Évariste Galois was born on October 25, 1811, in Bourg-la-Reine, France, which is now a suburb of Paris. He was the son of a Nicolas-Gabriel, a Bonapartist, who supported Napoleon and opposed royalty. Évariste was a prodigy, showing remarkable mathematical talent from a young age. His mother, Adélaïde-Marie, who was fluent in Latin and well-versed in classical literature, tutored Évariste until he was twelve years of age.
In October 1823, Évariste entered Lycée Louis-le-Grand. Though several of his teachers rated him as a poor student, his mathematics teacher Monsieur Richard, was, perhaps the only teacher who recognized his remarkable intellect. By age 14, Évariste’s passion for mathematics was ignited and he began reading Legendre’s Éléments de Géométrie. By age 15, he was devouring Lagrange’s Réflexions sur la résolution algébrique des équations and Leçons sur le calcul des fonctions.
In 1828, Galois took the oral examination for entrance to the prestigious École Polytechnique in Paris. His contempt for the mundane act of memorizing the proofs of the theorems in Euclidean geometry made him unable to demonstrate these proofs on demand and he failed the examination. Consequently, he enrolled at the much less prestigious École Normale.
While at École Normale, Galois published a paper on continued fractions proving that the regular continued fraction that represents a quadratic surd ζ is purely periodic if and only if ζ>1 and its conjugate η satisfies 
Then, on July 28, 1829, events in Galois’s life took another turn for the worse. His father, Nicolas-Gabriel, committed suicide after a bitter political dispute with the village priest. This traumatic event was followed two days later by Évariste’s second failed attempt to pass the admission test to the École Polytechnique. The reasons for his failure are not known, but it is suspected that it may have been an unfortunate collision of Évariste’s arrogance with the examiners’ incompetence.. On December 29, 1829, Galois passed his Baccalaureate examinations at the École Normale and his examiner reported, “This pupil is sometimes obscure in expressing his ideas, but he is intelligent and shows a remarkable spirit of research.”
In 1830, Galois submitted his paper on the roots of polynomial equations, once again, for the Academy’s Grand Prize in Mathematics. This time the Academy’s secretary Joseph Fourier was to referee the paper. However, Fourier died a short time later, and the manuscript was lost. In spite of these setbacks, Galois continued his research and in that year published 3 more papers including one that laid the groundwork for what would later be known as, Galois Theory.
In 1830, Charles X, who had succeeded Louis XVIII to the throne of France attempted a coup d’état to recover from an election loss, touching off what is known as the July Revolution. Charles X lost the struggle and Louis Philippe became the new king. Galois, following in his father’s footsteps as a Republican, wrote a scathing letter criticizing the Director of the École Normale and was expelled from the school. Galois joined the Republican artillery unit of the National Guard. However, Galois continued to work on mathematics amidst all the political turmoil and on January 17, 1831, at the request of Siméon Poisson, submitted his work on the theory of equations.
Around 4 July 1831, Poisson declared Galois’s work “incomprehensible”, declaring that “[Galois’s] argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor”; however, the rejection report ends on an encouraging note: “We would then suggest that the author should publish the whole of his work in order to form a definitive opinion
On May 9, 1831, Galois attended a banquet attended by some highly prominent celebrities, and in a moment of irrational exuberance, he proposed a toast in which he said, “To Louis Phillipe,” as he drew a dagger across his neck. The pro-republican attendees, interpreting the toast as a threat against the king’s life, cheered. Galois was arrested the following day and incarcerated at Sainte-Pélagie prison until June 15, 1831. However on July 14 (Bastille Day), just a month after his release, Galois was involved in another protest and was arrested and, once again incarcerated.
While in prison, Galois received word that Poisson had declared his paper “incomprehensible”, stating, “[Galois’s] argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor” … [we] would then suggest that the author should publish the whole of his work in order to [enable us to] form a definitive opinion.” Understandably, Galois was devastated. His father was gone, he had been expelled from school, his papers had been rejected, and he was in prison. Life seemed pointless.
When Galois was released from prison on April 29, 1832, he found himself embroiled in a personal confrontation that had to be resolved in a duel to defend his honor or the honor of a romantic interest. The details are unknown, but their are many theories supporting the suggestion that there was a romantic element. (See: Whom the Gods Love, by Leopold Infeld.)
On the evening of May 29, 1832, the night before the duel, Galois scrambled to finish a 63-page outline of his collective works that he would give to his only friend Auguste Chevalier to have published on his behalf. His frenetic scrawl is interrupted by an occasional sketch labelled “une femme” or “nuage.” He signed his note to Chevalier, “I die your friend, E. Galois.”
Early in the morning of 30 May 1832, a farmer found Galois lying in a ditch and dying from a gunshot wound to his stomach. He was brought to a hospital where his younger brother came to visit him the following morning. On seeing Alfred weep, Évariste said, “Ne pleure pas, Alfred ! J’ai besoin de tout mon courage pour mourir à vingt ans !” (Don’t weep, Alfred! I need all my courage to die at twenty!) Galois died at 10:00 a.m. that morning.
Four years after the death of Galois, the French mathematician Joseph Liouville published Galois’ manuscripts in the October–November 1846 issue of the Journal de Mathématiques Pure et Appliquées, revealing that the young mathematician had, indeed, developed a mechanism for determining whether a polynomial equation of any degree has a solution expressible by radicals. Though Niels Abel had proved this result for the specific case of polynomial equations of degree 5, Galois’ more general result applied to equations of arbitrary degree. Furthermore, Galois’ techniques laid the ground work for a field now known as Galois theory that influenced the development of abstract algebra and modern algebraic structures.
Galois, in a relentless pursuit of the hidden difficulties underlying deep problems, once stated, “Unfortunately, what is little recognized is the 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 difficulties.”
