Galois actually came from a good family, and his parents were intellectuals. /kloc-Before the age of 0/2, all his education was arranged by his mother. But his father's career is not very good. He is the mayor. Why do you say that? You know, France in the18th century is in a period of drastic changes. The * * * faction and the monarch faction are deadlocked and take turns to sit in the village. In the past 100 years, the French emperor alone has sent several people to the guillotine.
In France, as long as it has something to do with politics, whoever comes to power will basically die, such as lavoisier, the father of chemistry. Galois's father is a pacifist, with a good personality and integrity. This is in peacetime, and he is definitely a great person, but in that era, it was miserable.
Why, because of your good character and integrity, it means that the people like you very much, so public opinion is not biased towards * * * and the party, which is impossible. So monarchists basically want Galois' father to die every day.
Galois was very sensitive to politics since he was a child, because he witnessed the fierce confrontation between the two factions, which also laid a curse for him in the future.
In addition, when he 12 years old, he enrolled in Royal Louis Middle School. It happened that the headmaster was a monarchist, who directly expelled 100 students in a rebellion with a tendency to * * *. Galois was not implicated because he was young, but he left the seeds of hatred in his heart.
Mathematicians have been pursuing truth, but politics needs perseverance, forbearance and the art of compromise, which is contrary to the essence of mathematicians. People are prone to paranoia in such contradictions, and this chaotic era has also contributed to Galois' tragedy.
Here, I want to explain that Galois started to learn mathematics at the age of 16. After he came into contact with mathematics, his enthusiasm for mathematics exploded sharply, and he could no longer afford any interest in other subjects. Before that, Galois was excellent in other subjects. It was only after I became fascinated with mathematics that I began to stand out from the crowd. . .
The image of Galois in the film
His teacher once commented that he was only suitable for working in the highest field of mathematics. So I'm telling you, geniuses in every field will shine there without people looking for them.
At this time, the tragedy of his life began. First, his father committed suicide because he was maliciously slandered in the election. Well, politicians should not take part in politics if they are so emotional. . . The unjust death of an upright father has led to more extreme political views and outlook on life. But it also made him more addicted to the kingdom of mathematics.
We just said that Galois was 16 years old before he came into contact with mathematics. At that time, he couldn't have a primary school math class until the second grade. At that time, Galois saw the textbook and thought it was not worth reading at all. He thinks that these textbooks only talk about skills and not reasoning methods, which is misleading. Learning mathematics should look at the essence through phenomena and master clear and expressive language.
So in a year's time, he taught himself the geometric principle of Legendre, Lalange's lectures on the solution of numerical equations, analytic function theory and functional calculus, and gradually became familiar with the works of Euler, Gauss and jacoby.
Student, he hasn't studied mathematics before, and all these are thoroughly studied by himself.
So he was angry when he saw the teachers teaching mathematics at school, and thought they were too hasty. And the teacher just thinks he's crazy. Then he simply stopped listening. However, he still met a teacher who admired him, named Richard, and he evaluated him. He encouraged Galois to contribute, and the article was immediately published in the first French patent mathematics magazine "Mathematical Yearbook".
When Galois saw it, he was full of energy and planned to submit his first book to the Academy of Sciences. Unfortunately, the person in charge of the review he met was Cauchy.
Cauchy was an academician of the French Academy of Sciences and the most famous mathematician at that time. However, he has one characteristic. His papers are generally smelly and long. Because of the particularity of manuscript writing, he is considered to be second only to Euler in quantity. He wrote 789 papers and published several books in his life, some of which were classics, but not all his creations were of high quality. Therefore, he was criticized as prolific and reckless. Ordinary magazines simply can't hold his long speech, and the Academy of Sciences can't afford it.
So when he saw a paper with only six pages, he simply ignored it, happily took it home and lost him. In this paper, Galois wrote a proof paper about the nonexistence of algebraic solutions of quintic equations, and introduced the concept of "group" for the first time. It can be said that this paper directly answers the difficult problems in mathematics in the past 300 years.
However, if Cauchy takes a look at it, Galois may not be so miserable in the future. . . However, Cauchy not only lied to Galois, but also lied to Abel, that is to say, there is no limit to cheating. Cauchy, who has many achievements such as Cauchy inequality and Cauchy integral formula, was finally known, and it was also a sigh!
In the second year, Galois, unwilling to give up, continued to write three papers and submitted them to Fourier. However, Fourier died suddenly, without the following.
