Evariste Galois made a great contribution to the development of the theory of equations. He died at the age of 20, under very mysterious circumstances.

###### Childhood and early years

Evariste Galois was born on October 25, 1811 in the village of Bourg-la-Ren near Paris. His parents were well acquainted with classical literature, religious works and philosophy. The father of the boy, Nicolas-Gabriel Galois, was a Republican and headed the liberal party of Bour la Rena. After the restoration in 1814 on the throne of Louis XVIII, in 1815, Nicolas is appointed to the post of the mayor of the town. Until the age of twelve, his mother, the daughter of a lawyer, was engaged in the formation of Evarist, after which, in October 1823, the boy entered the Lyceum of Louis the Great in Paris. Despite the fact that the lyceum at the time of the Galois experience is not going through the best of times, and about a hundred pupils are expelled from the beginning, the boy from the very beginning achieves considerable success in school and, under the guidance of his mother, becomes the first in the class of Latin. But, at the age of 14, he loses interest in everything, except mathematics, on which he concentrates all his efforts. By February 1827, he was in the higher mathematical class, in which M. Verney taught. Evarist studies the work of Andrien Marie Legendre “The Foundations of Geometry” and develops it after the first reading. By the age of fifteen, Galois reads the original of Joseph Louis Legrange “Reflections on the Problem of Solving Algebraic Equations,” which, most likely, inspired the scientist in his work on the theory of equations. He also studied “Lectures on the calculation of functions”, intended for professional mathematicians. But his progress in other subjects during this period invariably falls. In 1828, Galois surrenders exams for admission to the Polytechnic School, the most prestigious higher institution in Paris, but fails them.

###### Scientific activity

In April 1829, in the journal “Annales de mathÃ©matiques”, Galois published his first mathematical article on continuous fractions. At about the same time, he is working on the theory of polynomial equations, two articles on which he will present at the Academy of Sciences on May 25 and June 1 this year. Augustine Louis Cauchy, a great mathematician and contemporary of Galois, praised the work of the young man highly, but, for unknown reasons, refused to print it.

Shortly thereafter, Evariste experiences personal tragedy: on July 2, 1829, his father committed suicide. The reason for this became lampoons, in which the priest from Bourg-la-Rena in every way reviled the name of the mayor of Galois. A respectable and respected man, Nicholas could not survive such a disgrace. He hanged himself in an apartment in the house next to the Lyceum of Louis the Great, at which time his son was studying. The sudden death of his father shocked the boy and had a great impact on his entire future life.

And again Evarist tries to enter the Polytechnic School, and again falls through the exams. However, different sources explain this failure in different ways. Some believe that the examiner gave the young man such a boring task that he, angry, threw the examiner in a rag. More popular is the version that the examiner simply did not keep up with the course of Galois’s thought, which led the youth out...

After he failed to enter the Polytechnic School, Galois passed the examinations for a bachelor’s degree in the Higher Normal School. December 29, 1829 he received a bachelor’s degree. According to his mathematician examiner, “it is sometimes difficult for a young man to express his thoughts, but he is perfectly educated and has outstanding ability to research the question.” On the other hand, the professor of literature said about him: “This is the only student who answered badly, he knows absolutely nothing, they say he has amazing abilities for mathematics.” This is extremely surprising to me, since after the exam I had the opinion that his mental abilities are very limited. “

Galois sends a number of his articles to Cauchy, and suddenly comes across Abel’s work, echoing his own research. In February 1830, Cauchy proposes Galois to raise in the new article the theme of “solving equations in radicals.” Former then secretary of the Paris Academy of Fourier filed an article published for consideration of assigning it to the author of the Grand Prix of the Academy in the field of mathematics. But, in April 1830 Fourier suddenly dies, the Galois article is lost in the archives and the only thing left to dream about is a prize. In spite of all these failures, Galois succeeds in finishing three more works this year. One of these articles lays the foundations of the “Galois theory”. The second concerns the numerical solution of equations. The third one made a significant contribution to the theory of numbers, first formulating the theory of finite fields.

In the days of Galois, France experienced serious political unrest. In July 1830, when the director of the Higher Normal School, M. Guignot, locked up students to prevent them from participating in the riots, Galois wrote a letter criticizing Guignot, so that in January 1831 he was expelled from the School. Galois was involved in a number of republican organizations – “Organization of the Republican Artillery of the National Guard of France” and “Society of Friends of the People” – and shared time between work on mathematics and political activities.

###### Death

May 30, 1832 Galois perishes in a duel. The true cause of this incident is not clear to this day, but around this death there are many rumors. His letters to some Mademoiselle Stephanie-Felicia Paterin du Motel, with whom Galois, probably had a personal conflict, that could lead to the aforementioned duel, have survived. There are also divergent opinions about the identity of the person with whom Galois got together in a duel. According to one statement, it was Peso d’Erbinville – a member of the team that had previously arrested the scientist, and the groom du Motel, but others believe that his opponent was one of his Republican friends. The night before the duel, Galois managed to send a letter to Augustus Chevalier, to which he attached three of his manuscripts. May 30, 1832 Galois was shot in the stomach in a duel. Many hours later, a peasant found him. The scientist was taken to the hospital, where he died the next morning, saying the last words to his brother Alfred. At the time of his death, he was 20 years old.

###### Basic work

“The Galois Group”;

“A general linear group over a prime field”.