In May of 1831 in a Paris restaurant, a young revolutionary stood among a group of like-minded men and gave a mocking toast to the then French King Louis Philippe. For his brash act the 19 year old was arrested and jailed marking the beginning of a year-long devolution to his tragic death. The scene could have been plucked from the pages of Victor Hugo’s classic “Les Miserables”. I envision the scene from the recent movie where the revolutionaries plot bold things in an upper room with disregard for the vast forces aligned against them. “Red…the blood of angry men…Black…the dark of ages past.” The young man was no fictional character however. He was Evariste Galois whose life of sorrow and tragedy could well have been penned by Hugo himself and nicely fit along with Fantine, Jean Valjean and Cosette. Galois happened to also be a mathematician of the highest caliber with an intellect that shined brilliantly for a brief time and was cut short by an almost impossibly improbable sequence of events.
Galois is best known for his theory of equations, specifically the solvability of polynomial equations. He created an entirely new approach to analysis adding to and surpassing work by Hermite and others…oh and he did it at the age of 19. Most readers will be familiar with the solution to the general quadratic equation, ax2 + bx + c = 0, likely committed to memory in 8th or 9th grade. There are similar general solutions for polynomials of the third and fourth degrees but curiously none for polynomials of the 5th degree or in fact for any order polynomial of greater degree than fourth. Galois, in an expression of pure genius proved why this is so. As a graduate student in physics I took a few courses in the Math department out of curiosity. One might believe this more common given the deep intertwined nature of math and physics, but physicists and mathematicians approach the practice of math differently. Physicists are too sloppy in their proofs for the tastes of mathematicians and mathematicians get too lost in minutia for physicists’ tastes. Physicists are like mathematicians in a hurry. I took a course in analysis which led up to one grand moment which was the proof of polynomial solvability using Galois’ approach. For a brief period of months I held the remarkable bit of reasoning in my head, by now though it has long expired. Galois created and reasoned through this logic over a period of a few furiously busy months at an age when most kids today are having their minds stultified by video games, Facebook and texts.
Born in October 1811, Galois lived just 21 years. His mathematical genius exploded at about age 14 when he obtained a copy of a geometry text written by Legendre. Galois blew through it at a rate others might pace themselves to read a comic book. His appetite for mathematics whetted Galois grew impatient with dim-witted fellow students and slow instructors. E.T. Bell in his classic “Men of Mathematics” uses the marvelous phrase “He was forced to lick up the stale leavings which his genius had rejected”. He was rejected for admission to the prestigious Ecole Polytechnique not once but twice. He submitted manuscripts of his work three times to the academy of sciences. The first time, Galois’ work to age seventeen was presented as a manuscript to Cauchy, one of the giants of early 19th century French mathematics. Though he promised to referee the paper, Cauchy forgot and to add insult he lost the manuscript. The second submission a few years later made its way to the secretary collecting the manuscripts but he died and Galois’ work was not found among the remaining papers. The final time he submitted at the urging of Poisson, another 19th century great, the latter failed to recognize the importance of the work. These experiences greatly embittered the young Evariste. His genius thwarted, Galois turned to politics and agitated against the establishment that he justly felt held him back. Political Instability reigned in France for Galois’ whole life. The establishment represented by the monarchy was in a tense conflict with mostly young romantic republicans who dreamed of an egalitarian society. He was released from prison not long after the arrest for his toast, but, now labeled as a radical revolutionary he was arrested again not long after, this time on trumped up charges. He spent almost a year in jail where he worked to write down the body of his mathematical work. At the end of May in 1832 a few months after release from prison Galois was somehow maneuvered into a duel in defense of the honor of a questionable woman. Details of the affair are sketchy and some speculate that he was tricked into the duel by his enemies.
The most moving incident in Galois’ life came the evening before the duel. Certain he was to die and facing his mortality at the age of 21, Galois’ mind raced with mathematical ideas. The night before his fateful contest, his thoughts in turmoil he picked off mathematical ideas, approaches and postulates as they swirled in his tortured mind throwing them madly down on paper to preserve them. Over and over in the margins he wrote “I have not time, I have not time”. The image that accompanies this post is one of the pages of Galois’ notebook. From the first time I heard Galois’ story and read of his pre-dawn anguish to somehow communicate the thoughts of his genius to a world that seemingly rejected him I was intrigued. The mad scribbling in the image speak to his passion and the urgency under which he labored. The image inspires me and I have a photo of it hung in my office so that I can remember the passion of inspired genius, the urgency of life and the dedication of men far greater than me.
The duel did end in Galois’ death on 31 May 1832. His collected works numbered 60 pages. Of these Bell states “What he wrote in those desperate last hours before the dawn will keep generations of mathematicians busy for hundreds of years”.