On the morning of May 30, 1832,
two men in Paris fought a duel.
Not an unusual event for those days.
One of the men was shot in the gut and died the following day.
His last words to his brother were
"Do not cry, Alfred!
I need all my courage to die at 20."
His name was Évariste Galois.
Galois was a fiercely political mathematical genius. The night before the duel Galois sent
several letters. Some were to his political colleagues, but one of his letters in particular
has become famous amongst mathematicians. Fearing that he might die, Galois assembled
his mathematical discoveries, and sent them to his friend with instructions to pass them
along to two of the best mathematicians of the day - Gauss and Jacobi. The papers lay
dormant until over a decade later, when the letter made its way to the mathematician Liouville,
who took the time to read through the manuscripts and saw to their publication. The world finally
learned that as a teenager, Galois had solved one of the most important problems in algebra.
In algebra you learn to solve equations. Basic equations are relatively simple - you just
solve for x. To solve quadratic equations, you use the quadratic formula. To solve cubic
equations, you use the less well-known cubic formula. And to solve equations of degree
4, you use the beastly quartic formula. Does this pattern continue? Are there formulas
for equations of degree 5, 6, 7 or higher? What Galois proved is -- no. There are general
formulas for solving equations of degrees 1, 2, 3 and 4, but that's it. For degrees
5 and higher, there are no general formulas. To prove this, Galois created new mathematics
which we now call "Galois theory" in his honor.
I wish I could tell you that if it weren't for some bad luck, Galois was well on his
way towards a happy life and a brilliant career. But this is just not the case. His tale was
tinged with frustration, trouble and tragedy.
Évariste Galois was born in a village outside of Paris. His father became mayor, and his
mother was his only teacher until he was 12 years old. When Évariste finally entered
school his teachers saw him as intelligent but eccentric. Galois poured through advanced
math books and quickly began making discoveries of his own. Unfortunately, he was not very
good at patiently explaining his ideas to others. He entered math contests, and sent
his work to leading mathematicians, but his writing was considered incomprehensible.
We now arrive at a sad sequence of events in his last few years. When he was old enough,
Évariste applied to the École Polytechnique - a top university in Paris - but was rejected.
Soon after, his father committed suicide. Galois applied again to the Polytechnique
and was rejected once more. He then enrolled in a less prestigious university, where he
was expelled. He was then arrested a couple of times, endured some heartache, and found
himself preparing for a duel which he lost. A troubled genius, indeed.