WEBVTT 00:00:02.029 --> 00:00:07.469 Hi, I absolutely enjoy running. Now, that does 00:00:07.469 --> 00:00:11.730 not mean every run is easy. Some mornings I'm 00:00:11.730 --> 00:00:16.370 tired. Some miles feel longer than others. And 00:00:16.370 --> 00:00:19.149 sometimes I have to persuade myself just to put 00:00:19.149 --> 00:00:23.269 on my shoes and walk out the door. Running still 00:00:23.269 --> 00:00:28.910 requires perseverance. But it helps that I enjoy 00:00:28.910 --> 00:00:32.789 it. I like the movement. I like to be outside. 00:00:33.509 --> 00:00:37.490 I like the quiet time to think. And I enjoy the 00:00:37.490 --> 00:00:39.890 feeling of accomplishing something difficult. 00:00:41.850 --> 00:00:45.310 Perseverance and enjoyment are not opposites. 00:00:45.850 --> 00:00:49.850 In some ways, they depend on each other. Part 00:00:49.850 --> 00:00:53.429 of what makes running satisfying is that it requires 00:00:53.429 --> 00:00:58.329 effort. I think the same thing is true of mathematics. 00:00:59.850 --> 00:01:02.950 We sometimes talk about perseverance as though 00:01:02.950 --> 00:01:06.030 it means forcing ourselves to continue to do 00:01:06.030 --> 00:01:11.090 something we do not like. Just keep going. Try 00:01:11.090 --> 00:01:15.069 harder. Do not quit. Now, there may be times 00:01:15.069 --> 00:01:18.430 when that kind of determination is good, but 00:01:18.430 --> 00:01:22.109 I'm not sure that it can sustain us forever. 00:01:23.489 --> 00:01:29.629 Joy gives perseverance a reason. Think about 00:01:29.629 --> 00:01:32.590 people who are wonderful musicians or artists. 00:01:33.010 --> 00:01:37.209 They may practice for thousands of hours. They 00:01:37.209 --> 00:01:41.269 repeat scales and they revise sketches. They 00:01:41.269 --> 00:01:46.390 create work that no one else will ever see. They 00:01:46.390 --> 00:01:50.950 persevere, but usually there is also something 00:01:50.950 --> 00:01:54.750 they love. Perhaps it is the sound of the instrument, 00:01:55.150 --> 00:01:58.959 the pleasure of creating. or the possibility 00:01:58.959 --> 00:02:02.379 of expressing something that they cannot communicate 00:02:02.379 --> 00:02:07.739 in any other way. I experience mathematics in 00:02:07.739 --> 00:02:13.020 a similar way, and so do many other people. We 00:02:13.020 --> 00:02:15.819 explore patterns because they are beautiful. 00:02:16.580 --> 00:02:20.080 I solve problems because they are interesting. 00:02:20.919 --> 00:02:25.469 Some problems are deeply interesting. And we 00:02:25.469 --> 00:02:29.110 continue even when no one is grading us and there 00:02:29.110 --> 00:02:34.069 is no practical reward. We do mathematics simply 00:02:34.069 --> 00:02:38.729 for the pleasure of doing mathematics. And this 00:02:38.729 --> 00:02:42.069 makes me wonder whether we sometimes begin in 00:02:42.069 --> 00:02:46.430 the wrong place when we're teaching math. We 00:02:46.430 --> 00:02:50.509 may focus on performance or emphasize speed or 00:02:50.509 --> 00:02:54.560 accuracy or grades. or even just avoiding mistakes. 00:02:55.199 --> 00:02:59.360 And then when students lose interest, we search 00:02:59.360 --> 00:03:05.539 for external rewards to motivate them. I believe 00:03:05.539 --> 00:03:08.879 the deeper opportunity is to help people discover 00:03:08.879 --> 00:03:13.120 that mathematics itself is beautiful and can 00:03:13.120 --> 00:03:18.099 bring great joy. That does not mean removing 00:03:18.099 --> 00:03:21.699 all the difficulty. If we remove every challenge, 00:03:22.250 --> 00:03:25.930 We may also remove the satisfaction of discovery. 00:03:26.490 --> 00:03:31.090 The moment of understanding feels meaningful 00:03:31.090 --> 00:03:35.289 partly because understanding did not come easily. 00:03:36.250 --> 00:03:41.210 A difficult problem invites us to wonder, to 00:03:41.210 --> 00:03:45.430 experiment, to struggle, and eventually to see 00:03:45.430 --> 00:03:49.449 something that we would not see before. So perhaps 00:03:49.449 --> 00:03:53.330 our goal is not to make mathematics effortless. 00:03:53.930 --> 00:03:57.650 Maybe it is to help people find that mathematics 00:03:57.650 --> 00:04:03.590 is worth the effort. Because fear of failure 00:04:03.590 --> 00:04:09.229 may keep us working for a while, but joy can 00:04:09.229 --> 00:04:11.729 keep us exploring for a lifetime.