The most famous duel in the history of mathematics, if not all of science, took place on 30 May 1832. It ended with Evariste Galois, a French mathematician, being shot in the abdomen. He died the very next day at the age of 20. But, by then, he had already done enough to initiate an entire field of mathematics, now termed the Galois Theory, apart from making a substantial contribution to a number of related areas.
It would be a difficult task to describe his work in a few lines, but it is possible to allude to one of its consequences for those familiar with the formula for solving quadratic equations (equations of the form ax^2 + bx + c= 0 where a is not zero) from school algebra. Similar formulas for polynomials—a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient—of degree 3 and 4 (with highest nonzero x^3 and x^4 terms, respectively) were found in the sixteenth century. In 1825, another brilliant mathematician, Niels Henrik Abel, showed that no such formula could be found for polynomial equations of degree 5. Galois’ work, apart from providing a new proof for Abel’s result, can be used to establish whether such a formula exists for polynomials of any degree and to determine it in the event that it does.
The story of Galois’ life and death is romantic enough without the embellishments that have accrued over the years. In one version, Galois stayed up the night before the duel, writing down the details of the theory that would be named after him. Facts don’t seem to bear this out but even attempts to correct this version of events add their own gloss, making Galois’ death no less tragic and the story no less fascinating. The Evariste Galois archive, set up to assemble all his work, provide translations and assemble a factual account of his life, describes the duel that ended Galois’ life in these terms:
The duel and the events leading to it are blurred by time and the fantasies of novelists and what's worse, biographers. …[I]t is highly improbable that the duel was a plot of the royalists to murder him.… Most probably it was Galois himself who incited this interpretation. He wanted … to appear as a victim of the government, (hoping to) enrage the masses to revolt. He dropped remarks pointing in this direction…in his last letters. The most likely reason is: He was weary of life because of his unhappy love affair, his fruitless efforts at gaining recognition for his mathematical work… and he felt (he had ended up in) a blind alley in politics as well. So his duel was like a staged suicide. One thing is clear … he didn't (set) down his mathematical theory the night before the duel.
Galois’ politics may not have been as consequential, but it was certainly as revolutionary as his mathematics. In 1830, Charles X—the last Bourbon king of France—was faced with the possibility of abdication as the liberal party in opposition gained a majority. In response, he carried out a coup and issued a set of directions that suspended the liberty of the press and excluded much of the middle-class from taking part in future elections. He was soon deposed after a popular uprising and a constitutional monarchy was put in place.