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 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:
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 in the far reaches of antiquity when people first went 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 algebraic abstraction (this making up a huge part of what mathematics is today, but it's not remotely like 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!). I can't help but wonder where we would be mathematically and technologically had he lived past twenty and contributed even more!
As to biographies, I still find it a bit hard to let go of the fully 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 giants in the field 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 works of Bell and Infeld 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 wistfully 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, who dies in a mysterious duel at age 20 the day before the death of General Lemarque which triggered the fighting portrayed in Les Miserables, who is left for dead on the field, and who 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 twenty - seems dramatic enough to me!
