Evariste Galois

The death of General Jean Maximilien Lamarque on June 1, 1832 was the catalyst for the fighting to break out in the Parisian June Rebellion of 1832.  This event is captured in Les Miserables by Victor Hugo.  Lemarque's death came one day after the fatal duel of young mathematician Evariste Galois (1811-1832) - whose death may have been purposeful and intended to trigger the raising of the barricades.  If so, so much the worse for Galois, and so much the worse for us.

There is a great deal of legend that has grown up around Galois's life, and it was easy for biographers such as E. T. Bell and Leopold Infeld to romanticize his life.  He died at 20 in a duel, and by that young age he had already revolutionized mathematics - though that wasn't recognized for at least a decade after his death.  He wrote out a great deal of mathematics the night before he died - as if he knew for sure he was going to die - almost as if he planned to die - and in this writing we find the phrase, "Je n'ai pas le temps!"  ("I have no time!")  My understanding is that he had no second in the duel and that only one shot was fired.  Galois was shot in the stomach and left for dead in the field of Glacier Pond in Gentilly, 13th Arrondisement, Paris.

I spent a great deal of time trying to find the location of the duel - wanting to visit, pay my respects, take photographs, but as I assumed and was later told much has changed in Paris since 1832.  Apparently the field was near swamps, and, as I was told by a mathematical correspondent in Germany who is familiar with Paris, "Definitely the old swamps ("Glacière") don't exist, they used to be swamps that froze in winter, and whose ice was stored on the outskirts of Paris, but this part of Paris has been entirely built, and even the river is underground now.  There is a street ("rue de la Glacière") which corresponds roughly to the place."

The following picture is of  "rue de la Glacière" - a very short street with no sign of a field or swamp on or near it!

A passing peasant found Galois a couple of hours after the duel and brought him to La Chochin Hospital - which, in my pilgrimage I also sought out.  Obviously this too has changed since 1832 - remodeling, new wings and buildings added - as one would hope for a hospital over the course of 184 years!  But, though updated, here it is, the hospital where Galois was taken.  It's only two blocks away from rue de la Glacière.

Galois died at the Cochin Hospital at 10:00am the following morning.  He had refused the offices of a priest, but his younger brother Alfred was there with him, and Galois's last words were to his brother, “Ne pleure pas, Alfred! J'ai besoin de tout mon courage pour mourir à vingt ans!” ("Don't cry, Alfred!  I need all my courage to die at twenty!")

Galois was buried in a common grave at Montparnasse Cemetery, and no trace of it is left.  A cenotaph memorializing him has been raised in the Bourg-la-Reine Cemetery near where family members are buried.  The following are pictures of Montparnasse Cemetery - his remains being somewhere inside:

The reason I began this post with a picture of the flag is that Galois was very political.  He was part of the Artillery of the National Guard, of which 19 officers were arrested late in 1830 for conspiracy to overthrow the government.  They were acquitted in May 9, 1831, and 200 republicans gathered for a dinner to celebrate the acquittal.  During the dinner Galois appeared to make threats against King Louis Phillipe - standing and raising both a glass and an unsheathed dagger.  It was said that he stated, "To Louis-Phillipe, if he betrays."  But the reality is that his words were drowned out in the surrounding noise.  Galois was arrested but, surprisingly, acquitted, however on July 14, Bastille Day, he was arrested again because he was wearing the uniform of the Artillery of the National Guard, which was illegal; he was also carrying loaded guns and a dagger.

While in prison he tried to commit suicide by stabbing himself with a dagger, but the other prisoners stopped him.  In 1832 all the prisoners were moved to another location due to a cholera epidemic.  It seems that it was here that he fell in love with Stephanie-Felice du Motel, daughter of the attending physician.  She later spurned Galois, and this is involved at least in some way with his death.  In letters he wrote to friends not long before he died he says, "I was provoked by two patriots  .  .  .  it was impossible to refuse" and "I die a victim of an infamous coquette."

We don't know for certain what the cause of the duel was.  Was it purely a duel of love and honor?  Was it a set-up by other political forces to get rid of him (using Stephanie as a convenient ruse)?  Was it a way of "honorably" committing suicide, which he had been unsuccessful with in prison?  Was it self-sacrifice - him laying his life down for the cause he believed in, to be a trigger for barricades to go up and fighting to begin?

What we do know for certain is that his mathematical work - all done by the age of 20 - has altered the face of mathematics.  As mathematician Arthur Cayley said of Galois's work, "The idea of a group as applied to permutations or substitutions is due to Galois, and the introduction of it may be considered as marking an epoch in the progress of the theory of algebraic equations."  Biographer John Derbyshire also views the work of Galois as the beginning of a new epoch in algebra - the first being when people when from asking, "This plus this equals what?" to "This plus what equals that?" - the second being the development of "literal notation" (i.e. using letters in algebra in order to "relieve the imagination") in the 1500s and 1600s (if you think algebra is hard because they threw the alphabet in with the numbers, try doing it without the letters!) - and the third being Galois's move to higher levels of abstraction (this making up a huge part of what mathematics is today, but it's not at all the "algebra" you see in middle school, high school or junior college - it has to do with such things as fields, rings, ideals, groups - both abelian and non-abelian, as well as kernels and so on - and that's just the beginning of what his revolution has brought forth!).

As to biographies, I find it hard to let go of the romanticized versions of his life that I'd always heard.  It seems E. T. Bell wanted to inspire young people to go into mathematics (as Sophie Germain had been inspired by the story of Archimedes) and so played fast and loose with the facts in biographies of mathematicians in his book Men of Mathematics, of which there is a chapter on Galois.  (I don't know if I can fault him TOO much as this book did inspire such phenomenons as John Forbes Nash and Freeman Dyson to go into mathematics, and his book The Last Problem inspired Andrew Wiles to pursue and finally solve Fermat's Last Theorem, but still  .  .  .).  I first fell in love with the story of Galois when I read Leopold Infeld's biography Whom the Gods Love twenty-five years ago or so.  So if you want a lovely, romanticized version of Galois's life, these are the places to go.

If you want the cold, clarifying water of well-researched reality splashed in your face, check out Tony Rothman's essay on the facts surrounding the events at the end of Galois's life.

If you'd like a brief, accurate, and interesting biography of Galois read either the chapter "Pistols at Dawn" in John Derbyshire's book Unknown Quantity, or the chapter "The Romantic Mathematician" in Mario Livio's book The Equation that Couldn't be Solved.

Though as I've researched further into his life and have begun to feel that "ignorance is bliss," I don't know that we need all the romanticizing that has taken place.  The bare facts are intriguing enough in my mind - a genius whose mathematics changes the discipline entirely, who engages in questionable political activities, dies in a mysterious duel at age 20 the day before the death of General Lemarque which triggered the fighting portrayed in Les Miserables, is left for dead on the field, and dies in his brothers arm's the next day asking his brother not to cry since he needs all of his courage to die at 20 - seems dramatic enough to me!