
Wow! Did you notice what I noticed? Evarist Galois didn't live very long and he is considered a famous mathematician. Can you imagine accomplishing something so big by the time that you were 21 that books were written about you? Well, Evarist Galois didn't discover anything huge, but what he did do was characterize equations as solvable by radicals by improving on Lagrange's ideas and deriving suggestions from the works of Legendre, Gauss, and Abel. Still, it is something to marvel at that he did all this before his 22nd birthday. Which brings to mind another thought, what could he have done if he would have lived longer? To be able to begin to answer this question, let's take a look at the brief life of Evarist Galois. As was the case with many famous mathematicians, scientists, astronomers, and the like, Galois was born to an affluent family that resided in France. His parents were both educated people and ensured that Galois began studying mathematics at the age of fifteen. Unlike most students of today, mathematics became his passion. However, very much like students of today, he neglected the rest of his studies to devote his time to his passion, mathematics. Galois wanted to enter the Ecole Polytechnique, which was a very prestigious school in France. He tried to gain acceptance and entrance to the school on two occasions and on both was rejected. It is speculated that he was rejected because of one of the two following reasons: he either failed to explain in sufficient detail the question presented to him orally or the examining professors simply did not understand him. Because of this, Galois entered what was considered a much inferior school. While he was in school, Galois published four papers. In 1829 he submitted two papers on the solution of equations to the Academy of Sciences. He had been studying carefully the works of Lagrange, Gauss, Cauchy, and Abel and worked endlessly on the task of determining which equations are solvable by radicals. The papers that he submitted to the Academy were entrusted to Cauchy who conveniently lost them. In January of 1830 Galois presented to the Academy another paper on his research. This paper was also lost. During that same year, 1830, during the revolution, Galois was expelled from school for publicly criticizing the director of his school for failing to support the Revolution. Based on the suggestion of a friend Galois wrote a new paper on his research though. "Sur les conditions de re'solubilite' des e'quations par radicaux," is the only finished article on his theory of the solution of equations. Unfortunately, the Academy returned his paper stating that he needed to write a fuller explanation. Shortly after being expelled from school, Galois was arrested for political offenses and spent most of the last year and a half of his life in prison. He did write a scratchy and hastily written account of his researches which he entrusted to his friend August Chevalier. This account was written the night before his death and has been preserved. He was killed in a dual on May 31, 1832. The first full and clear presentation of Galois theory was given in 1870 by Camille Jordan in a book. O.K., lets recap briefly.
A famous quote from Galois: "Unfortunately what is little recognized is that the most worthwhile scientific books are those in which the author clearly indicates what he does not know; for an author most hurts his readers by concealing his difficulties." 
Contributed by S. Anderson 
References: Quoted and paraphrased from Mathematical Thought from Ancient to Modern Times. Kline, Morris. Oxford University Press. Volume 2. Pg. 755771. 