0:00:08.269,0:00:10.979
On the morning of May 30, 1832,

0:00:10.988,0:00:13.038
two men in Paris fought a duel.

0:00:13.038,0:00:15.791
Not an unusual event for those days.

0:00:15.791,0:00:17.738
One of the men was shot in the gut and died the following day.

0:00:19.056,0:00:20.626
His last words to his brother were

0:00:20.871,0:00:21.126
"Do not cry, Alfred!

0:00:22.029,0:00:22.852
I need all my courage to die at 20."

0:00:22.852,0:00:23.965
His name was Évariste Galois.

0:00:24.072,0:00:26.047
Galois was a fiercely political mathematical genius. The night before the duel Galois sent

0:00:26.172,0:00:28.049
several letters. Some were to his political colleagues, but one of his letters in particular

0:00:28.175,0:00:47.390
has become famous amongst mathematicians. Fearing that he might die, Galois assembled

0:00:47.390,0:00:51.829
his mathematical discoveries, and sent them to his friend with instructions to pass them

0:00:51.829,0:00:57.989
along to two of the best mathematicians of the day - Gauss and Jacobi. The papers lay

0:00:57.988,0:01:03.669
dormant until over a decade later, when the letter made its way to the mathematician Liouville,

0:01:03.670,0:01:09.310
who took the time to read through the manuscripts and saw to their publication. The world finally

0:01:09.310,0:01:16.079
learned that as a teenager, Galois had solved one of the most important problems in algebra.

0:01:16.078,0:01:21.089
In algebra you learn to solve equations. Basic equations are relatively simple - you just

0:01:21.090,0:01:26.880
solve for x. To solve quadratic equations, you use the quadratic formula. To solve cubic

0:01:26.879,0:01:32.078
equations, you use the less well-known cubic formula. And to solve equations of degree

0:01:32.078,0:01:39.078
4, you use the beastly quartic formula. Does this pattern continue? Are there formulas

0:01:39.778,0:01:46.539
for equations of degree 5, 6, 7 or higher? What Galois proved is -- no. There are general

0:01:46.539,0:01:52.478
formulas for solving equations of degrees 1, 2, 3 and 4, but that's it. For degrees

0:01:52.478,0:01:58.039
5 and higher, there are no general formulas. To prove this, Galois created new mathematics

0:01:58.039,0:02:02.459
which we now call "Galois theory" in his honor.

0:02:02.459,0:02:07.810
I wish I could tell you that if it weren't for some bad luck, Galois was well on his

0:02:07.810,0:02:14.060
way towards a happy life and a brilliant career. But this is just not the case. His tale was

0:02:14.060,0:02:18.319
tinged with frustration, trouble and tragedy.

0:02:18.319,0:02:24.299
Évariste Galois was born in a village outside of Paris. His father became mayor, and his

0:02:24.300,0:02:28.780
mother was his only teacher until he was 12 years old. When Évariste finally entered

0:02:28.780,0:02:34.840
school his teachers saw him as intelligent but eccentric. Galois poured through advanced

0:02:34.840,0:02:40.280
math books and quickly began making discoveries of his own. Unfortunately, he was not very

0:02:40.280,0:02:45.140
good at patiently explaining his ideas to others. He entered math contests, and sent

0:02:45.139,0:02:52.029
his work to leading mathematicians, but his writing was considered incomprehensible.

0:02:52.030,0:02:57.099
We now arrive at a sad sequence of events in his last few years. When he was old enough,

0:02:57.099,0:03:02.629
Évariste applied to the École Polytechnique - a top university in Paris - but was rejected.

0:03:02.629,0:03:07.370
Soon after, his father committed suicide. Galois applied again to the Polytechnique

0:03:07.370,0:03:12.310
and was rejected once more. He then enrolled in a less prestigious university, where he

0:03:12.310,0:03:16.909
was expelled. He was then arrested a couple of times, endured some heartache, and found

0:03:16.909,0:03:22.740
himself preparing for a duel which he lost. A troubled genius, indeed.