If we ask ourselves what mathematicians do for us, or what kind of people do math, we can look for some answers in the life of Evariste Galois. Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician and political activist.
Living a short but mathematically productive life, this young man displayed genius and stupidity at the same time. To many, mathematics seems like a cold, abstract subject. However, this passionate and lively young man presents us with another model of the mathematician.
Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem that had been open for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra. He was a staunch republican and was heavily involved in the political turmoil that surrounded the French Revolution of 1830. As a result of his political activism, he was arrested repeatedly, serving one jail sentence of several months. For reasons that remain obscure, shortly after his release from prison he fought in a duel and died of the wounds he suffered.
The world of mathematics developed very rapidly after the invention of algebra. With the unique contributions of Ömer Hayyam and Harezmi, he was able to put forward general rules that can always be useful for solving the equation in situations where the degree of the root is 2 or 3 in equation systems. However, when the degree of the root reaches 5 or greater limits, it has not been able to put forward definite rules that will always work. This of course creates a mystery. And there is no doubt that this mystery will create many mathematicians to pursue it.
What Did Evariste Galois Do?
At this point, Evariste Galois appears and brings a completely different dimension to the issue. He claims that there can be a direct connection between the two structures, the object and the permutation group structures, which is impossible to detect at the first moment, and proves this claim.
In summary, he proved that there are some special changes in the permutation groups as a result of 2nd and 3rd-degree expansions, but that they do not occur regularly but in a meaningless way in the permutation groups associated with the expansions formed by the equations of degree 4 and above, and no general solution can be found. It turned out that the search was also a futile effort. That was the summary of what he did.
I should point out that a significant number of Galois's theorems will never appear before an undergraduate mathematician. His anti-response to a problem with a history of more than a thousand years was undoubtedly a big deal. The one who did this job was a 21-year-old young man after all. He wrote this staggering work one night, working until morning. So where's the love in that anyway? I think we should tell the story from the beginning.
Evariste Galois in brief
Evariste was born in 1811 when the Great French Revolution was defeated by Napoleon. His family was wealthy and influential, but he was a Republican to the last drop in the years when it was most dangerous to be a Republican in France. The unyielding and stubborn quarrelsomeness in his personality is perhaps the result of this political atmosphere.
Although there were no mathematicians in his family background, he had an incredibly great mathematical grasp. It is said that when he was only 14 years old, he read Legendre's Elements de Geometrie as if he were reading a novel and became an expert in this field in a short time. And in the same year, he reads and finishes many great mathematical works on his own. Then, with the encouragement of many families and relatives, he took the exam of France's most competent educational institution, Ecole Polytechnique, without any preparation. But he still cannot inexplicably pass the exam.
Vazgeçmez sends two important articles about algebraic structures to Cauchy, one of the great mathematicians of the time. He expects that Cauchy will help him get into Polytechnique as a reference. But this does not happen. Because Cauchy will tell him that he has lost his studies and that it is not possible for him to find them. (It is a serious question mark that Cauchy referred to these two studies in some of the articles he published in later years.)
Since he has no references, he will take the exam again. He is 15 years old. In reality, it is like a summary of his whole life that he lived during the entrance to the Polytechnique exams. A few days before the exam, his father, the Mayor, will pay the price for his republicanism. During this period, his father is accused of very serious accusations in front of the community by the "royal" priest of the town. His father can't make him proud of this situation. As a result, he hangs himself while his son continues to work on the upper floor of his son's study. This is a grave wound for Evariste that will never heal.
Ecole de Normale
He starts Ecole de Normal, which is a very low school for his level. Here, he had the opportunity to do serious studies on algebra, and he compiled these works and sent them to the famous mathematician Fourier, the secretary of the French Academy of Sciences, for a competition. If we want to understand the life of Galois, we must understand that the main summary of his life is bad luck. Because Fourier dies before he can read his work. And in that turmoil, Galois's work disappears and is not considered.
In the same year, Vazgeçmez published three important articles on algebra and number theory. And in these studies, the group, which can be called the cornerstone of modern algebra, forms the concepts of normal subgroups. He is only 19 years old.
During the 1830 revolution, he wrote an article harshly criticizing the school principal, who locked them in school and prevented them from participating in the revolution, and published it in the Gazette des Ecoles under his name. Naturally, he was expelled from school. He joins the Artillery of the National Guard, which includes many Republican soldiers, and begins to work for the revolution. But the government abolished this military unit and imprisoned its officers. At a dinner in honor of these officers, Galois puts a knife over his glass and raises his glass for everyone to hear, saying, "I drink to the king." This is perceived as a threat and the young man is thrown in jail. (Alexander Dumas, who was at the dinner, describes this event in his memoirs.)
Misfortune Was the Summary of His Life
Misfortune was his destiny. And he was defying that fate. Maybe he loved this destiny and created it with his hands. He was released from prison soon after; On July 14, 1831, he participated in the Bastille protests with the uniform and rifle of the closed unit. This time he was arrested for wearing illegal uniforms and spent 6 months in prison. After 6 months, he came out of prison sick and tired. Love was the last link in his destiny. Stephanie, the daughter of the doctor in the center where he was treated after prison, was the girl he would fall in love with. She was an incredibly beautiful girl and damn it she was engaged. Galois didn't care, he declared his love for her…
Evariste Galois is unlucky, as his opponent is one of the officers in his squad and is a really good marksman. Galois's hands are the hands of a mathematician. Galois was too brave to refuse an impossible challenge to a duel. He accepts the duel invitation. He is 21 years old and now he is in a hurry. On the night of May 29, the night before the duel, he tried to combine all his work and make it tidy.
He wrote the following notes in the margin of his work. “There is no time”, “the sun is almost up”, “I wish I had a little more time”. At the end of his notes, he wrote to his friend Chevalier: “Ask Jacobi or Gauss openly for their opinion of these theorems, not as to whether they are true, but about their importance. Later, I hope, there will be some who will realize that it is in their interest to unravel this mess.” He handed the letter to his brother Alfred to complete and deliver to Chevalier.
In the early hours of the morning of 30 May 1833, Evariste Galois fell to the ground in the duel. The doctorate cannot be completed in time. The 21-year-old young man dies on the morning of the night he made a revolution in mathematics. His brother delivers the letter to Chevalier. Ten years after Galois's death, the Academy approves Galois' work. And all the love in his heart in the relentless battle against the young man's evil fortune; the love of knowing, the love of love, the love of revolution collide with each other and reach eternity, its eternity.
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