A Mathematical Melodrama

On the 30th of May 1832, when the day had barely started to dawn in the southern suburbs of Paris, a young man called Evariste Galois, still drowsy, but with a gun in his hand, already stood facing an artillery officer named Pescheux d’Herbinville. A classic duel was about to take place, one where opponents use weapons to defend their honors and reputations. Today, it is not known precisely what the argument was really about, but it seems likely that the main cause of dispute between the two men was the lovely Stéphanie Félice Poterine du Motel.

From the distance of twenty-five feet the rivals aimed the barrels of their guns at each other and only a moment later the young Evariste fell to the ground, wounded. The bullet hit him in the stomach, puncturing his intestines, and only an immediate operation might have saved his life. However, no doctor was at hand and those watching the duel as well as Evariste’s opponent left the scene as soon as he fell. It was only three hours later that the injured Galois was noticed by a passer-by who managed to get him to a nearby hospital. At that particular moment Galois was still fully conscious, but he was aware that his time was quickly running out. When his younger brother came to see him, he uttered his last words: “Don’t cry Alfred! I’ll need all my courage to die at twenty years of age.” The next morning he would not wake up.

Even before this fatal May morning, Galois was well aware that accepting the duel would almost certainly sentence him to death. He was a brilliant mathematician, but hardly as skilled in wielding weapons as his opponent d’Herbinville, the soldier. And so he spent the night before the duel trying to jot down as many mathematical ideas as he could, but had not managed to before. We all know that we are usually much more productive when haunted by a deadline than when we have plenty of time at our disposal. However, it is something quite different to be only twenty years old and, in your head, see the solutions to several mathematical problems to which you are certain nobody else knows the answers, while a duel that you are bound to lose is due the very next morning.

That night, Galois filled several sheets of paper with equations and sent them to a good friend, asking him to pass them on to the famous mathematicians Jacobi and Gauss. On these sheets he tried to gather all the ideas that he thought to be relevant. However, as the remaining notes imply, he found it difficult to focus on mathematics alone. The edges of the pieces of paper contain the words “une femme” (a woman) and a cry of desperation: “Je n’ai pas le temps!” (I’m running out of time).

Evariste Galois was undoubtedly a great mathematical genius, but his short life was not without difficulties. Even though he came from a fairly wealthy family – his father was the mayor of a small town near Paris – and received a good education, the trouble was that his teachers, at least when it came to mathematics, could not measure up to his standards. At the early age of fifteen he was already reading – in the original – through every possible paper published by his contemporaries. In order to find a more appropriate study environment, he tried to enroll into the prestigious Ecole Polytechnique, but unfortunately failed to pass the entry exams. When he had already published his first scientific paper later he tried his luck at the Polytechnic again, but was no more successful in convincing the board of admissions than he was the first time.

He also sent his mathematical ideas to be evaluated by the French Academy of Sciences Académie des sciences) which was at that time at the centre of scientific work. Galois’ work was reviewed by the Baron Cauchy, one of the giants of the French school of mathematics, who praised the achievements of the young mathematician and suggested that he be given a special award from the Academy. Galois developed his ideas further and sent them to the Academy’s secretary, but he died shortly after, and the young mathematician’s article was nowhere to be found, so he regrettably never received the award even though everybody agreed that he was a most talented young man.

After Galois’ sudden death rumors started spreading that the unfortunate incident was not really the result of an honorable duel, but a murder, plotted against the young mathematician because he was thought to be an ardent republican. It is true that he was often present in the first lines of protests and was therefore arrested on several occasions, but there is no proof to support the theory of premeditated murder. It was actually when serving a prison sentence because of his political beliefs that he made the acquaintance of the fatal Stéphanie. She was the daughter of the doctor of the clinic to which the youngest prisoners were transferred during a cholera epidemic.

Galois’ friend and brother tried to save Evariste’s notes after his death, to organize them as much as possible and to pass them on to renowned mathematicians so they could prepare them for publication. However, it took several decades before the world of mathematics came to understand the extraordinary significance of the ideas of this young mathematician who so unfortunately ended his brief, but extremely productive scientific career.

Anyone who has gone to school in the past couple of decades has to remember the unusual mathematical structure called the group. Such knowledge escapes from the head of the average student right after he hands in his last math test, but we should be aware of the fact that modern physics would be quite inexplicable without the use of the group theory. Groups are not only essential to describing the elementary particles which make up the universe; they are a fundamental mathematical tool used by experts from all fields of science. Groups as a basic mathematical structure which is one of the foundations of modern mathematics came into existence on that very fatal night in 1832 when Evariste Galois decided to scribble down equations from his head when he would have done better to practice his shooting.