WEBVTT 00:00:02.160 --> 00:00:08.259 Hi, the year was 1985. I was a senior in college. 00:00:08.519 --> 00:00:12.699 I wanted to join a mathematics fraternity. How 00:00:12.699 --> 00:00:15.679 exciting. Anyway, it seemed like a small thing 00:00:15.679 --> 00:00:18.739 at the time, but it changed my perspective on 00:00:18.739 --> 00:00:22.879 math for the rest of my life. As part of the 00:00:22.879 --> 00:00:26.000 application process, I was asked to present an 00:00:26.000 --> 00:00:29.280 original mathematics problem. Now, at first, 00:00:29.280 --> 00:00:32.250 that did not sound too difficult. After all, 00:00:32.270 --> 00:00:34.990 I had solved hundreds of math problems before. 00:00:35.590 --> 00:00:38.630 But then I realized I had never created one. 00:00:39.429 --> 00:00:42.729 Until that moment, math had mostly been something 00:00:42.729 --> 00:00:45.829 that I'd received from other people. Teachers 00:00:45.829 --> 00:00:49.450 assigned problems, textbooks provided exercises, 00:00:49.929 --> 00:00:55.329 and professors explained concepts. And now, I 00:00:55.329 --> 00:00:59.689 had to come up with my own problem. And that 00:00:59.689 --> 00:01:03.710 was much more difficult than I expected. So after 00:01:03.710 --> 00:01:07.430 days of trial and error, I settled on a sports 00:01:07.430 --> 00:01:10.890 problem. Imagine you're kicking a field goal. 00:01:11.310 --> 00:01:14.430 If the ball is in the center of the field, moving 00:01:14.430 --> 00:01:18.150 closer to the goal posts only increases the angle 00:01:18.150 --> 00:01:20.629 between them. But if the ball is placed on a 00:01:20.629 --> 00:01:24.189 hash mark off to one side, then the problem becomes 00:01:24.189 --> 00:01:28.310 more interesting. First, moving closer improves 00:01:28.310 --> 00:01:32.390 the angle. But eventually, the angle begins to 00:01:32.390 --> 00:01:36.730 shrink. And that means there must be an optimal 00:01:36.730 --> 00:01:41.530 spot. A place where the angle is as large as 00:01:41.530 --> 00:01:45.870 possible. An optimal perspective, if you will. 00:01:46.549 --> 00:01:49.909 Now, as I worked through the problem, I discovered 00:01:49.909 --> 00:01:53.090 that the same mathematics also applies to other 00:01:53.090 --> 00:01:57.159 situations. Imagine sitting off to one side while 00:01:57.159 --> 00:02:01.340 watching television. There is an ideal place 00:02:01.340 --> 00:02:06.459 to sit that maximizes your viewing angle. Different 00:02:06.459 --> 00:02:11.259 situation, but the same mathematics. Now, what 00:02:11.259 --> 00:02:14.659 mattered most was not the problem, but it was 00:02:14.659 --> 00:02:19.500 the perspective shift. For the first time, I 00:02:19.500 --> 00:02:23.000 realized that all those formulas All those ideas 00:02:23.000 --> 00:02:26.400 and relationships that I had learned were not 00:02:26.400 --> 00:02:32.860 isolated facts. They were like tools. Tools I 00:02:32.860 --> 00:02:37.240 could use to explore the world around me. It 00:02:37.240 --> 00:02:40.439 felt like I had discovered a math tool belt that 00:02:40.439 --> 00:02:44.340 I had been carrying all along. And suddenly I 00:02:44.340 --> 00:02:47.919 started seeing opportunities to use those tools 00:02:47.919 --> 00:02:51.979 everywhere. Math was no longer just about learning 00:02:51.979 --> 00:02:55.840 concepts for the next exam. It had become a way 00:02:55.840 --> 00:02:59.240 of looking at the world, a way of noticing patterns 00:02:59.240 --> 00:03:04.599 in relationships, and even possibilities. Now 00:03:04.599 --> 00:03:07.379 perhaps that is one of the most valuable perspective 00:03:07.379 --> 00:03:11.219 shifts that I've experienced. Not seeing mathematics 00:03:11.219 --> 00:03:15.180 as a collection of answers, but ideas and principles 00:03:15.180 --> 00:03:19.750 that are a collection of tools. Tools that I 00:03:19.750 --> 00:03:23.229 needed to understand and practice and learn how 00:03:23.229 --> 00:03:26.650 to use. And the more familiar I became with those 00:03:26.650 --> 00:03:30.310 tools, the more connections I began to see between 00:03:30.310 --> 00:03:34.430 them. What once felt like separate topics gradually 00:03:34.430 --> 00:03:39.110 became a connected whole. Now there was another 00:03:39.110 --> 00:03:41.849 benefit that I did not expect. When I started 00:03:41.849 --> 00:03:45.169 viewing mathematics as a tool belt, I put less 00:03:45.169 --> 00:03:48.909 pressure on myself to perform perfectly. on any 00:03:48.909 --> 00:03:51.949 single test or assignment. Now, of course, I 00:03:51.949 --> 00:03:54.629 still wanted to do well, but the goal became 00:03:54.629 --> 00:03:58.729 larger than a grade. The goal was to add another 00:03:58.729 --> 00:04:02.270 tool to my tool belt to become a little better 00:04:02.270 --> 00:04:06.210 prepared for future problems. A difficult exam 00:04:06.210 --> 00:04:10.550 no longer defined me. A tricky problem no longer 00:04:10.550 --> 00:04:13.289 discouraged me as much because those moments 00:04:13.289 --> 00:04:17.290 became part of the process of learning. And looking 00:04:17.290 --> 00:04:20.850 back, I think that perspective gave me something 00:04:20.850 --> 00:04:25.370 more valuable than a good test score. It actually 00:04:25.370 --> 00:04:29.490 gave me a more reasonable hope. Hope that growth 00:04:29.490 --> 00:04:33.170 matters more than perfection. And hope that today's 00:04:33.170 --> 00:04:37.430 struggles can become tomorrow's tools. And hope 00:04:37.430 --> 00:04:40.610 that learning is not about proving what we know. 00:04:41.089 --> 00:04:46.069 It is about preparing for what comes next. See 00:04:46.069 --> 00:04:46.410 you tomorrow.