WEBVTT 00:00:01.960 --> 00:00:05.839 Hi, this week we've talked about humility. And 00:00:05.839 --> 00:00:08.460 to be honest, we probably haven't learned anything 00:00:08.460 --> 00:00:12.339 new. But maybe it's been a good reminder. We've 00:00:12.339 --> 00:00:15.080 seen that mathematics teaches us to submit to 00:00:15.080 --> 00:00:19.079 logic rather than our own preferences. It reminds 00:00:19.079 --> 00:00:23.120 us that our intuition can be wrong and that mistakes 00:00:23.120 --> 00:00:26.019 are just part of learning. We've learned that 00:00:26.019 --> 00:00:28.800 other people may see solutions that we did not. 00:00:29.359 --> 00:00:32.960 and that truth does not always depend on status 00:00:32.960 --> 00:00:36.539 or reputation. I want to end our week with the 00:00:36.539 --> 00:00:40.020 idea that no one does mathematics by themselves. 00:00:41.200 --> 00:00:45.280 Think about it. Every theorem you study, every 00:00:45.280 --> 00:00:48.259 technique that you learn, and every notation 00:00:48.259 --> 00:00:52.460 that you use is part of a conversation that has 00:00:52.460 --> 00:00:55.859 been going on probably for thousands of years. 00:00:57.070 --> 00:01:00.469 When you solve a problem using derivatives, you 00:01:00.469 --> 00:01:03.250 are building on the work of people like Newton 00:01:03.250 --> 00:01:06.670 and Leibniz. And when you use algebraic notation, 00:01:07.129 --> 00:01:10.829 you're benefiting from ideas that evolved over 00:01:10.829 --> 00:01:15.069 centuries. Even the equal signs had to be invented 00:01:15.069 --> 00:01:18.290 because someone wanted mathematical ideas to 00:01:18.290 --> 00:01:22.310 be communicated more clearly. Mathematics is 00:01:22.310 --> 00:01:26.680 not just a collection of facts. It is a story. 00:01:27.500 --> 00:01:31.480 It's a story of countless people asking questions, 00:01:31.579 --> 00:01:36.620 making mistakes, refining ideas, and then passing 00:01:36.620 --> 00:01:40.579 their discoveries to the next generation. That 00:01:40.579 --> 00:01:44.579 perspective keeps us humble because history always 00:01:44.579 --> 00:01:47.939 reminds us what happens when pride gets in our 00:01:47.939 --> 00:01:51.659 way. And one of the most famous examples is the 00:01:51.659 --> 00:01:55.290 dispute between Isaac Newton and Gottfried Wilhelm 00:01:55.290 --> 00:02:00.469 Leibniz. They disputed who deserved credit for 00:02:00.469 --> 00:02:05.370 inventing calculus. Both made extraordinary contributions, 00:02:05.829 --> 00:02:11.330 yet the debate over priority became bitter, and 00:02:11.330 --> 00:02:15.710 it divided mathematicians across Europe for years. 00:02:16.629 --> 00:02:20.710 Looking back, it's difficult not to think that 00:02:20.710 --> 00:02:24.199 the energy spent defending personal credit could 00:02:24.199 --> 00:02:26.379 have been better spent advancing mathematics. 00:02:27.240 --> 00:02:31.620 And the irony is that neither Newton nor Leibniz 00:02:31.620 --> 00:02:35.539 created calculus from nothing. Both were building 00:02:35.539 --> 00:02:39.520 on centuries of earlier work, and every mathematician 00:02:39.520 --> 00:02:44.860 since has continued building on theirs. That's 00:02:44.860 --> 00:02:48.659 just how mathematics progresses. One person contributes 00:02:48.659 --> 00:02:52.740 an idea, someone else improves it. Another finds 00:02:52.740 --> 00:02:56.039 a new application, and then another discovers 00:02:56.039 --> 00:03:00.620 a limitation. Generation after generation, the 00:03:00.620 --> 00:03:06.379 structure grows. So here's a famous quote many 00:03:06.379 --> 00:03:10.180 think came from Newton. If I have seen further, 00:03:10.479 --> 00:03:13.740 it is by standing on the shoulders of giants. 00:03:15.479 --> 00:03:19.159 So whether we're aware of it or not, every one 00:03:19.159 --> 00:03:23.340 of us is doing the same thing. If you're studying 00:03:23.340 --> 00:03:26.319 actual mathematics, for example, you're benefiting 00:03:26.319 --> 00:03:30.199 from thousands of years of human curiosity and 00:03:30.199 --> 00:03:33.400 persistence. You're certainly not starting from 00:03:33.400 --> 00:03:37.000 scratch. You're actually joining a conversation 00:03:37.000 --> 00:03:40.819 that began long before you and will continue 00:03:40.819 --> 00:03:45.340 long after you're gone. I find that encouraging. 00:03:45.800 --> 00:03:50.539 It's like we are playing a role in a much bigger 00:03:50.539 --> 00:03:56.280 story. than ourselves. My contribution may be 00:03:56.280 --> 00:04:01.219 small but others can build from it and then more 00:04:01.219 --> 00:04:04.520 people will learn from those people and we see 00:04:04.520 --> 00:04:08.539 an exponential growth equation building right 00:04:08.539 --> 00:04:13.719 in front of us. In the end math teaches us that 00:04:13.719 --> 00:04:18.660 truth is bigger than any one person. We are grateful 00:04:18.660 --> 00:04:22.519 for those who came before us and we are willing 00:04:22.519 --> 00:04:26.379 to learn from those besides us. And hopefully, 00:04:26.600 --> 00:04:30.959 through our own work and generosity, we'll make 00:04:30.959 --> 00:04:34.540 things just a little easier for those who come 00:04:34.540 --> 00:04:39.079 after us. This is Dave from Intersecting Us.