WEBVTT 00:00:01.870 --> 00:00:05.490 Hi. One of the quickest ways to become frustrated 00:00:05.490 --> 00:00:08.710 with mathematics is to believe that making mistakes 00:00:08.710 --> 00:00:15.210 means you are bad at math. It doesn't. It simply 00:00:15.210 --> 00:00:19.609 means you are doing math. Mathematics is difficult, 00:00:19.750 --> 00:00:23.769 and if it weren't, we would not be spending years 00:00:23.769 --> 00:00:27.670 studying it. The problems become more complex, 00:00:27.929 --> 00:00:32.810 the ideas become more abstract, and the connections 00:00:32.810 --> 00:00:37.149 become less obvious. Mistakes are not an exception. 00:00:37.390 --> 00:00:41.670 They're simply a part of the process. In fact, 00:00:41.729 --> 00:00:44.469 one of the biggest differences that I see between 00:00:44.469 --> 00:00:48.210 students who continue to grow and those who get 00:00:48.210 --> 00:00:52.250 stuck is not intelligence, but it is humility. 00:00:53.130 --> 00:00:56.229 The humble student assumes they might have made 00:00:56.229 --> 00:00:59.070 a mistake, so they check their algebra. They 00:00:59.070 --> 00:01:02.409 revisit their assumptions. they ask, where could 00:01:02.409 --> 00:01:06.109 I have gone wrong? While the prideful student 00:01:06.109 --> 00:01:09.390 assumes the answer must be right because they 00:01:09.390 --> 00:01:12.430 got it. If something does not match the solution, 00:01:12.709 --> 00:01:15.310 they're more likely to think the book is wrong, 00:01:15.489 --> 00:01:18.890 the calculator is wrong, or the problem is simply 00:01:18.890 --> 00:01:23.109 unfair, before ever considering that maybe they 00:01:23.109 --> 00:01:27.010 made a mistake. Of course, we've all been there. 00:01:27.560 --> 00:01:30.159 I cannot tell you how many times I've stared 00:01:30.159 --> 00:01:33.459 at a solution, convinced it had to be incorrect, 00:01:34.000 --> 00:01:37.939 only to discover that I had dropped a negative 00:01:37.939 --> 00:01:42.439 sign 20 minutes before. And those experiences 00:01:42.439 --> 00:01:45.879 are quite humbling. But they're also healthy. 00:01:46.260 --> 00:01:50.439 So one habit I've developed is to expect mistakes. 00:01:50.900 --> 00:01:54.519 Not because I lack confidence, but because I 00:01:54.519 --> 00:01:57.189 know I'm shooing. So when I finish a problem, 00:01:57.370 --> 00:02:01.769 I don't just ask, did I get the answer? I ask, 00:02:01.829 --> 00:02:05.549 does this answer make sense? So if I'm calculating 00:02:05.549 --> 00:02:09.409 the probability of an event, is the answer between 00:02:09.409 --> 00:02:14.370 0 and 1? Or if I'm finding someone's age, did 00:02:14.370 --> 00:02:17.750 I somehow end up with a negative number? Or if 00:02:17.750 --> 00:02:20.490 an insurance company should collect about $500 00:02:20.490 --> 00:02:24.090 in premiums, why did my calculation produce $50 00:02:24.090 --> 00:02:28.539 ,000? Those simple reasonableness checks have 00:02:28.539 --> 00:02:32.020 saved me countless times. Now, they do not prove 00:02:32.020 --> 00:02:34.759 the answer is correct, but they often reveal 00:02:34.759 --> 00:02:38.479 when something has gone terribly wrong. And that 00:02:38.479 --> 00:02:41.800 mindset changes everything. Rather than viewing 00:02:41.800 --> 00:02:44.860 checking your work as a chore, it simply becomes 00:02:44.860 --> 00:02:49.120 part of doing mathematics well. Professional 00:02:49.120 --> 00:02:52.020 mathematics do this all the time. They share 00:02:52.020 --> 00:02:54.199 their papers with colleagues before they publish 00:02:54.199 --> 00:02:58.150 them. They ask others to look for mistakes. And 00:02:58.150 --> 00:03:00.129 they know that no matter how experienced they 00:03:00.129 --> 00:03:02.770 are, they can still be overlooking something. 00:03:03.370 --> 00:03:06.990 And that's not weakness. I would consider that 00:03:06.990 --> 00:03:10.210 wisdom. And there's a subtle difference between 00:03:10.210 --> 00:03:14.530 confidence and humility. Confidence says, I think 00:03:14.530 --> 00:03:18.650 this is correct. And humility says, let's make 00:03:18.650 --> 00:03:23.300 sure. And those two ideas are not enemies. In 00:03:23.300 --> 00:03:26.939 fact, they often work better together. So do 00:03:26.939 --> 00:03:30.060 not be discouraged by mistakes and do not let 00:03:30.060 --> 00:03:33.879 them become a judgment on your ability. Instead, 00:03:34.060 --> 00:03:37.080 let them become reminders that mathematics is 00:03:37.080 --> 00:03:41.259 not about protecting your ego. It is about pursuing 00:03:41.259 --> 00:03:42.080 the truth.