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Evariste Galois Vimal Bellamkonda Evariste Galois Vimal Bellamkonda Portrait of Evariste Galois Galois' life The French mathematician Evariste Galois had a very interesting life, in a time and place of great revolution. He was born on October 25th of 1811 in a small commune name Bourg-La-Reine, about 10 kilometers south of Paris. The commune is now a suburb of Paris. His family was well educated and respected. Both of Galois' parents were educated in philosophy, religion, and classical literature. These were the subjects which were considered to be the most important at the time. Interestingly, neither parents had any substantial background in mathematics. Neither, until a certain age, did Galois himself. One of the quirks that his father, Nicholas-Gabriel Galois, had was his talent for writing rhymed couplets. Evariste Galois supposedly inherited this talent, and he consistently entertained his family at gatherings. When Galois was only ten years old, his parents decided to send him to college in Reims. This would have been a great opportunity to kickstart his career in mathematics, but at the last moment, his mother unenrolled him and decided to keep him at home. As a result, Galois continued to be educated in Latin, Greek, and rhetoric, but his background in mathematics didn't start until later. When Galois was twelve, he enrolled in his first school, the lycee of Louis-le-Grand, located in Paris. Evi- dently, however, he didn't like it. He described the school as seeming more like a prison. Additionally, the school underwent massive political changes, involving multiple rapid successions of headmasters, leaving it in administrative turmoil. Some sort of political student rebellion also took place, leading to the expulsion of 40 students. Nevertheless, Galois had no involvement in the rebellion, and made it through his first year, receiving several awards. When enrolled in school, Galois actually enrolled as a third year student, skipping the first two classes. This, coupled with his success in school, are evidence that the preparation being home schooled helped him greatly. However, during the school year of 1825 to 1826, his attitude and performance in school changed greatly. That winter, he underwent serious earache, most probably due to dirty conditions in his school building. This caused a drop in his performance that eventually led to the headmaster of the school writing a letter to Galois' father, advising that Galois repeat the year. However, after considerable pushing from his father, Galois was able to resume class as normal. The Uniform for the Louis-le-Grand at the time that Galois attended February of 1827 was a turning point for Galois, as that was when he started his first course in mathematics, by M. Vernier. In this class, he worked with Legendre's text on geometry and become familiar with the theory of equations outlined in Lagrange's works. Galois lagged behind in his other courses, instead pouring his attention into math. One teacher wrote of him: \What's dominating him is the fury of mathematics; also I think that it would be better for him if his parents would agree to let him study solely mathematics. He is wasting his time here and he does nothing but torment his teachers and by doing so heaps punishments on himself. " Galois seemed to have a natural gift for mathematics. His teachers described him as having an extremely quick rate of learning. However, he supposedly paid little attention to homework, either making trivial mistakes or not doing it altogether. Galois made it his mission to attend the Ecole, as this was the single best school to launch his career in mathematics. As of ten years prior, the Ecole no longer officially were militarily oriented. Still, though, their mission was to train scientists for government service, making it a very politically charged atmosphere. In June of 1828, Galois took the entrance exam at Ecole. In a surprising turn of events, he actually failed the exam and didn't make it in. Nevertheless, he published his first mathematical paper in April 1829, on continued fractions in the Annales de mathematiques. On May 25th and then again on June 1st, he published articles on the algebraic solution of equations in the journal, Academie des Sciences. In July 1829, tragedy struck his life. That year, tensions were rising between political and religious factions in France. These tensions extended to Bourg-la-Reine, where a young priest, seeking the downfall of the mayor Nicolas-Gabriel Galois, banded together with more of his opponents and spread vulgar poems, with Evariste's father appearing as the author. This was a huge scandal, and he was forced to leave Bourg-la-Reine and flee 2 to Paris. Once there, he rented a small apartment, where he committed suicide. His funeral turned into a procession of liberals, and eventually the priest was brought to justice. Evariste Galois, despite his devastation over his father's death, decided to take the entrance exam to the Ecole once again. This time, however, the stakes were higher. If Galois failed, he would not be allowed to take the test again. According to the story, Galois faced two examiners, one of whom, asked him to describe the theory of the arithmetic logarithms. Galois, with all of his mathematical genius, criticized his the professor, stating that there are no arithmetic logarithms. He asked why the professor had not instead asked for the theory of the logarithms, refusing to explain the obvious (according to him) propositions about logarithms. One account even depicts Galois unable to find a use for the chalk and sponge with which he was supposed to write his explanations. Upon being asked the offensive, he threw the sponge at the professor's face. While it is likely that this is a heavily dramatized account of events, it still accurately portrays Galois' struggle to communicate the ideas that he held in his head. While it is indisputable that he had a genius level intellect and brilliant ideas, he consistently failed to effectively communicate those ideas to others. At one point earlier in his schooling, Galois, seeking to be involved in the political uprisings that surrounded him, joined the \Societe des Amis du Peuple, " French for \Society of Friends of the People. " It comprised the most active republicans who were portrayed as a very dangerous, subversive group, particularly by the government-controlled press. Galois gained a reputation for being radical and dangerous among his peers. He asked for the students to be armed and wear uniforms in order to help train them for the military. His ideas frequently brought him into conflict with authority. On December 9th, Galois was publicly expelled from the school. It was believed that he had written an anonymous letter to the school paper which framed the chancellor for the events of the revolution earlier that year, despite him never admitting to writing the letter. Galois enlisted in the Artillery of the National Guard, which was comprised mostly of republicans, immediately after. However, on December 31st, 1830, the National Guard was disbanded, and Galois found himself without work. With his mother unable to support him financially, he attempted to start a private class in algebra to support himself. On the following January 13th, it started with about 40 kids attending. However, the students were unable to follow Galois' abstract lectures. He continued to be involved in radical events, leading to his arrest and trial, with his ultimate acquittal. However, shortly after, he was arrested for dressing in the forbidden Artillery Guard uniform and for carrying weapons. He was sentenced to nine months in prison until April 1832. His stay there was cut short by the Cholera epidemic that took hold of the world in 1832. Several prisoners, including Galois, were transferred to a clinic for their safety. While in this clinic, he met Stephanie, one of the daughters of the doctors. While the nature of their relationship is not very clear, it can be gleaned from their letters that Galois was irrevocably in love with Stephanie, but ultimately the feeling was not reciprocated. Perhaps the most dramatized and most interesting part of Galois' life is the very endthe duel that killed him. While there have been several theories as to how the duel came about, it is most likely that Galois was simply weary of life, due to his rejection by Stephanie, his lack of recognition for his work, his persecution for his political activism, and his terrible financial situation. Thus, the duel was more of a suicide for him. Contrary to what many believe, Galois did not write out his mathematical theory the night before he died. However, he did compose a letter to his friend Chevalier that outlined the scientific progress he had made, so that all his work would not be lost. 3 Galois' mathematical works The last lines of Galois' letter to Chevalier, written May 29, 1832, before his death, are as follows: \Tu prieras publiquement Jacobi ou Gauss de donner leur avis, non sur la vrit, mais sur l'importance des thormes. Aprs cela, il y aura, j'espre, des gens qui trouveront leur profit dchiffrer tout ce gchis. " This translates to, \Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of these theorems. Later there will be, I hope, some people who will find it to their advantage to decipher all this mess. " Jacobi and Gauss were, of course, to very prominent mathematicians of the time. This seemed to be Galois's last hope that his life's work could make some sizeable contribution to the field of mathematics.
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