems and study the motion of particles on a curve under the action of gravity field. This article is very important in the history of mathematics, because it gives the solution of integral equation for the first time. However, it was not valued by other mathematicians at that time.

1822-1in the winter of 823, he wrote a long paper in the university to be published, but unfortunately the manuscript was lost.

Professor Rasmussen, who teaches astronomy, gave Abel a sum of money to meet Duggan in Copenhagen in the summer of 1823, hoping that he could see and broaden his horizons outside. After returning from Denmark, Abel reconsidered the solution of the quintic equation of one yuan. In this way, the problem that has been solved for hundreds of years has finally been solved correctly: the general solution of the roots of the quintic equation cannot be expressed by algebraic operations such as+,-,×, ⊙ and the coefficient of the equation. This result was obtained by Italian mathematician Paolo Ruffini (1765-1822) in 1799, but his proof is not complete enough, but now the above result is called Abel-Ruffini theorem in mathematics.

Abel thought the result was very important, so he printed his paper in the local printing house. In order to let more people know that the paper was written in French, but because he was poor, he reduced the result to a six-page booklet in order to reduce the printing cost.

Then I confidently sent this booklet to foreign mathematicians, including Gauss, a famous old mathematician in Germany at that time, hoping to get some responses. Unfortunately, this article is so concise that no one can understand it. When Gauss received this pamphlet, he felt that it was impossible to prove this world-famous problem in such a short space-including the problem that he could not solve, so he didn't even bother to cut the pages with a knife to read the content, so he put him in his other books.

Abel's work was thus ignored.

Asking about studying abroad.

Abel graduated, but there was no place to teach. He can no longer live on donations from his friends. He is engaged. Last time he was in Denmark, he was dragged to a dance by a friend. When he saw a girl, he liked her a little, so he asked her to dance. They stopped dancing for less than 2 minutes and laughed at each other: neither of them knew how to dance.

The girl's name is Christine Kemp, the daughter of the poor, but she is very independent, working as a tutor and sewing in other people's homes. She is not beautiful, but Abel fell in love with her purity and kindness. When I returned to Norway, I introduced her to work in a small town near Oslo and got engaged to her. How can we live without money?

He applied to the government for a travel scholarship so that he could do research abroad for two years. I hope the environment will improve after coming back and he can find a formal job.

1825, he and his friends left Norway, went to Hamburg and lived in Berlin for six months. This time is the happiest time in his life. He lives in an apartment with his friends, and happens to be neighbors with the famous German philosopher Hegel. This group of young people just visit museums, places of interest, theaters or picnics on weekends, and sometimes drink and chat at night, which is a very annoying thing for Hegel who likes to study quietly at night. One day he couldn't help asking the landlord who this class was. The landlord said, "It's a group of young Norwegian students." Hegel said, "Ah! I thought it was a group of Russian bears. "

Abel met the famous engineer Koehler (A.L. Crelle1780-1855) in Germany. Koehler is engaged in some highway and railway construction, but he likes reading and writing math articles in his spare time. His mathematics is self-taught. Abel knew that he was a math lover and went to see him, but because of his stuttering German, Koehler didn't recognize his purpose at first, guessing that he wanted to be a student in a business school in the city. Finally Abel said disappointedly, "NiX exam (the correct German is nicht) is not math."

Koehler later met Abel. He knows something about this young man and likes him very much. Although he didn't fully understand Abel's work, he thought it was very important in mathematics. Koehler felt that there was no publication of a mathematical magazine in Germany, which did not greatly promote the development of mathematics. He came up with a magazine of pure mathematics and applied mathematics, and Label wrote the manuscript. Abel approved of his plan and promised to write a manuscript.

Koehler's mathematical magazine: Journal Fur Die Reine und Angewande Mathematick (Journal of Pure and Applied Mathematics) was published in 1826, and it is still a world-famous mathematical magazine. Its first volume published five important articles by Abel.