Fourier
In the third year, Galois, who was still unwilling, gave it to Poisson, an academician of the Academy of Sciences. Unfortunately, Poisson's level is too low to understand at all, so he directly criticized a few words of "I don't understand".
Galois, who was completely disappointed, began to turn to politics, while Galois, who was violent and extreme, was more difficult to play politically. We can see Galois' character through one thing.
Galois wants to apply for further study in a comprehensive engineering university. However, at the age of 65,438+06, he was not prepared for the first exam. At the age of 65,438+08, he couldn't stand the stupidity of the examiner, so he threw it in the examiner's face with a blackboard eraser. In this way, the door of the comprehensive engineering university was completely closed to him.
Later, I had no choice but to go to a higher normal school. However, in July of 1830, the royalist forces perished, and the headmaster of the higher normal school locked the students in the high wall, which caused strong dissatisfaction from Galois. 12 In June, Galois attacked the headmaster in the school newspaper and was expelled from the school.
Later, the young man led the masses to take to the streets to protest against the autocratic rule of the king. Unfortunately, he was arrested and imprisoned for "attempting to assassinate the king". More unfortunately, he was infected with cholera in prison.
As a result, I just got out of prison and wanted to publish my own mathematics achievements, but I was framed in prison and spent the last year in prison. Why, because he fell in love with a fireworks girl in prison, it happened that the rival of this fireworks girl was still an officer. It is said that marksmanship is famous all over the country. This idiot agreed to compete with his rival in love. . .
It is estimated that he will regret it after agreeing. I guess he also knows that he shouldn't live. He intends to record all his research results in the past five years on the last night. It is said that the blank of the manuscript also says "I don't have time, I don't have time." . . "
Ladies and gentlemen, you should know that what he recorded this night is the only research achievement in his life for more than 20 years. That is, everything he left behind was also driven out that night. . . Think about it, how difficult it will be, to ensure that every step is good and not to miss every step.
A page in Galois's manuscript
The next day, as he expected, one shot was turned over by an officer and directly punched through the intestines. Before he died, he said to his brother who was crying beside him, "Don't cry, I need enough courage to die at the age of 20." He was buried in the ordinary trench of the cemetery, so today his grave is nowhere to be found. Summarizing Galois' short life of 265,438+0 years old, we can say that he is in the golden age of his life. If he were allowed to live for another ten years, what changes would happen in mathematics? Maybe he would become Euler and Gauss.
His friend Chevalier followed Galois's wishes and sent his math papers to Gauss and jacoby, but they all fell into the sea. Gauss once achieved a brilliant life because he met Bole, but he lost his sight when he needed Bole most!
It was not until 10 years later that the famous French mathematician joseph liouville saw Galois's manuscript. After careful calculation, he finally affirmed the correctness, originality and profundity of Galois's results. He also spent a long time explaining it, and finally published it in the journal Pure Mathematics and Applied Mathematics of 1846, and recommended it to the mathematics community.
joseph liouville
Since then, Galois's achievements in that night have finally become known to the world. I'll tell you how much he contributed that night!
Galois used the idea of group theory to discuss the solvability of equations. The whole idea is now called Galois Theory, which is recognized as one of the most outstanding mathematical achievements in19th century. It is one of the basic pillars of contemporary algebra and number theory. It also directly created the mathematical branches of abstract algebra, abstract algebra, topology and functional analysis. Modern mathematical theory is supported by these three pillars.
This theory has a great influence on the development of physics and chemistry, and even on the emergence and development of structuralist philosophy in the twentieth century. Abstract algebra is also one of the foundations of modern computer theory.
He systematically explained why there is no formula solution for the equation with more than five degrees, but there is a formula solution for the equation with less than four degrees. He also beautifully proved Gauss's assertion that regular heptagons can be drawn. In addition, he also solved two of the three major drawing problems in ancient times: "You can't divide any angle into three parts" and "Cubes can't be doubled".
Professor jean-pierre ramis introduces the legendary life of Galois.
Finally, once again, Galois has only been in contact with mathematics for five years, and this is his own research achievement recorded in just one night. If we give him a few more days, I believe he will record more things, and then it is estimated that all science students will complain bitterly.
If Galois was not so paranoid, sensitive and irritable, if he could visit Gauss in person, he would discuss and study with Gauss. After all, Gauss is also an excellent teacher and has trained a large number of excellent students such as Riemann.
Unfortunately, there is no if in history. Galois's talent is so high, unfathomable and hard to find in ancient and modern times that it cannot be reproduced.