With films like A Beautiful Mind, about the far less eventful life of John Nash, it’s a little surprising that no one’s run with the idea of a biopic about Évariste Galois, whose life ticks all the boxes in the “romanticized mathematician” schema. The real story is so good that it seems unnecessary to fictionalize it further, but there are more myths about Galois than about pretty much any other scientist or mathematician. October 25 will mark the bicentenary of his birth (I guess there’s still some time until the bicentenary of his death).
Galois was born in 1811 in France. These were tumultous times in French politics, and he would soon get caught up in the events. Napoleon was finally beaten at Waterloo in 1815, and Louis XVIII became king. Galois’s parents were liberals, and he inherited their political disposition. Galois didn’t discover mathematics until he was sixteen, but quickly became consumed with it; at twenty, he was killed in a duel, most likely over a woman, and left behind what was to become Galois theory, an important step forward in mathematics. The young Évariste was an eccentric fellow, and he showed little regard for things outside of mathematics and politics. Although he was clearly brilliant, he failed to pass the entrance exam to the elite university École Polytechnique twice, once because he didn’t bother to prepare, the second time, apparently, because he considered the interviewer to be stupid and refused to play by the rules. Just days before his second attempt at the exam, his father committed suicide. Évariste’s father had been mayor of Évariste’s home town of Bourg-la-Reine, and the town priest, a political opponent, had forged slanderous letters in Galois’s father’s name.
Outside of his original research in the theory of equations, Galois was a devoted republican and couldn’t seem to keep out of trouble. During the 1830 revolution, while he was still in school, Galois (and other fellow students) wanted to join the rebellion in the streets, but the school detained them. Galois wrote a letter denouncing the school director. The letter got him expelled, and Galois joined the Artillery of the National Guard, a branch of the militia composed mostly of republicans. At a dinner celebrating the acquittal of nineteen National Guard officers who had been accused of planning to distribute cannons to the people, Galois proposed a toast to the king, holding a dagger over his cup. His toast was met with applause, but the next day, he was arrested and thrown in jail, where he continued researching cutting-edge mathematics. During his time in prison, there was reportedly also an episode where fellow inmates goaded him into downing liquor, after which he made a drunken suicide attempt.
Galois would be released, arrested and once again released before his death. Although his research suffered during his political involvement, Évariste did attempt to publish his revolutionary findings. The traditional story says that he was a misunderstood genius and that was the reason why he wasn’t recognized until after his death; closer readings seem to indicate that a combination of bad luck and Galois’s own eccentricity and lack of discipline also played a part. An example of his bad luck: he submitted an important paper to the Academy of Sciences, represented by its secretary Joseph Fourier. Fourier died before the paper could be published, and the original couldn’t be found in his papers.
Finally, we come to the tragic end: the duel on May 31, 1832. Much has been written about it. Much is false. Some have suggested that he was killed by the government, but circumstantial evidence suggests that his killer was a fellow republican, and that the duel was about a girl’s honor. (Duels were not uncommon at the time.)
The night before the duel, Galois, certain that he would die, furiously scribbled down notes and wrote letters to his friends; according to the legend, he finally put down into words his revolutionary findings, while in fact he only annotated papers he had already submitted elsewhere. In his letters to friends, he wrote that he was sorry he couldn’t die in service of his country and its ideals. Galois was shot in the stomach, and died of the wounds. Reportedly, two or three thousand republicans attended his funeral, and the government feared riots would erupt.
As for the nature of Galois’s actual mathematical research, it’s not very accessible to laymen. Like Fermat’s theorem, the solution is really hard, but the problem that motivated it is simpler to state: why can we solve all polynomial equations of degree four or lower using only arithmetic and radicals (square roots, cube roots, fourth roots etc.)—but not fifth-degree polynomials and higher? The answer, Galois realized, has to do with a group of permutations related to the polynomial. The theory he developed to account for this is today known as Galois theory. (I won’t pretend that I’m qualified to explain it to you. I’m not. But Galois’s story is really interesting.)
More about Évariste Galois’s life story and the legends surrounding him, here. If you’re a braver person than I, and want to truly understand Galois theory, this might be a place to start.
The Atlantic discusses a deadly culture-bound syndrome. When you’re dreaming, your body becomes paralyzed, so that you don’t act out your dreams in sleep. There are two ways this mechanism could fail: either you could not be paralyzed in sleep, in which case you might sleepwalk or worse. Alternatively, you could wake up while paralyzed, and this feeling, known as sleep paralysis, is usually accompanied by feelings of intense dread and the belief that a malevolent entity is in the room, if not actually on top of you. Sleep paralysis is known in all cultures, and different non-scientific beliefs attach to it in. The Hmong call it tsog tsuam, and have a system of beliefs surrounding it.
The article discusses an epidemic among ethnically Hmong who had immigrated to the US: in the early 1980s, 117 men, most of them healthy and relatively young, died in their sleep of unknown causes. The Hmong believe that, if you don’t worship the right spirits, evil spirits can cause tsog tsuam. The article argues that intense belief in this phenomenon could have triggered an “obscure genetic cardiac arrhythmia that is prevalent in southeast Asia.” Their belief in the spirit world, in a sense, scared them to death.
Planets are not cube-shaped. There’s no physical mechanism that would allow a cubic planet to form naturally, certainly not one the size of Earth, and even if you somehow built one, gravity would eventually turn it into a sphere. This is nothing more than a light-hearted thought experiment. But assuming you had a cube-shaped Earth, what would it be like?
If you were dropped in the middle of one of the six faces, you’d be standing in an ocean, because that’s where all the water would go, in the middle. If you move out of the ocean, you’d face a very, very steep climb up one of the mountains that form the corners, jutting out of the planet’s atmosphere. If there was life on this planet, it would most likely evolve independently on each face, separated by impossibly high mountains. On top of one of the corner-mountains, you’d have a spectacular view:
On the plus side, the view is like none on earth, or on any planet anywhere. You can sight down one edge of the cube to a far corner, a distance of some 6,400 miles. Even more strikingly, you see all the atmosphere and water has been concentrated by gravity into a blob in the middle of each face, with the corners and edges poking out into space. You realize your cubical planet isn’t one world but six, each face’s segment of the biosphere isolated from the others by the hopeless climb.