WEBVTT

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This week, math is on trial, and today, mathematics

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is accused of building new understanding on what

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has already been learned. Math does not start

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over with every new problem, or with every new

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person, or every new generation. It remembers

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what came before and uses it to move forward.

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Long before Pythagoras was thinking about triangles,

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People in ancient Babylon were already thinking

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about the relationship between the sides of a

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right triangle. And the same relationship also

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appeared in ancient India and China. Over time,

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mathematicians found ways to explain why that

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relationship works. So the relationship for the

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sides of a right triangle became a theorem. Our

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beloved Pythagorean theorem. And that was a gift

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to the future world. So today, 2 ,000 years later,

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we can learn in a few classes what took people

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centuries to develop. We do not have to rediscover

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everything for ourselves. We begin with what

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others have already learned. And that's simply

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how mathematics grows. One discovery becomes

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the starting point for another. An idea that

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once seemed difficult eventually becomes a tool

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for solving a bigger problem. Algebra prepares

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us for calculus, and calculus prepares us for

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differential equations, and those equations describe

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motion, engineering, economics, and really much

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of the physical world. Yes, the symbols and methods

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may change, but mathematics keeps a faithful

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ledger of what has been learned. When I begin

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studying a new math topic, it almost always seems

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difficult. The ideas seem foreign, and figuring

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out how to solve the problems often feels daunting.

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But I have to remind myself that this is how

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I've always learned math. The calculus I understand

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now was once a complete mystery. I knew almost

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nothing about actual science when I graduated

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from college. Each new exam seemed impossible.

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And yet, I passed the exams and learned the concepts.

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What once felt like a foreign language eventually

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became almost like common sense. Mathematics

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does not start over with every generation, and

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neither do we. What I struggled to understand

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yesterday can become the foundation for what

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I'm ready to learn tomorrow. That is just how

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learning math works. So on the charge of building

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new understanding on what was already learned,

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mathematics is guilty. So our question to finish

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with is what feels difficult today that may be

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preparing you to understand something greater

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tomorrow?