WEBVTT

00:00:01.870 --> 00:00:04.969
What do you think about when we talk about mathematics?

00:00:06.269 --> 00:00:09.250
Do you picture a subject that's filled with rules?

00:00:09.570 --> 00:00:13.869
Rules to memorize, formulas to apply, and procedures

00:00:13.869 --> 00:00:17.890
to follow? But mathematics is not just about

00:00:17.890 --> 00:00:22.210
following rules. It's also about creating them.

00:00:23.010 --> 00:00:27.489
The mathematicians that we admire think Euclid,

00:00:27.550 --> 00:00:32.130
Euler, etc. They were not simply solving problems.

00:00:32.490 --> 00:00:37.990
They were inventing new ways to think. They created

00:00:37.990 --> 00:00:43.149
definitions to describe new ideas. They introduced

00:00:43.149 --> 00:00:46.170
notation to communicate those ideas efficiently.

00:00:46.649 --> 00:00:51.130
They made assumptions that allowed them to explore

00:00:51.130 --> 00:00:57.530
entirely new mathematical worlds. Even something

00:00:57.530 --> 00:01:00.710
as simple as choosing a variable or deciding

00:01:00.710 --> 00:01:05.269
how to approach a problem is an act of creativity.

00:01:07.390 --> 00:01:12.349
Francis Hsu reminds us that mathematics flourishes

00:01:12.349 --> 00:01:17.849
through imagination, not just reasoning. And

00:01:17.849 --> 00:01:21.090
that idea is captured beautifully in this week's

00:01:21.090 --> 00:01:25.370
quote by Augustus de Morgan. Here's the quote.

00:01:33.440 --> 00:01:38.200
One of my favorite examples is Rene Descartes'

00:01:38.299 --> 00:01:43.859
idea of placing numbers on a plane. Points and

00:01:43.859 --> 00:01:47.400
shapes had been studied for centuries. We also

00:01:47.400 --> 00:01:51.079
knew about equations. And then Descartes asked,

00:01:54.640 --> 00:01:59.579
had a pair of numbers. And with that one imaginative

00:01:59.579 --> 00:02:05.719
step, geometry and algebra became one subject.

00:02:06.599 --> 00:02:10.400
Curves could now be described by equations, and

00:02:10.400 --> 00:02:14.479
equations could be visualized as pictures. An

00:02:14.479 --> 00:02:18.620
entire branch of mathematics was born because

00:02:18.620 --> 00:02:23.240
someone imagined a new way to represent reality.

00:02:25.360 --> 00:02:28.740
This creative power is not reserved for famous

00:02:28.740 --> 00:02:32.120
mathematicians. Every time you choose your own

00:02:32.120 --> 00:02:36.120
notation or make a simplifying assumption or

00:02:36.120 --> 00:02:39.159
maybe develop a strategy for solving a problem,

00:02:39.340 --> 00:02:43.819
you are exercising that same kind of creative

00:02:43.819 --> 00:02:47.319
thinking. You're not just doing mathematics.

00:02:47.680 --> 00:02:53.979
You are participating in it. So as we begin this

00:02:53.979 --> 00:02:58.009
week, I invite you to think of mathematics differently.

00:02:59.050 --> 00:03:01.870
Rather than seeing it as a collection of rules

00:03:01.870 --> 00:03:05.810
that's handed down through history, see it as

00:03:05.810 --> 00:03:10.669
a language that people have built over thousands

00:03:10.669 --> 00:03:15.569
of years and one that you are capable of contributing

00:03:15.569 --> 00:03:21.830
to as well. Okay, tomorrow we will look at another

00:03:21.830 --> 00:03:24.759
kind of power that mathematics gives us. the

00:03:24.759 --> 00:03:28.460
power to see patterns and structure that might

00:03:28.460 --> 00:03:29.879
otherwise remain hidden.