WEBVTT

00:00:01.899 --> 00:00:04.919
Hi, from the past two days, we have seen that

00:00:04.919 --> 00:00:07.559
mathematics gives us the power to create new

00:00:07.559 --> 00:00:10.460
ideas and the power to recognize patterns and

00:00:10.460 --> 00:00:14.259
structure. Today, I would like to suggest that

00:00:14.259 --> 00:00:17.379
maybe math's greatest gift is something even

00:00:17.379 --> 00:00:21.699
more personal. Mathematics changes the way we

00:00:21.699 --> 00:00:25.539
think. Now, many believe that success in math

00:00:25.539 --> 00:00:30.120
comes from memorizing formulas. Now, while formulas

00:00:30.120 --> 00:00:33.740
certainly have their place, they are only tools.

00:00:34.340 --> 00:00:39.259
The real work of mathematics is deciding which

00:00:39.259 --> 00:00:44.799
tools to use and why it works and how to adapt

00:00:44.799 --> 00:00:49.820
when the problem changes. That is why two students

00:00:49.820 --> 00:00:52.740
can know the exact same formulas but approach

00:00:52.740 --> 00:00:56.770
a problem in different ways. One student might

00:00:56.770 --> 00:00:59.469
immediately start plugging numbers into an equation.

00:01:00.490 --> 00:01:04.609
The other might pause and ask what information

00:01:04.609 --> 00:01:09.069
is important, draw a diagram, consider different

00:01:09.069 --> 00:01:12.489
strategies, and develops a plan before beginning.

00:01:13.370 --> 00:01:17.230
This second student is thinking mathematically.

00:01:18.930 --> 00:01:22.010
One of the beautiful things about math is that

00:01:22.010 --> 00:01:26.109
there is more than one path to a solution. You

00:01:26.109 --> 00:01:29.569
may solve a problem using algebra, by graphing,

00:01:29.709 --> 00:01:33.969
or numerically, or even through a clever insight.

00:01:34.810 --> 00:01:38.689
And as you gain experience, you begin building

00:01:38.689 --> 00:01:41.709
what I like to think of as a mathematical toolbox.

00:01:43.049 --> 00:01:47.489
Every theorem and every formula and every technique

00:01:47.489 --> 00:01:51.109
becomes another tool that you can reach for.

00:01:51.769 --> 00:01:55.840
The challenge is not memorizing every tool. but

00:01:55.840 --> 00:01:59.920
it is learning when each tool is most useful.

00:02:01.900 --> 00:02:04.659
And these habits do not stay in the classroom.

00:02:05.540 --> 00:02:08.960
Mathematics teaches us to ask good questions,

00:02:09.139 --> 00:02:13.500
to examine assumptions, and to recognize when

00:02:13.500 --> 00:02:16.759
an argument does not follow logically from its

00:02:16.759 --> 00:02:21.340
premises. These same skills helps us evaluate

00:02:21.340 --> 00:02:24.509
claims that we hear in the news. to make thoughtful

00:02:24.509 --> 00:02:28.050
decisions at work, and to communicate our own

00:02:28.050 --> 00:02:32.770
ideas more clearly. Now, our goal is not to become

00:02:32.770 --> 00:02:36.069
someone who always has the right answer. Our

00:02:36.069 --> 00:02:38.870
goal is to become someone who knows how to think

00:02:38.870 --> 00:02:45.069
carefully when the answer is not obvious. Okay,

00:02:45.150 --> 00:02:48.530
tomorrow we will see these ways of thinking can

00:02:48.530 --> 00:02:52.169
lead us to make more informed decisions during

00:02:52.169 --> 00:02:55.949
uncertainty, by using probability and mathematical

00:02:55.949 --> 00:02:56.629
modeling.