Galois - "This guy only deals with the highest levels of mathematics"

First chapter in a series of articles and biographies on the history of mathematics, written by Liran Zeidman. And this time about Everist Galois - the genius mathematician whom the world lost at a too young age in a duel

When I was in high school I had a math teacher. This sounds completely natural, but the emphasis is on the word teacher, since his love for the profession was so great that it was impossible not to absorb from this love, who more and who less. During these 3 wonderful years, together with my classmates, I was privileged to get to know the world of mathematics as I had never known it before, the proofs became human when he combined the stories of the fallen people behind the numbers and equations and this is my starting point when it comes to this beautiful profession. In one of the lessons that is etched in my memory, the teacher was asked his opinion regarding the greatest mathematicians of all time. Hella claimed that it is difficult to define who is the greatest of all because there is no single definition of a genius, but if he could point to one whose intellectual abilities in mathematics are the highest, it would be Evariste Galois, one of the tragic heroes of the world of mathematics. One sentence from this dialogue made me start to be interested In people and not just numbers: "He was so smart that he took for granted ideas that mathematicians have to study all their lives to really understand them, and this was even before he was 20 years old." I dedicate the first article to the teacher who influenced me more than any other teacher, the mathematician Silvio Stetzel

Galois was born in France in 1811 to educated parents who took upon themselves the education of the boy until the age of 12 when in the background revolutions on a global scale were taking place in his country, which greatly influenced the course of his life and unfortunately also his death.

The beginning of his educational journey is in the middle school "Louis-Hagadol", where he achieved relatively good success and even won several awards, but at one point he had to stay in class because the level of his rhetoric did not meet the institution's expectations. The turning point came at the age of 16 when his first math teacher, M. Vernier, recognized the tremendous potential in him with these words: "Mathematics dominates him completely, it would be best for his parents to send him to study only this subject." He wastes his time here, which causes him to bully other teachers and receive endless punishments." The school reports were not kind to him and described his faults as "closed, lonely and original", it is strange to think that the most original mathematician the world has known was given this derogatory title. At the age of 17, Galois tried to be admitted to the most important academic-mathematical institution in France (and so on in the world at that time) "Polytechnique" but failed. He continued to study higher mathematics at "Louis the Great" and focused mainly on conducting personal research while studying the writings of the giants of mathematics Legendre and Lagrange. Moro wrote about it: "This guy only deals with the highest levels of mathematics. This guy only deals with the highest levels of mathematics."

In April 1829, when he was only 18 years old, Galois wrote his first mathematical article for a French scientific journal. About two weeks later, he sent a number of papers on algebra to the Academy of Sciences, which was examined by the great French mathematician of the time, Augustine Louis-Cauchy. While his works were being examined, his father committed suicide and this greatly affected the course of Galois's life. A few weeks later, he seems to have recovered from his deep depression and returned to take the "Polytechnic" exam for the second time, but failed again. It seems that a combination of the persistent depression factor and his inability to clearly explain his ideas that were ahead of their time caused this. Galois decided to give up trying to be admitted to this institution even though he really wanted to, the level it was at was the highest that could be achieved and also a number of very strong political associations were active in it. He decided as a last resort to be admitted to an institution called "Normal", where he successfully passed the exams. His supervisor in mathematics wrote about him: "This guy has a bit of a problem explaining his ideas, but you can clearly see his great intelligence and his attraction to research." It is amusing to hear that his literature teacher claimed: "I was told that this guy has amazing mathematical abilities, but according to what I saw, he knows nothing and the only one who answered me in a poor way, in my opinion, he is not really as smart as everyone thinks."

Galois continued at the same time to send researches in algebra to Kushi but he was told that the specific field he was focusing on was being studied at the same time by the elite mathematician Nils Abel and Hele suggested that he focus on another research (so-called his most important from the point of view of our time) on solving equations. Galois took this advice and wrote an article which he sent to the mathematician Fourier who was at that time the secretary of the Parisian Academy, his goal was to win the grand prize in mathematics that year. Bad luck seems to have continued to haunt Galois as Fourier died soon after and his work never reached its destination and was thus forgotten. The guy didn't say desperate and studied Jacobi's research on Burin and but once again submitted a brilliant paper but for some reason it was not checked again, while the grand prize was won by these two mathematicians. The year 1830 was of great importance in France mainly in what concerned the government and the politics surrounding it, riots began in France and Galois's support for them led the director of the "Normal" to be removed immediately from the walls of the academy, which pushed him to join the artillery regiment of the French army.

That year, when Galois was 19 years old, he wrote two more articles which were the last publications of his life. The mathematician Poisson asked him to consider rewriting his previous work on equations, and he did so. During the writing, Galois was arrested several times and thrown into prison for political reasons, at this time Poisson informed him that his work was again not accepted because, in the opinion of the judges, this work could not be seriously tested due to problems in the ways of proving the ideas and solutions he proposed. Galois took this message hard and tried to commit suicide in his cell but the other prisoners prevented him from doing so. For the first time, Galois poured out his heart to those inmates about being completely lonely since his father died and looking for someone who could love true love. In 1832, a cholera disease broke out in the area where he was imprisoned and all the prisoners were transferred to another prison facility, where Galois fell in love with the daughter of one of the doctors, Stéphanie-Felice de Mottel, with whom he began to exchange letters (today the name Stéphanie can be seen in some of his records as a side note). For a reason that is not clear enough, but it is probably related to his connections with Septani, Galois was asked to enter a duel with another person and this is where the incredibly romantic (but slightly exaggerated) story comes in, that on the evening before the battle, Galois wrote down everything he knew about what is now called "Torat Galois" because who assumed that he was likely to die. Galois did indeed write down a considerable amount of theory on this matter that evening, but a small line on one side of the pages made the paper immortal:

"There is something that needs to be completed in this example, but I don't have time to do it." The next day he was shot, wounded and abandoned by his villainous opponent who, as it happened, was helped by another person during the battle. Galois died shortly after and his funeral soon became a major political demonstration. Galois's brother and his friend Mr. Chevalier found his writings in which he wrote as a note: "Send this for the perusal of Gauss and Jacobi, who will publicly comment on their importance and not necessarily on their correctness. I hope that in the future there will be others who will manage to bring order to this mess." The two sent copies to these mathematicians but no reference was found on their part to the studies. However, the pages reached the mathematician Liouville and he insisted on their monumental importance to the world of mathematics in general and algebra in particular and published them publicly.