WEBVTT 00:00:03.619 --> 00:00:09.179 Hi. In 1985, I was a junior in college when I 00:00:09.179 --> 00:00:11.740 decided to go to a concert with a group of friends. 00:00:12.140 --> 00:00:15.240 At the time, it seemed like just a fun thing 00:00:15.240 --> 00:00:18.420 to do on a Friday night. My focus was simply 00:00:18.420 --> 00:00:21.239 enjoying the evening, nothing special planned. 00:00:21.760 --> 00:00:25.260 But during intermission, a friend introduced 00:00:25.260 --> 00:00:30.140 me to a woman named Julie. Fast forward to today. 00:00:30.890 --> 00:00:33.909 Julie and I have been married nearly 40 years. 00:00:34.090 --> 00:00:37.229 We have four children and nine grandchildren. 00:00:38.409 --> 00:00:41.810 Needless to say, that one Friday night grew into 00:00:41.810 --> 00:00:44.289 something far bigger than I could have imagined. 00:00:45.350 --> 00:00:48.530 And I have found mathematics has developed in 00:00:48.530 --> 00:00:52.409 similar ways. Back in the 15th century during 00:00:52.409 --> 00:00:55.090 the Renaissance, mathematicians were fascinated 00:00:55.090 --> 00:00:58.920 with solving cubic equations. Those are algebra 00:00:58.920 --> 00:01:02.140 problems involving an x to the power 3 term. 00:01:02.820 --> 00:01:05.579 But while they were working on these equations, 00:01:05.920 --> 00:01:09.400 they hit a wall. In the middle of the calculations, 00:01:09.719 --> 00:01:12.640 they needed to take the square root of a negative 00:01:12.640 --> 00:01:16.459 number. But something like the square root of 00:01:16.459 --> 00:01:21.219 negative 3 did not seem possible. But still, 00:01:21.459 --> 00:01:28.750 calculations required it. what mathematicians 00:01:28.750 --> 00:01:34.650 do. They created a new idea. They defined a new 00:01:34.650 --> 00:01:39.170 number called i, where i equals the square root 00:01:39.170 --> 00:01:43.510 of negative one. At the time, this seemed like 00:01:43.510 --> 00:01:46.590 a strange workaround to solve an algebra problem 00:01:46.590 --> 00:01:50.709 and nothing more. In fact, people called them 00:01:50.709 --> 00:01:54.390 imaginary numbers because they did not seem, 00:01:54.629 --> 00:01:59.890 I don't know, real. But centuries later, mathematicians 00:01:59.890 --> 00:02:04.010 realized these imaginary numbers could be visualized 00:02:04.010 --> 00:02:07.829 geometrically on what we now call the complex 00:02:07.829 --> 00:02:13.849 plane. An abstract algebraic idea suddenly gained 00:02:13.849 --> 00:02:19.469 shape and motion. And even more surprising, this 00:02:19.469 --> 00:02:23.969 strange invention became foundational for things 00:02:23.969 --> 00:02:28.409 like electricity. sound waves, quantum physics, 00:02:28.689 --> 00:02:34.710 engineering, and rotations. What began as a small 00:02:34.710 --> 00:02:39.210 mathematical seed eventually branched into entirely 00:02:39.210 --> 00:02:44.030 new dimensions of understanding. This is one 00:02:44.030 --> 00:02:47.449 of the reasons I love mathematics. It is not 00:02:47.449 --> 00:02:51.289 a static collection of disconnected facts. It 00:02:51.289 --> 00:02:57.669 is alive, growing, branching. One discovery gives 00:02:57.669 --> 00:03:01.909 rise to another. Old ideas produce entirely new 00:03:01.909 --> 00:03:06.550 fruit. The deeper you explore math, the more 00:03:06.550 --> 00:03:09.770 you realize you are not studying isolated branches. 00:03:10.090 --> 00:03:15.889 You are exploring a living tree. And this living 00:03:15.889 --> 00:03:19.129 tree picture extends to my life and my faith 00:03:19.129 --> 00:03:25.419 as well. Life is filled with small seeds. A conversation 00:03:25.419 --> 00:03:30.419 or a friendship. Maybe a decision or a loss. 00:03:31.199 --> 00:03:34.759 And sometimes those small beginnings completely 00:03:34.759 --> 00:03:39.419 reshape the trajectory of our lives. A friendship 00:03:39.419 --> 00:03:43.199 becomes love. Love eventually encounters grief. 00:03:43.680 --> 00:03:47.639 Small things unfold into dimensions we never 00:03:47.639 --> 00:03:53.099 expected. Transformation rarely begins with dramatic 00:03:53.099 --> 00:03:56.729 moments. More often, it begins through small 00:03:56.729 --> 00:03:59.949 beginnings that slowly grow into something much 00:03:59.949 --> 00:04:03.509 larger. And when I step back and look at the 00:04:03.509 --> 00:04:07.789 larger picture, I see patterns of growth, patterns 00:04:07.789 --> 00:04:12.550 of beauty, and even patterns of loss. What gives 00:04:12.550 --> 00:04:15.909 me hope is believing those patterns are connected 00:04:15.909 --> 00:04:20.329 to something larger than themselves, to a living 00:04:20.329 --> 00:04:25.100 whole. Now, remaining in our current dimensions 00:04:25.100 --> 00:04:30.079 may feel comfortable, but perhaps there is a 00:04:30.079 --> 00:04:34.860 new dimension drawing you forward, a new relationship, 00:04:35.120 --> 00:04:40.399 a new career, a transformed faith, or just a 00:04:40.399 --> 00:04:44.680 deeper way of seeing life. Growth always carries 00:04:44.680 --> 00:04:50.040 uncertainty, but maybe hope is trusting that 00:04:50.040 --> 00:04:54.079 small steps taken today can eventually grow into 00:04:54.079 --> 00:04:56.899 fruit we cannot yet imagine.