WEBVTT 00:00:01.960 --> 00:00:05.360 Leonard Euler never seemed to be the kind of 00:00:05.360 --> 00:00:09.580 person who would change the world. But at the 00:00:09.580 --> 00:00:13.839 court of Frederick the Great, Voltaire captivated 00:00:13.839 --> 00:00:18.179 people with his wit while Euler humbly pursued 00:00:18.179 --> 00:00:22.579 mathematics. Later, Euler even lost most of his 00:00:22.579 --> 00:00:27.559 eyesight. And yet today, Euler's ideas remain 00:00:27.559 --> 00:00:31.699 foundational to mathematics. to science and even 00:00:31.699 --> 00:00:35.960 engineering. His life reminds me that lasting 00:00:35.960 --> 00:00:39.759 influence is not built on charisma or recognition. 00:00:40.179 --> 00:00:43.439 It is built on faithfully pursuing the truth. 00:00:44.759 --> 00:00:48.060 This week, we're seeing how math can teach us 00:00:48.060 --> 00:00:52.159 humility. And that is a good thing. So today 00:00:52.159 --> 00:00:55.119 our focus is that mathematics does not play favorites. 00:00:55.320 --> 00:00:59.409 It does not care who you are. It doesn't care 00:00:59.409 --> 00:01:01.810 how old you are, or how much money you have, 00:01:01.929 --> 00:01:04.969 or what country you came from, even what language 00:01:04.969 --> 00:01:08.150 you speak, or what title comes before your name. 00:01:09.109 --> 00:01:12.650 A correct proof is correct because of the reasoning, 00:01:12.790 --> 00:01:16.430 not because of the person presenting it. And 00:01:16.430 --> 00:01:19.250 likewise, an incorrect proof does not become 00:01:19.250 --> 00:01:21.469 correct just because it was written by someone 00:01:21.469 --> 00:01:25.650 famous. And that's one of the things I find so 00:01:25.650 --> 00:01:30.290 refreshing about mathematics. In many areas of 00:01:30.290 --> 00:01:33.109 life, it is easy to be influenced by status. 00:01:33.590 --> 00:01:36.849 We naturally give more weight to people with 00:01:36.849 --> 00:01:39.969 impressive credentials or strong personalities. 00:01:40.189 --> 00:01:44.209 And sometimes that is okay. Experience certainly 00:01:44.209 --> 00:01:48.810 matters. But mathematics gives us a powerful 00:01:48.810 --> 00:01:53.030 reminder that authority and truth are not the 00:01:53.030 --> 00:01:57.250 same thing. A professor can make an algebra mistake. 00:01:58.189 --> 00:02:02.409 Think me, a beginning student can notice it. 00:02:02.890 --> 00:02:06.989 The mathematics does not become offended. It 00:02:06.989 --> 00:02:10.909 simply asks, which argument is logically valid? 00:02:11.969 --> 00:02:16.110 Now, in my mind, that should give us all a little 00:02:16.110 --> 00:02:20.090 dose of humility. It reminds us to evaluate ideas 00:02:20.090 --> 00:02:22.990 on their merits rather than on the reputation 00:02:22.990 --> 00:02:27.099 of the person who is presenting the ideas. It 00:02:27.099 --> 00:02:29.979 also reminds us that every person is worth listening 00:02:29.979 --> 00:02:33.699 to. You just never know who might notice the 00:02:33.699 --> 00:02:37.280 assumptions that everyone else overlooked or 00:02:37.280 --> 00:02:40.240 might discover a simpler way to solve a problem. 00:02:41.659 --> 00:02:45.060 Some of the greatest advances in math have come 00:02:45.060 --> 00:02:48.479 from people who challenged accepted ideas, not 00:02:48.479 --> 00:02:52.340 by being louder or more influential, but by presenting 00:02:52.340 --> 00:02:57.389 better reasoning. Think Euler. And that's how 00:02:57.389 --> 00:03:01.169 mathematics progresses, not by popularity or 00:03:01.169 --> 00:03:05.229 hierarchy, but by truth. Now, this does not mean 00:03:05.229 --> 00:03:08.169 expertise is not valuable, because it clearly 00:03:08.169 --> 00:03:12.110 is. Experienced mathematicians have developed 00:03:12.110 --> 00:03:16.009 intuition and judgment, and a deep understanding 00:03:16.009 --> 00:03:19.289 that beginners simply have not had time to build. 00:03:19.710 --> 00:03:24.340 But even experts remain accountable. to the same 00:03:24.340 --> 00:03:27.719 logical standards as everyone else. So in that 00:03:27.719 --> 00:03:32.520 sense, mathematics is wonderfully fair. We are 00:03:32.520 --> 00:03:37.219 all playing by the same rules. I think that extends 00:03:37.219 --> 00:03:40.319 beyond mathematics because humility is about 00:03:40.319 --> 00:03:43.979 being willing to listen. It means recognizing 00:03:43.979 --> 00:03:47.099 that good ideas can come from unexpected places. 00:03:48.259 --> 00:03:52.909 So I think one of our greatest challenges especially 00:03:52.909 --> 00:03:56.490 for the smart folks out there, is that our own 00:03:56.490 --> 00:04:00.689 ideas should be examined just as carefully as 00:04:00.689 --> 00:04:05.689 everyone else's. When we approach math with that 00:04:05.689 --> 00:04:08.810 attitude, we do not just become better problem 00:04:08.810 --> 00:04:14.550 solvers, we become better learners. Okay, I'm 00:04:14.550 --> 00:04:17.310 going to end on a positive note with this quote 00:04:17.310 --> 00:04:21.970 from Paul Lockhart. mathematics is a means of 00:04:21.970 --> 00:04:27.230 constantly evolving and changing myself, becoming 00:04:27.230 --> 00:04:31.970 reborn as a person who sees in a new way, I love 00:04:31.970 --> 00:04:36.529 this part, and cannot unsee. I feel so grateful. 00:04:36.829 --> 00:04:41.209 I get to have this amazing playground in my head, 00:04:41.310 --> 00:04:43.089 and so do you.