WEBVTT 00:00:08.269 --> 00:00:10.979 On the morning of May 30, 1832, 00:00:10.988 --> 00:00:13.038 two men in Paris fought a duel. 00:00:13.038 --> 00:00:15.791 Not an unusual event for those days. 00:00:15.791 --> 00:00:17.738 One of the men was shot in the gut and died the following day. 00:00:19.056 --> 00:00:20.626 His last words to his brother were 00:00:20.871 --> 00:00:21.126 "Do not cry, Alfred! 00:00:22.029 --> 00:00:22.852 I need all my courage to die at 20." 00:00:22.852 --> 00:00:23.965 His name was Évariste Galois. 00:00:24.072 --> 00:00:26.047 Galois was a fiercely political mathematical genius. The night before the duel Galois sent 00:00:26.172 --> 00:00:28.049 several letters. Some were to his political colleagues, but one of his letters in particular 00:00:28.175 --> 00:00:47.390 has become famous amongst mathematicians. Fearing that he might die, Galois assembled 00:00:47.390 --> 00:00:51.829 his mathematical discoveries, and sent them to his friend with instructions to pass them 00:00:51.829 --> 00:00:57.989 along to two of the best mathematicians of the day - Gauss and Jacobi. The papers lay 00:00:57.988 --> 00:01:03.669 dormant until over a decade later, when the letter made its way to the mathematician Liouville, 00:01:03.670 --> 00:01:09.310 who took the time to read through the manuscripts and saw to their publication. The world finally 00:01:09.310 --> 00:01:16.079 learned that as a teenager, Galois had solved one of the most important problems in algebra. 00:01:16.078 --> 00:01:21.089 In algebra you learn to solve equations. Basic equations are relatively simple - you just 00:01:21.090 --> 00:01:26.880 solve for x. To solve quadratic equations, you use the quadratic formula. To solve cubic 00:01:26.879 --> 00:01:32.078 equations, you use the less well-known cubic formula. And to solve equations of degree 00:01:32.078 --> 00:01:39.078 4, you use the beastly quartic formula. Does this pattern continue? Are there formulas 00:01:39.778 --> 00:01:46.539 for equations of degree 5, 6, 7 or higher? What Galois proved is -- no. There are general 00:01:46.539 --> 00:01:52.478 formulas for solving equations of degrees 1, 2, 3 and 4, but that's it. For degrees 00:01:52.478 --> 00:01:58.039 5 and higher, there are no general formulas. To prove this, Galois created new mathematics 00:01:58.039 --> 00:02:02.459 which we now call "Galois theory" in his honor. 00:02:02.459 --> 00:02:07.810 I wish I could tell you that if it weren't for some bad luck, Galois was well on his 00:02:07.810 --> 00:02:14.060 way towards a happy life and a brilliant career. But this is just not the case. His tale was 00:02:14.060 --> 00:02:18.319 tinged with frustration, trouble and tragedy. 00:02:18.319 --> 00:02:24.299 Évariste Galois was born in a village outside of Paris. His father became mayor, and his 00:02:24.300 --> 00:02:28.780 mother was his only teacher until he was 12 years old. When Évariste finally entered 00:02:28.780 --> 00:02:34.840 school his teachers saw him as intelligent but eccentric. Galois poured through advanced 00:02:34.840 --> 00:02:40.280 math books and quickly began making discoveries of his own. Unfortunately, he was not very 00:02:40.280 --> 00:02:45.140 good at patiently explaining his ideas to others. He entered math contests, and sent 00:02:45.139 --> 00:02:52.029 his work to leading mathematicians, but his writing was considered incomprehensible. 00:02:52.030 --> 00:02:57.099 We now arrive at a sad sequence of events in his last few years. When he was old enough, 00:02:57.099 --> 00:03:02.629 Évariste applied to the École Polytechnique - a top university in Paris - but was rejected. 00:03:02.629 --> 00:03:07.370 Soon after, his father committed suicide. Galois applied again to the Polytechnique 00:03:07.370 --> 00:03:12.310 and was rejected once more. He then enrolled in a less prestigious university, where he 00:03:12.310 --> 00:03:16.909 was expelled. He was then arrested a couple of times, endured some heartache, and found 00:03:16.909 --> 00:03:22.740 himself preparing for a duel which he lost. A troubled genius, indeed.