Galois's sketch
It's a pity that when the department of mathematics in universities talks about abstract algebra, it pays too much attention to the definitions and theorems of groups, rings and fields, and almost no one can explain clearly how to prove that the general equation of quartic or higher order has no radical solution with Galois theory. This greatly deviates from the original intention of Galois to establish this field at the earliest, and it must be said that it is a kind of sorrow! Mathematics has lost its starting point, just like losing the source of life, becoming soulless, no longer vivid art but rigid theory.
Galois 18 1 165438 was born in Larrenburg, a small town on the outskirts of Paris. His full name is Evarist Galois. Unlike Abel, another French mathematician who studied the same problem, Galois was born in a rich family. His grandfather and father are both principals, and his mother is the daughter of a judge.
When Galois was four years old, Napoleon proclaimed himself emperor for the second time, the so-called Hundred Days Dynasty. During this period, Galois's grandfather and father were keen on politics, and Galois's father was elected as the mayor, which laid the groundwork for Galois's later life tragedy.
Napoleon and the Hundred Days Dynasty
Galois's educational experience was quite bumpy. /kloc-Before the age of 0/2, his mother educated him in all aspects. Galois's mother is proficient in classical literature and can read Latin skillfully, which made Galois accept the influence of classical literature very early and laid the foundation for his good grades in middle school in the future.
1823, when galois 12 years old, he skipped primary school and went directly to the Louis School, the Royal Middle School in Paris, which is also the alma mater of the famous writer Hugo and politician robespierre. At that time, the school was famous for its cold buildings, strict discipline and lack of food. What is more exaggerated is that their work and rest time is from 5: 30 pm to 8: 30 am, and they also use candles in class at night.
Louis high school
1824 1 month, French king Louis Stanislas Xavier led a group of senior officials to inspect the school. At the dinner party, a group of students didn't propose a toast to the king and his party, which made the school leaders furious and fired 1 17 students. As a first-year student, Galois escaped, but this incident left a deep impression on his mind and planted the seeds against the royal family.
1826, 15-year-old galois did not get good grades, so the principal asked him to repeat the grade for one year. It is this repetition that gives Galois the opportunity to fully demonstrate his mathematical talent. When she was in the first grade, Galois met an excellent math teacher, Wiener, who recommended Legendre's Principles of Geometry to her classmates. It is said that Wiener was supposed to talk about this book for two years, and Galois finished it in only two days. This experience made Galois deeply addicted to reading the original mathematics. He began to read a lot of works by Lagrange, a great French mathematician, but neglected other courses. As a result, Galois, who was 1828 and 17 years old, took the entrance examination of the Paris Institute of Technology, but lost his reputation in Sun Shan because he had too much knowledge in one field and too little knowledge in another. Fortunately, he entered Richard's math major class, and all the teachers were impressed by his math talent, not only giving him a first-class scholarship, but also keeping all his classroom notebooks.
Not surprisingly, Galois has done outstanding work in the field of mathematics. /kloc-at the age of 0/8, he officially published his first paper, which was about continued fractions. More importantly, he independently gave a proof that the root solution of an equation with degree higher than 4 does not exist. This proof was first brought to Cauchy by Richard, and then submitted to the French Academy of Sciences with the title "Conditions for Solving an Equation with Roots" to participate in the competition for the Mathematics Prize. Unfortunately, Cauchy neglected Galois's work. To put it another way, Cauchy appreciated Galois's work very much and suggested that he resubmit the paper in the form of a special topic. In any case, the paper went to Fourier, secretary of the Academy of Sciences, but Fourier died suddenly and Galois's paper was lost. The final math prize was also awarded to jacoby and Abel.
Galois's dying manuscript
These are not the worst. /kloc-at the age of 0/8, galois applied for the Paris Institute of Technology again, and the result was even more tragic: a student with high IQ was rejected by a group of examiners with low IQ. Because you can only apply twice, this school closed the door of Galois forever. In addition to being rejected by the school, the bigger blow came from his father's suicide. Galois's father, as the head of a town, likes to write poems and usually supports citizens against priests. The priests used his hobby to write a dirty poem for his family, which made the decent father unable to face his family and citizens, secretly ran to Paris and turned on the gas not far from his son's school to commit suicide.
Galois, who failed to enter the polytechnic, was admitted to the unknown normal school at that time. However, the good times did not last long. Galois, who actively participated in politics, was expelled from school for participating in the revolution, and was arrested as a political prisoner twice in 183 1. Galois is a radical partisan. "A young man, with a glass and a dagger in his hands, is trying to make others listen to him." This is his image when he attended the party rally.
1832 In the spring, because of the cholera epidemic in Paris, Galois was paroled and transferred to the "Rehabilitation Home", where she met Stephanie, the daughter of the owner. 17 years old, she was very coquettish and experienced the only love in her life, but she was deeply hurt. In a letter to my friend August, he wrote, "My illusions about everything, even love and fame, have been shattered." .
This year, Galois came to the end of his life. He died in a duel. There are many versions about this duel, rival in love? Political enemies? Girl father? Whoever it is, the ending is the same. The talented Galois got the one of the two pistols without bullets and was shot in the abdomen by his opponent and died. After being taken to the hospital by a farmer, he died the next day. My last words to my brother are: "Don't cry, I need all the courage to die at the age of 20".
Genius is probably more intuitive. Before the duel, Galois felt that he might not live. He left three last letters: two to political parties, asking them not to blame his killer, and the other fully expressed Galois Theory.
In the cemetery of Galois's hometown, there is a monument in memory of him, standing beside the graves of his relatives. As for the real location of Galois' body, we only know that it is in Mon Bannas Cemetery, and the exact location is unknown.
Galois cemetery
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