WEBVTT 00:00:02.310 --> 00:00:05.990 Hi, this week has been about how math has changed 00:00:05.990 --> 00:00:10.509 me. And to be honest, I rarely like change as 00:00:10.509 --> 00:00:13.470 it is happening because it is usually difficult. 00:00:14.089 --> 00:00:17.649 But when I look back in retrospect, I appreciate 00:00:17.649 --> 00:00:22.289 how I have been changed. And this all leads to 00:00:22.289 --> 00:00:25.870 our final idea this week that is a beautiful 00:00:25.870 --> 00:00:30.469 paradox at the heart of mathematics. Amidst all 00:00:30.469 --> 00:00:35.390 our discussion of change, consider this. Mathematical 00:00:35.390 --> 00:00:41.670 truth can remain stable while mathematics continually 00:00:41.670 --> 00:00:46.509 changes the people who encounter it. A proof 00:00:46.509 --> 00:00:49.710 does not become false because a civilization 00:00:49.710 --> 00:00:55.289 disappears or a century ends. Once a relationship 00:00:55.289 --> 00:00:58.270 has been established from its definitions and 00:00:58.270 --> 00:01:02.350 assumptions, it remains available for someone 00:01:02.350 --> 00:01:07.870 else to discover. Languages change, empires rise 00:01:07.870 --> 00:01:12.930 and fall, cultures meet, conflict and influence 00:01:12.930 --> 00:01:17.750 one another, and yet mathematical ideas pass 00:01:17.750 --> 00:01:23.030 through time, carried from one human mind to 00:01:23.030 --> 00:01:29.829 another. The ideas endure, but we are changed 00:01:29.829 --> 00:01:34.549 by them. This week I have reflected on some of 00:01:34.549 --> 00:01:38.189 those changes in me. Mathematics has led me to 00:01:38.189 --> 00:01:41.870 higher ground and has given me a more encompassing 00:01:41.870 --> 00:01:44.870 view. It has taught me to search for connections 00:01:44.870 --> 00:01:50.090 between things that appear separate. It has enlarged 00:01:50.090 --> 00:01:53.590 my imagination through infinities I cannot picture. 00:01:54.409 --> 00:01:58.170 And it has shown me the power and danger of abstraction. 00:01:59.109 --> 00:02:03.090 It has challenged fixed beliefs about my own 00:02:03.090 --> 00:02:07.189 abilities. And it has welcomed me into a human 00:02:07.189 --> 00:02:11.030 conversation that began long before I arrived. 00:02:12.430 --> 00:02:16.990 All of this has changed what I allow myself to 00:02:16.990 --> 00:02:21.800 hope for. Reasonable Hope It is not the belief 00:02:21.800 --> 00:02:25.020 that everything will work out exactly as I want. 00:02:26.460 --> 00:02:29.840 Mathematics does not promise that kind of certainty. 00:02:30.199 --> 00:02:34.580 It reminds me that constraints are real, assumptions 00:02:34.580 --> 00:02:38.400 matter, and some outcomes are more likely than 00:02:38.400 --> 00:02:43.020 others. But mathematics also warns me not to 00:02:43.020 --> 00:02:47.039 confuse what I have previously seen with all 00:02:47.039 --> 00:02:51.169 that is possible. My intuition can be incomplete. 00:02:52.530 --> 00:02:55.030 Problems can have an approach that I have not 00:02:55.030 --> 00:03:00.289 yet considered. Two disconnected ideas can suddenly 00:03:00.289 --> 00:03:05.650 meet. A small change, repeated and shared, can 00:03:05.650 --> 00:03:10.349 alter an entire pattern. Again, back to Francis 00:03:10.349 --> 00:03:14.110 Hsu. He argues that mathematics can serve basic 00:03:14.110 --> 00:03:19.979 human desires for play, beauty, freedom, justice, 00:03:20.479 --> 00:03:26.340 love, and belonging, and cultivate virtues that 00:03:26.340 --> 00:03:31.699 help us flourish. That vision moves mathematics 00:03:31.699 --> 00:03:36.300 far beyond calculation. Mathematics becomes one 00:03:36.300 --> 00:03:40.419 of the ways that we practice being fully human. 00:03:41.259 --> 00:03:45.280 And perhaps that is why math has survived across 00:03:45.280 --> 00:03:49.090 cultures and centuries. We preserve it not only 00:03:49.090 --> 00:03:52.729 because it is useful, but because human beings 00:03:52.729 --> 00:03:57.729 continue to find wonder in patterns, satisfaction 00:03:57.729 --> 00:04:03.030 in understanding, and joy in discovering that 00:04:03.030 --> 00:04:07.889 the world is richer than we thought. Mathematics 00:04:07.889 --> 00:04:11.810 has not taught me that change is easy or inevitable. 00:04:12.409 --> 00:04:16.699 It has taught me that change is possible. It 00:04:16.699 --> 00:04:21.139 has taught me to look again, to try another representation, 00:04:21.420 --> 00:04:25.480 or to question the boundaries of my imagination, 00:04:25.959 --> 00:04:30.079 to learn from others, and to remain open to becoming 00:04:30.079 --> 00:04:35.819 someone who sees differently. Math has changed 00:04:35.819 --> 00:04:39.819 more than the way I solve problems. It has changed 00:04:39.819 --> 00:04:44.939 me. And from this higher ground, I can see farther. 00:04:45.470 --> 00:04:50.250 than I could before. And that is where my reasonable 00:04:50.250 --> 00:04:57.189 hope begins. So how about you? Are you open to 00:04:57.189 --> 00:05:01.069 be changed? To see a different reality than you 00:05:01.069 --> 00:05:06.310 currently see? Doing math will take you to a 00:05:06.310 --> 00:05:07.649 larger landscape.