WEBVTT 00:00:02.160 --> 00:00:06.240 Hi, let's recap this week. We have explored failure 00:00:06.240 --> 00:00:09.539 and perseverance. We've seen that failing an 00:00:09.539 --> 00:00:12.599 exam is not the same as failing at mathematics. 00:00:13.480 --> 00:00:17.920 We've considered how joy can sustain perseverance 00:00:17.920 --> 00:00:24.019 and why not knowing can be a gift and how mathematical 00:00:24.019 --> 00:00:29.940 struggle can resemble climbing a mountain. We've 00:00:29.940 --> 00:00:34.179 also seen that 2 ,000 years of failing to prove 00:00:34.179 --> 00:00:38.399 the parallel postulate opened the door to new 00:00:38.399 --> 00:00:43.380 geometries. And we've seen how an error in Andrew 00:00:43.380 --> 00:00:46.719 Weil's proof became part of one of mathematics' 00:00:47.200 --> 00:00:53.079 greatest stories. All these stories have a common 00:00:53.079 --> 00:00:58.000 idea. The people were willing to work on questions. 00:00:58.750 --> 00:01:04.590 where the answer was not easily seen. Now this 00:01:04.590 --> 00:01:08.549 seems obvious, but it does run against much of 00:01:08.549 --> 00:01:12.090 what we learn in school. In school, we are often 00:01:12.090 --> 00:01:14.510 given problems that someone else has already 00:01:14.510 --> 00:01:18.629 solved. We already know the method. The answer 00:01:18.629 --> 00:01:23.030 is in the back of the book. And our job is to 00:01:23.030 --> 00:01:28.260 just reproduce it. And if we can't, We conclude 00:01:28.260 --> 00:01:34.120 we are not good at math. But mathematicians work 00:01:34.120 --> 00:01:38.780 differently. They look for questions difficult 00:01:38.780 --> 00:01:42.780 enough that they do not know what to do next. 00:01:43.159 --> 00:01:49.159 They expect false starts. They make conjectures 00:01:49.159 --> 00:02:00.650 that turn out to be wrong. Nowhere. Their unsuccessful 00:02:00.650 --> 00:02:04.730 attempts are not evidence that they cannot do 00:02:04.730 --> 00:02:08.870 mathematics. They are evidence that they are 00:02:08.870 --> 00:02:14.629 doing mathematics. So never confuse an unsuccessful 00:02:14.629 --> 00:02:19.969 result with an unsuccessful person. A test score 00:02:19.969 --> 00:02:22.409 may describe your performance on a particular 00:02:22.409 --> 00:02:25.930 set of questions on a particular day. But it 00:02:25.930 --> 00:02:30.469 cannot measure your curiosity, your creativity, 00:02:30.770 --> 00:02:35.849 your potential, or your capacity to understand. 00:02:37.490 --> 00:02:43.409 Yes, doing math is difficult. And that is part 00:02:43.409 --> 00:02:47.090 of its beauty. The most interesting problems 00:02:47.090 --> 00:02:52.949 rarely surrender their secrets immediately. They 00:02:52.949 --> 00:02:57.969 ask us to experiment. to become confused, and 00:02:57.969 --> 00:03:02.090 to reconsider our assumptions, and then to try 00:03:02.090 --> 00:03:08.169 again. So, I want to encourage you to find a 00:03:08.169 --> 00:03:13.509 question that awakens your curiosity. It does 00:03:13.509 --> 00:03:17.229 not need to be famous. It only needs to matter 00:03:17.229 --> 00:03:23.590 to you. So pursue it with your best effort. Give 00:03:23.590 --> 00:03:27.780 yourself permission. to move slowly. Let every 00:03:27.780 --> 00:03:32.300 false start teach you something. And when you 00:03:32.300 --> 00:03:36.860 are stuck, remember being stuck is not the end 00:03:36.860 --> 00:03:42.240 of the journey. It may be the exact place where 00:03:42.240 --> 00:03:46.780 deeper understanding begins. I have seen this 00:03:46.780 --> 00:03:52.419 over and over again in my life. Perseverance 00:03:52.419 --> 00:03:56.919 is not simply refusing to quit. It is learning 00:03:56.919 --> 00:04:02.319 to see each failure as part of the search. So, 00:04:02.400 --> 00:04:06.039 what we'll learn this week is the greatest failure 00:04:06.039 --> 00:04:11.120 is not arriving at the wrong answer, but it's 00:04:11.120 --> 00:04:15.740 allowing the fear of being wrong to keep us from 00:04:15.740 --> 00:04:17.139 exploring at all.