Abel didn't go to G? ttingen, Germany to find Gauss. Maybe he found this great mathematician difficult to approach and helpful. Because all his previous works were sent to him, but there was no reply at all. )

1826 In July, he left Germany for France. During his stay in Paris, he found it difficult to talk about his research results with French mathematicians because they were too old to pay attention to the work of young people. Poisson is busy with his theory of heat, electricity and probability. Fourier and ampere study electricity. At that time, 74-year-old Legendre studied number theory, geometry, geodesy and astronomy, but his ability to accept new mathematical ideas was very low. Abel thinks Cauchy, the authority of pure mathematics, is the founder of complex variable function theory, but he is a royalist, extremely reactionary and selfish, and other mathematicians don't like him.

Abel, who felt lonely in Paris, wrote a letter to Humboldt, Norway: "In a word, I don't like French and Germans. The French are very silent to strangers, and it is difficult to get close to them. I don't want that. Each of them only cares about his own work and doesn't take care of others. Everyone wants to teach others, but doesn't want to learn. Absolute selfishness dominates everything. ..... Everyone thinks only of himself, but he can invent theoretical things by himself. This is their idea. So you can understand that it is difficult for novices to pay attention! "

While in France, Abel hoped that one of his long papers could be published in the French Academy of Sciences, and he gave it to Le Jean. Lelang didn't quite understand it, so he gave it to Cauchy, but this guy who "goes to the rich door and is fat at dusk" didn't pay attention to this thing, just flipped through it and threw it in a corner.

Abel's thesis is an important mathematical work. He had been looking forward to news for a long time, but there was no news at all, and finally he had to go home disappointed. When he returned to Berlin, he was ill. He didn't know he had tuberculosis. He thought it might be the lonely life in France that made him weak.

The future is bleak. Go home.

Rasmussen, an old professor who helped Abel travel to Denmark, retired at the end of 1825. The University of Oslo will hire someone to take over his job. Only two people can handle it: Abel and his teacher, Hong Boyi.

Professor Hans Christian is the most decisive when considering candidates. He knows that Hong Boyi is not a talent in mathematics, but he has been teaching for eight years, and his long-term loyalty is helpful to his geomagnetic survey. If Abel gets this position, Humboldt will have no chance at university. Hans Christian wants to measure the earth's gravity field and electromagnetic field in Siberia for two years. He can give up his teaching position to Abel, and when things get better two years later, he can ask the government to set up another position for Abel. He thought this arrangement was the best, so he gave Rasmussen's position to Humboldt. But I didn't expect Abel to have no property This decision made Abel have no job when he came back!

Abel was a little sad when he learned that his teacher was chosen as a professor abroad instead of him. In a letter to his fiancee, he said that the wedding date was a little far away. Although he said how much he loved her, how could they live without money? "Drink enough" is just an illusion in this real world!

Abel returned to Oslo 1827 at the end of May. Not only does he have no money, but he also owes some money to his friends. His brother borrowed some money in his name and he had to pay it back. The university gave him some scholarships, but they were too few to live and pay off debts. In order to pay off his debts, he had to borrow money from the bank through the guarantee of Professor Hans Christian and Humboldt.

Abel went back to his old job as a student teacher. From primary school students to students preparing for college, from German and French to elementary mathematics. Kohler in Germany knows Abel very well. He wants to find a permanent position for this kind genius in Berlin. He pinned his hopes on a newly-built technical college. He wanted Abel to get the job through his influence on the Prussian government.

Before leaving Siberia, Professor Hans Christian recommended Abel to the military academy where he taught, taking his place in mechanics and theoretical astronomy. Fortunately, Abel was approved, and he can get two-thirds of Professor Hanstin's salary, which is an important thing for him. He can write a book on elliptic function theory with peace of mind.

Euler first determined the elliptic function. It can be regarded as a generalization of trigonometric function, but it has special properties: trigonometric function has only one real period (period 2π, such as Sin(2π+x)=Sinx), exponential function lx has only one imaginary period (this period is 2π), but elliptic function f(u) has double periodicity, that is, there are two complex numbers m and n, which makes f (u) = f (u+). This property was discovered by German mathematician Gauss as early as 1800, but it was not published. Between 1827 and 1828, Abel's work in this field was published in a magazine run by Koehler. At the same time, a young Jewish mathematician in Germany, C.G. Jacoby, also published the same result in a German magazine. At first, Gauss was very angry and thought that these people had plagiarized his knowledge and published it, but after reading Abel's article in detail, he thought Abel would publish it.

