Galois’s 200th birthday

Évariste Galois was a French mathematician who died under mysterious circumstances after a duel when he was only 20 years old!
Even though he was so young, he is considered the father of modern algebra and he is the founder of Galois theory.
He was the first to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, the first to use the term group in mathematics in the modern way and so on.

 

In 1828, he attempted the entrance exam to École Polytechnique, the most prestigious institution for mathematics in France at the time, without the usual preparation in mathematics, and failed for lack of explanations on the oral examination. In that same year, he entered the École Normale (then known as l’École préparatoire), a far inferior institution for mathematical studies at that time, where he found some professors sympathetic to him.

In the following year, Galois’ first paper, on continued fractions,[3] was published. It was at around the same time that he began making fundamental discoveries in the theory of polynomial equations. He submitted two papers on this topic to the Academy of Sciences. Augustin Louis Cauchy refereed these papers, but refused to accept them for publication for reasons that still remain unclear. However, in spite of many claims to the contrary, it appears that Cauchy recognized the importance of Galois’ work, and that he merely suggested combining the two papers into one in order to enter it in the competition for the Academy’s Grand Prize in Mathematics. Cauchy, a highly eminent mathematician of the time, considered Galois’ work to be a likely winner.

On July 28, 1829, Galois’ father committed suicide after a bitter political dispute with the village priest. A couple of days later, Galois made his second and last attempt at entering the Polytechnique, and failed yet again. It is undisputed that Galois was more than qualified; however, accounts differ on why he failed. The legend holds that he thought the exercise proposed to him by the examiner to be of no interest, and, in exasperation, threw at the examiner’s head the rag used to erase the blackboard. More plausible accounts state that Galois made too many logical leaps and baffled the incompetent examiner, evoking the student’s rage. The recent death of his father may have also influenced his behavior.

Having been denied admission to the Polytechnique, Galois took the Baccalaureate examinations in order to enter the École Normale. He passed, receiving his degree on December 29, 1829. His examiner in mathematics reported, “This pupil is sometimes obscure in expressing his ideas, but he is intelligent and shows a remarkable spirit of research.”

In April 1829 Galois had his first mathematics paper published on continued fractions in the Annales de mathématiques. On 25 May and 1 June he submitted articles on the algebraic solution of equations to the Académie des Sciences. Cauchy was appointed as referee of Galois’ paper.

Galois sent Cauchy further work on the theory of equations, but then learned from Bulletin de Férussac of a posthumous article by Abel which overlapped with a part of his work. Galois then took Cauchy‘s advice and submitted a new article On the condition that an equation be soluble by radicals in February 1830. The paper was sent to Fourier, the secretary of the Paris Academy, to be considered for the Grand Prize in mathematics. Fourier died in April 1830 and Galois’ paper was never subsequently found and so never considered for the prize.

Galois, after reading Abel and Jacobi‘s work, worked on the theory of elliptic functions and abelian integrals. With support from Jacques Sturm, he published three papers in Bulletin de Férussac in April 1830. However, he learnt in June that the prize of the Academy would be awarded the Prize jointly to Abel (posthumously) and to Jacobi, his own work never having been considered.

There is a movie that is based on his life http://www.imdb.com/title/tt0205913/

In 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.

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.”

More on his work in subsequent post

 

 

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