WEBVTT 00:00:03.140 --> 00:00:07.540 Hi, Eddie Wu is a famous YouTube math instructor 00:00:07.540 --> 00:00:11.500 who gave a TED Talk called Mathematics is the 00:00:11.500 --> 00:00:16.120 Sense You Never Knew You Had. One of the things 00:00:16.120 --> 00:00:18.480 I appreciate about Eddie is that he believes 00:00:18.480 --> 00:00:22.000 that everyone has a math brain because all of 00:00:22.000 --> 00:00:26.160 us naturally recognize patterns. But Eddie goes 00:00:26.160 --> 00:00:29.219 even further. He suggests that doing mathematics 00:00:29.219 --> 00:00:33.729 creates a new sense within us. that allows us 00:00:33.729 --> 00:00:37.530 to see the world in a different way. Eddie says 00:00:37.530 --> 00:00:41.070 that we begin noticing patterns in life, patterns 00:00:41.070 --> 00:00:44.329 that appear in winding rivers, towering trees, 00:00:44.710 --> 00:00:50.289 spiral shelves, and raging storms. As Eddie says, 00:00:50.490 --> 00:00:54.130 there is a mathematical reality woven into the 00:00:54.130 --> 00:00:56.990 fabric of the universe that we share with the 00:00:56.990 --> 00:01:01.460 world around us. Life changes. when we become 00:01:01.460 --> 00:01:04.959 aware of those patterns. And that awareness becomes 00:01:04.959 --> 00:01:09.079 like a new dimension in our lives. And the connections 00:01:09.079 --> 00:01:12.900 inside mathematics itself are equally remarkable. 00:01:13.459 --> 00:01:17.200 For instance, we often think of algebra and geometry 00:01:17.200 --> 00:01:21.140 as completely different subjects. In algebra, 00:01:21.319 --> 00:01:24.859 we may begin with the equation y equals x squared. 00:01:25.299 --> 00:01:29.319 But then we graph the equation and suddenly... 00:01:29.629 --> 00:01:33.609 we see a parabola, the same shape traced by a 00:01:33.609 --> 00:01:37.989 golf ball flying through the air. Or we can create 00:01:37.989 --> 00:01:41.930 that same parabola geometrically by slicing a 00:01:41.930 --> 00:01:47.430 cone at an angle. Or, if x represents the side 00:01:47.430 --> 00:01:50.849 length of a square, we can think of y equals 00:01:50.849 --> 00:01:55.189 x squared as describing how the area of a square 00:01:55.189 --> 00:02:01.109 changes as its side length changes. And what 00:02:01.109 --> 00:02:04.450 fascinates me is that the graph now lets us see 00:02:04.450 --> 00:02:09.349 that change continuously. Rather than isolated 00:02:09.349 --> 00:02:13.409 squares with fixed side lengths, we now see a 00:02:13.409 --> 00:02:18.310 flowing, changing relationship. We see squares 00:02:18.310 --> 00:02:23.110 in motion. We often take graphing equations for 00:02:23.110 --> 00:02:28.020 granted. But it was a revolutionary idea. An 00:02:28.020 --> 00:02:31.520 equation was no longer just symbols on a page. 00:02:31.740 --> 00:02:37.360 It now had a shape. The mathematician Paul Lockhart 00:02:37.360 --> 00:02:41.219 captures this beautifully when he says that every 00:02:41.219 --> 00:02:47.719 algebraic equation now has a look to it. Something 00:02:47.719 --> 00:02:52.860 once abstract suddenly became visible. And this 00:02:52.860 --> 00:02:58.300 transformed mathematics in a profound way. Algebra 00:02:58.300 --> 00:03:01.919 often gives us discrete information, plug in 00:03:01.919 --> 00:03:06.960 an X, solve for a Y. But geometry introduces 00:03:06.960 --> 00:03:12.699 motion, curves, surfaces, and continuous change. 00:03:13.520 --> 00:03:16.939 For example, if we solve two equations with two 00:03:16.939 --> 00:03:21.599 unknowns algebraically, we find a solution. But 00:03:21.599 --> 00:03:25.840 if we graph both equations, the solution becomes 00:03:25.840 --> 00:03:30.639 something visual, the intersection of two curves. 00:03:31.979 --> 00:03:36.080 Yes, both perspectives matter. Together, they 00:03:36.080 --> 00:03:40.000 create a deeper understanding than either perspective 00:03:40.000 --> 00:03:44.979 by itself. And to me, this is where mathematics 00:03:44.979 --> 00:03:49.569 feels less like isolated branches and more like 00:03:49.569 --> 00:03:54.009 a living connected tree. Algebra and geometry 00:03:54.009 --> 00:03:57.909 are not competing subjects. They are different 00:03:57.909 --> 00:04:03.710 ways of seeing the same underlying reality. And 00:04:03.710 --> 00:04:06.349 we see this in life if we compare what we learn 00:04:06.349 --> 00:04:09.270 by reading something compared to experiencing 00:04:09.270 --> 00:04:13.469 something. Reading can give me knowledge, but 00:04:13.469 --> 00:04:17.250 experience can give me understanding and perspective. 00:04:18.670 --> 00:04:22.370 Reading about love is different from loving someone. 00:04:22.750 --> 00:04:26.649 Reading about grief is different from losing 00:04:26.649 --> 00:04:30.889 someone. When knowledge and perspective come 00:04:30.889 --> 00:04:35.029 together, we begin developing what Eddie describes, 00:04:35.370 --> 00:04:40.490 a new sense of seeing reality. And seeing this 00:04:40.490 --> 00:04:45.069 new reality can transform knowledge into wisdom. 00:04:47.850 --> 00:04:50.949 So my thought to end today is thinking about 00:04:50.949 --> 00:04:55.509 where does wisdom come from? Perhaps wisdom does 00:04:55.509 --> 00:04:58.769 not come from separating life into disconnected 00:04:58.769 --> 00:05:03.370 categories. But perhaps it comes from learning 00:05:03.370 --> 00:05:08.170 how the branches connect to the larger living 00:05:08.170 --> 00:05:09.170 whole.