Abel's health is getting weaker and weaker. /kloc-in the summer of 0/828, he was ill, had a fever and coughed. He is optimistic in front of his friends, but when he is alone, he feels depressed and his future is really bleak.

He didn't know that Le Jean of France appreciated his work very much. Knowing his predicament, he personally wrote to the King of Sweden, asking for a position for the genius of this century. Le Jean wrote to him, praising the perfection and progress of his work. Abel was very happy and wrote back: "When I saw that my work deserved the attention of one of the greatest mathematicians of this century, it was one of the happiest moments in my life." He also said that he wanted to publish the math article he was writing, but it was a pity that no publisher was willing to take the risk and he had no money himself.

1828 Christmas is coming, Abel is invited to Frohland for a holiday, and his fiancee works there. Winter in Norway is very cold. He put on all his clothes, but he still felt cold. He coughed, shivered and felt uncomfortable in his chest, but in front of friends and lovers, he pretended to be fine and often joked to cover up his discomfort.

It's too late to send charcoal in the snow.

Koehler of Germany is very concerned about and sympathizes with Abel's situation. He tried to get some money for Abel as a "reward" for publishing articles in his math magazine, so as to reduce Abel's mental burden. He often wrote to encourage him and told him about the work of the young German mathematician jacoby. When he knew that Abel had a book about elliptic functions, but he had no money to publish it, he suggested that Abel send it to him, and he would publish it all in his magazine, no matter how long the paper was.

When he received Abel's reply, he said, "... I have been ill for some time, and I was forced to lie in bed. I really want to work, but even if I recover now, my doctor warned me that any worry would do me great harm. " Koehler was very sad. He feels that the officials above him are too indifferent, procrastinating and outrageous in recruiting academic talents.

Between Christmas and New Year, he tried to run and write letters for Abel's work. He was supported by the famous scientist Alexander von Norbert and collected letters from Gauss and Le Jean praising Abel's work. He also wrote to the Minister of Education in a provocative way: "Dear Sir, I hope you can approve Abel's career as soon as possible. Now that this great genius is famous, he may be hired to work elsewhere. I just got the news that the university in Copenhagen, Denmark wants to hire him, so he will not work here. "

1829 On April 8, Koehler happily wrote to Abel: "I learned from the head of the Ministry of Education that you must have a job. ..... I want you to know the good news as soon as possible. I believe you don't have to worry now. You belong to us, safe and sound. I am very happy, as if I got the job. You can prepare for your journey here. ……"

But Koehler did not know that Abel's condition began to deteriorate in March. He not only has chest pain, but also vomits blood. He often coughs and is very weak, so he has to stay in bed all the time. Sometimes he wants to do some math, but he can't start writing. Sometimes he is in a coma. He seems to live in the past. He talked about his poverty. He talked about Mrs. Hastings' kind care for him.

On the evening of April 5, he felt very uncomfortable and didn't get better until the early morning and noon the next day. In the afternoon, his fiancee Christine was waiting by his bed. Abel is fighting death, and his mind is a little confused: "... I want to live!" I still have a lot of work to finish. Take care of your mother, brother and sister. ..... Koehler helped me find a job. Why haven't I heard from you for so long? ..... poor Christine, dear, how far away our home is. ..... My beautiful girl, you are like a daisy in spring, you are noble and pure. ..... What if I go? ..... don't! I'll be fine, spring is coming, and our days will be better ... "

Abel's hand holding Christine suddenly loosened, and his big eyes were still full of tears! Christine fell on him and cried. The person she loved most had passed away.

The news of Koehler came too late. One of the few wizards in the world left this world with a heavy heart. Abel was buried in the cemetery in Frohland.

In June of the following year, the French Academy of Sciences awarded the famous Grand Prix to Abel and Jacobi, two mathematicians with the most mathematical achievements at that time. Half of 3000 francs will be given to Abel's mother as living expenses.

