WEBVTT

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Hi, yesterday we talked about mathematics as

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a creative endeavor. Mathematicians do not just

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discover ideas, they create definitions, notation,

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and new ways of thinking. But once those ideas

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exist, they give us another remarkable power,

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the power to see structure. Imagine looking at

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a forest. Most people see thousands of individual

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trees. A forester begins to notice patterns,

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the types of trees, how they grow, and how the

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ecosystem fits together. Mathematics does something

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quite similar. It trains us to look beyond individual

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facts and recognize the underlying patterns that

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connect them. describes this as the power of

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abstraction. Abstraction allows us to ignore

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unimportant details so we can focus on what really

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matters. It lets us see that two problems that

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look completely different may actually have the

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same mathematical structure. For example, compound

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interest, population growth, and the spread of

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a virus seem like unrelated topics. One belongs

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to finance, another to biology, and another to

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public health. Yet mathematically, they can all

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be described by the same idea. Exponential growth.

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We see exponential growth all over the place

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in actual science. It even exists in music when

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we compare notes in different octaves. And once

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you recognize that structure, Understanding one

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situation helps you understand the others. The

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same thing happens again and again in mathematics.

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Doubling our money and investing is the same

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math as going from a C in one octave to a C in

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a different octave. A theorem learned in geometry

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might help solve a problem in physics. A probability

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model might explain a business decision. A graph

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can reveal relationships that are difficult to

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see just by looking at an equation. This ability

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to recognize structure is one of the reasons

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mathematics is so powerful and why I just love

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it. It allows us to simplify complexity without

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oversimplifying reality. Rather than memorizing

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thousands of disconnected facts, we begin to

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see how those facts fit together. So, as you

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do math, don't just ask, how do I solve this

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problem? Also ask, what pattern do I recognize?

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Seeing these patterns requires time and patience.

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It requires asking questions and looking at things

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in different ways. But that investment in time

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and effort can become priceless in your math

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journey.