WEBVTT 00:00:02.060 --> 00:00:05.719 Hi, when I studied to become an actuary, I did 00:00:05.719 --> 00:00:08.919 not have access to all of the educational tools 00:00:08.919 --> 00:00:12.939 that we have today. There were no online videos 00:00:12.939 --> 00:00:16.899 or manuals or practice problems or discussion 00:00:16.899 --> 00:00:20.559 boards. There definitely was nothing that adapted 00:00:20.559 --> 00:00:24.179 to my level of understanding. Usually what I 00:00:24.179 --> 00:00:28.839 had was a textbook, a set of problems, and maybe 00:00:28.839 --> 00:00:34.119 a solutions manual. When I was stuck, I usually 00:00:34.119 --> 00:00:38.460 remained stuck for a while. I would reread the 00:00:38.460 --> 00:00:41.299 problem. Maybe I would search through earlier 00:00:41.299 --> 00:00:45.259 chapters. I would try an approach, and then I 00:00:45.259 --> 00:00:48.899 would realize it did not work, and then I would 00:00:48.899 --> 00:00:53.219 start over. Sometimes I might spend hours trying 00:00:53.219 --> 00:00:57.859 to understand a single idea. Now, at that time, 00:00:57.939 --> 00:01:01.100 I'm not sure I considered all of this a gift. 00:01:01.539 --> 00:01:07.239 But in some ways, I think it was. Because an 00:01:07.239 --> 00:01:10.879 explanation was not immediately available, I 00:01:10.879 --> 00:01:16.019 had to learn how to ask my own questions. What 00:01:16.019 --> 00:01:19.480 do I know? What am I trying to find exactly? 00:01:20.459 --> 00:01:25.829 Which assumption am I making? Where exactly does 00:01:25.829 --> 00:01:30.290 my understanding break down? Here's a specific 00:01:30.290 --> 00:01:34.230 example. How does the force of interest relate 00:01:34.230 --> 00:01:39.310 to the force of mortality? These questions taught 00:01:39.310 --> 00:01:45.510 me more than the formulas did. So, 20 years later, 00:01:45.670 --> 00:01:49.030 I helped create tools that made it easier to 00:01:49.030 --> 00:01:53.010 understand actuarial concepts. I believe good 00:01:53.010 --> 00:01:56.989 explanations are valuable. The right hint or 00:01:56.989 --> 00:02:00.950 the right illustration can open a door that might 00:02:00.950 --> 00:02:05.390 otherwise remain closed. But I have also come 00:02:05.390 --> 00:02:11.909 to recognize a tension. The tension is if help 00:02:11.909 --> 00:02:15.990 arrives too quickly, it can take something away. 00:02:16.949 --> 00:02:20.090 We may learn to follow someone else's reasoning. 00:02:20.750 --> 00:02:24.789 without developing our own. We may know which 00:02:24.789 --> 00:02:28.909 formula to use without understanding why it works. 00:02:29.569 --> 00:02:35.050 We may become so conditioned to immediate answers 00:02:35.050 --> 00:02:39.949 that we interpret confusion as a sign that something 00:02:39.949 --> 00:02:44.689 has gone wrong. But confusion is not always a 00:02:44.689 --> 00:02:49.370 problem to eliminate. Sometimes confusion is 00:02:49.370 --> 00:02:53.750 the beginning of learning. Not knowing creates 00:02:53.750 --> 00:03:00.349 space for curiosity. It forces us to slow down, 00:03:00.629 --> 00:03:04.189 to notice what we have overlooked, and to form 00:03:04.189 --> 00:03:07.310 questions that we would never ask if the answer 00:03:07.310 --> 00:03:11.349 was already there. Now, this does not mean we 00:03:11.349 --> 00:03:14.930 should try to withhold help indefinitely or make 00:03:14.930 --> 00:03:19.020 learning unnecessarily frustrating. It just means 00:03:19.020 --> 00:03:22.740 that good help should not merely rescue us from 00:03:22.740 --> 00:03:26.319 the struggle. It should help us to participate 00:03:26.319 --> 00:03:31.039 more fully in it. There is a difference between 00:03:31.039 --> 00:03:35.439 being abandoned in confusion and being given 00:03:35.439 --> 00:03:41.919 room to think. Mathematical perseverance grows 00:03:41.919 --> 00:03:47.180 in that space. So the next time you become stuck, 00:03:48.110 --> 00:03:50.930 Perhaps you do not need to escape the feeling 00:03:50.930 --> 00:03:56.569 right away. Simply pause. Try to describe what 00:03:56.569 --> 00:04:00.289 you understand and where the mystery begins. 00:04:02.310 --> 00:04:05.650 What I have learned is that sometimes the most 00:04:05.650 --> 00:04:09.150 valuable thing a teacher can give is not an answer. 00:04:09.490 --> 00:04:15.550 It is enough time and enough confidence for you 00:04:15.550 --> 00:04:17.089 to continue the search.