Abel's younger brother began to stand on his own feet, and they taught family education like their older brother. My brother who plays around has also changed his style.

Abel wrote to his good friend Kyle Howe before his death, hoping that he could take care of and help his fiancee. Kaihao wrote to Christine after Abel's death, explaining that although he had never met her, he knew her very well from Abel's letters and conversations. He took the liberty of asking whether he could be his wife, and Christine later agreed.

Consequences of death

After hearing the news of Abel's death from 65438 to 0829, Abel's friend Segai in France felt that the French Academy of Sciences was responsible for his death. So he angrily picked up a pen and wrote an article in a magazine, lashing out at the stale bureaucracy in the Academy of Sciences and appealing: "But we said: Young scientists should not listen to other authorities except their inner voices, because that is more suitable for your interests and abilities. Read and meditate on the works of genius, but don't be a gentle and honest student or selfish compliment. Our suggestion is: be objective in the face of facts and dare to choose your own views freely. "

The most violent attack on members of the Academy of Sciences should be a speech delivered by Francois Vincent Laspeyres in the National House of Representatives 40 years later. Rasmussel is a household name in France, and streets in many cities are named after him, especially one avenue in Paris called Rasmussel Avenue.

Rasbel was originally a priest and a theological teacher, but he was dismissed because the church thought he had heresy. Therefore, he became an outstanding biologist and a revolutionary who struggled for the welfare of the proletariat. He wrote comments on botany, was a pioneer in plant physiology, and studied organic chemistry. He was also a worker leader during the French Revolution in 1830 and 1840. What the French know most about him is a book about family treatment of diseases written in popular language. He had the concept of "bacteria" earlier than Pastour. Old as he was when he was young, he was fearless of powerful people and imprisonment, and boldly attacked the unreasonable things in France and the corruption of those in power.

Now let's go to the Paris House of Representatives in 1870 and listen to Rasbel, an old radical, who made an exciting attack on the crimes of selfish capitalist vampire society:

"... it was 40 years ago, when greedy members of the Academy of Sciences were on high, a young Swede came to my friend. My friend read the mathematical manuscript he wanted to submit to the graduate school, and felt that this paper had a perverted fantasy. (audience laughs. )

"He said to him," My friend, take your manuscript to Mr. Fourier, but don't give it to anyone else. Find him yourself. He will read the whole newspaper and then make an appointment to talk to you. But the young man gave this paper to Cauchy. At that time, this gentleman earned 50,000 francs from his position, almost as much as paleontologist Ju Weiye earned 60,000 francs. But many young people died of hunger at this time. Someone in the audience shouted: Yes, we workers only earn one franc a day until we are half dead. )

"The young man then went to Fourier, who met him in his small room, just as he usually met any scientist. He cares about all of them and does not refuse to discuss their research with them. Cauchy, an aristocratic capitalist, put the young people's papers on his side and didn't read them; Poisson himself got a paper, but he also lost it.

"That young man was received by my friend. He is an expert in caring for and taking care of people in need. But today, he still needs to rely on his own labor to maintain his life, and he still lives a poor and miserable life. (The audience shouts: Speak louder! Speak louder! We can't hear you. Someone shouted: his name, what's his name? )

"He is Mr. Seck, and his name is unfamiliar to many of you! But scientists know him very well, and I believe some people here know him, too.

"Psyche gave him some money and invited him home for dinner. But the young Swede felt ashamed to live on other people's income. One day he told him that he would go back to Sweden. Actually, he went back to Sweden, but he walked back! (The audience gives some exclamations. )

"He left a note for Le Jean. You all know this person. Lezhen read this article and said,' Look, how can this young man brag like this? He believed that he had found the answer to a question, and it took me 40 years to solve it. "So he left the article on the table.

But when the young man traveled in Berlin, he left his job to a scientific magazine run by scientists. Scientists are more friendly and understanding to him. Lerang is a generous person. His conscience troubled him when he read the published paper. When he got home, he found the paper left by the young man and sighed:' In fact, he really found something I wanted to solve for a long time. He made the most difficult discovery in the world, and he found the answer I have been looking for for for 40 years! ”"