WEBVTT

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Hi. Two days ago, I shared how I spent time going

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deeper into calculus. And yesterday, I shared

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a specific calculus problem and how my perspective

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on math changed when I stopped seeing it as a

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collection of answers and started seeing it as

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a collection of tools. And those tools have helped

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me explore the world in new ways. But over time,

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I discovered the tools themselves had a story.

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They did not appear out of anywhere. Every idea,

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every formula and technique that I learned came

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from somewhere. Someone discovered it. Someone

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developed it and someone passed it on. And that

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realization, however obvious, led me to another

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perspective that has stayed with me ever since.

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The deeper I explored calculus, the more I realized

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that calculus is not standing alone. Now, when

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students first encounter calculus, it often feels

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like a completely new subject. We've got derivatives

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and integrals and limits. A whole new world.

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But over time, I realized that calculus is built

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on ideas that came before it. It depends on the

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real numbers, on algebra, geometry, and trig.

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and many of its biggest ideas can be traced back

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more than 2 ,000 years back to the ancient Greeks.

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What first looked like a separate branch of mathematics

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began to look more like a tree. Now, calculus

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was not the whole tree. It was one branch connected

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to roots that ran much deeper than I had imagined.

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connections everywhere. One idea leading naturally

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to another. One generation building on the work

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of another. What seemed like separate subjects

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became a connected story. And in a way, I think

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people are a bit like calculus. Our lives are

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rich in meaning. We're always changing and developing.

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We're growing in new directions. But just as

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calculus has roots that reach deep into the history

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of math, each of us has roots that have helped

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us become who we are. We have parents and teachers

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and friends and maybe even mentors. People who

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have encouraged us, challenged us, and even sacrificed

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for us. Now, I know for myself, it is easy to

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be so focused on where I am today. that I forget

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the roots that helped me get here. So here are

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my questions for today. Who are the roots in

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your life? Who helped make you who you are? And

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is there someone today that you should give a

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little thanks? See you tomorrow.