Evariste Galois: the tragedy of a young mathematician

2011/10/01 Etxebeste Aduriz, Egoitz - Elhuyar Zientzia Iturria: Elhuyar aldizkaria

• Historia
• Biografiak
• Matematika

"Two nationalists have provoked me... I find it impossible to renounce. I apologize to you for not telling me. But my rivals have asked me a word of honor not to inform my friends... Please remember me, because destiny has not given me enough life for my people to remember me. Your friends die to me. J. Galois."

This was written by Évariste Galois to two people within a few hours of May 30, 1832, on the eve of his death. And his friend the botanist Chevalier: "I have made new discoveries in the analysis. The first refers to the theory of equations, the other to complete functions... Everything is in these three memories... He asks Jacobi or Gauss to comment not on the veracity of these theories, but on their importance. I hope that no one will find it profitable to order all this mess."

Galois was a normal boy until he encountered mathematics. He started with 12 years and had good notes. But with 15, when he began to take the first classes of mathematics, things began to change. He abandoned all subjects that were not mathematics. He was not interested.

In mathematics he was insatiable; he devoured the texts of the Legend and the memoirs of Lagrange as if they were novels. This is what the head of studies wrote: "The passion for mathematics dominates; I think it would be best for him for fathers and mothers, and nothing, to stop learning. Here is wasting time, not only does the teacher suffer and drown in penalties."

A year before normal and without usual training, he studied the possibility of entering the prestigious École Polytechnique to learn mathematics. But he did not overcome it. And he had to continue in school.

When the teacher of mathematics of the new course saw the talent of the boy, proposed that without doing a study they would have to accept it in École Polytechnique, but they did not take it into account. Despite this, Galois was the teacher who gave him strength and at the age of 17 he published his first work in the magazine Annales de Gergonne: "Proof of the theorem of periodic continuous fractions". In addition, he began working on the theory of equations and that same year he sent two new articles to the Academy of Sciences.

He conducted for the second time a study for the inclusion of École Polytechnique. But, again, the street, when the examiner asked him to prove his explanations, refused to answer that it was obvious.

As on the first occasion, it seemed a great injustice to Galois to deny access to the École Polytechnique. He was a prestigious university that, in addition to academic reasons, attracted the political movement among his students, as well as his parents, being an enthusiastic Republican. But he had to settle for École Normale simpler.

From the Academy of Sciences, Cauchy recommended that he collect and adapt the submitted articles in a single memory. He did so and sent the new work to Fourier, secretary of the academy, to participate in the Grand Prize for Mathematics. Unfortunately, Fourier died two months later and Galois' work was lost with him.

During the July 1830 revolution, which ruined Charles X, the director of École Normal locked the students in college so that they would not take part in the street unrest. Galois tried to escape, but did not get it. Subsequently, in a magazine, the director reported that he had locked them. Galois was expelled from the university. And he entered the Artillery of the National Guard made up of the Republicans. At the end of the year the team was destroyed in the hope that Luis Felipe could be a threat to the new king.

Galois did not abandon mathematics. In January 1831, at the request of Poisson, he sent to the academy the third version of his memoirs. For this time, the situation of Galois was not very good, as shown by a letter written by Sophie Germain to his friend Libri on April 18: "...of Cauchy, the death of Fourier, has been too much for Galois, a student who, apart from irreverences, has shown signs of intelligence... He is without money and his mother also has very little. When he returns home, he continues his tendency to offend... The sick mother has had to leave her home leaving her son enough to live... They say the young man will end up crazy and I fear it will not be true."

On May 9, 200 Republicans gathered at a dinner where Galois stood up and shouted raising in the same hand the cup and the open knife: "By King Luis Felipe! ". He was arrested the following morning. And after he remained in prison until June 15, he was tried for threatening the king's life. He was free.

On July 14, the day of France, he was detained wearing the uniform of the Artillery Guard and armed from top to bottom. It was considered a gesture of challenge and was forbidden. He was sentenced to six months.

In jail he discovered that Poisson rejected the work presented. "We have tried to understand Mr. Galois. But their arguments are not sufficiently clear or developed so that we can judge their correction," Poisson wrote.

In jail, Galois passed from despair to anger and rage. He would also commit suicide if his friends had not prevented him.

In March 1932 the prisoners were taken to Sieur Faultrier boarding school to protect themselves from a cholera epidemic. Galois fell in love with his doctor's daughter, Stephanie du Motel. And it seems that the next day's mourning on leaving the jail was related to her.

The night before the duel, in addition to writing letters to several people, he hurried to his memories. So he wrote it on a page border: "Here it is necessary to complete some things. I have no time."

The duel took place on May 30 in the morning, next to a pond that was not far from Sieur Faultrier. Bala crossed the belly. It was discovered in the land by a peasant who was hospitalized. The next day he said the last words in his brother's arms: "Do not call Alfred! I need all my courage to die at age 20."

P.S. : In 1846, the mathematician Liouville published the work of Galois. This work laid the foundation for what is now known as group theory. Galois himself was the first to use the concept of group.