WEBVTT

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Hi. Let's face it, life is about change, and

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mathematics quantifies it beautifully. Calculus

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can open our eyes to change at the smallest scales

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and shows how finite processes can approach the

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infinite. But rather than focus on the mathematics

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of change, I want to spend this week reflecting

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on how mathematics has changed me. Math has changed

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what I notice. It's changed how certain I need

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to be. It's changed where I place my effort and

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even what I allow myself to hope for. Mathematician

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Paul Lockhart describes mathematics as a search

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for beauty and understanding that leads us to

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a higher ground and a more encompassing view.

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I just love that image. When we climb to higher

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ground, the world below has not changed, but

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our view of it has. We see hidden connections.

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We recognize how one path meets another. What

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seemed random begins to reveal a pattern. And

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this is one way that math has changed me. Before

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learning a new mathematical idea, I often cannot

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imagine what there is to see. So consider proving

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that the square root of two is irrational. Now,

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at first, the question may not seem important

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or even really interesting. The proof can feel

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difficulty and foggy. How can we possibly prove

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it? And then something clicks. The contradiction

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comes into focus. The waters part. You see that

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it must be true. And after seeing it, you cannot

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unsee it. This is more than just acquiring information.

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Information adds to what we know. Understanding

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can change the person doing the knowing. Lockhart

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writes that mathematics is a way of constantly

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evolving and changing myself. Becoming, get this.

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reborn as a person who sees in a new way and

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cannot unsee. That is much larger than the vision

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of mathematics that many of us encounter in school.

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Math is often presented as a collection of procedures,

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memorize this formula, follow these steps, and

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then find the correct answer. Instead, Lockhart

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describes a playground of the mind, a place to

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explore patterns. to make connections, and discover

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unexpected beauty. I'll be honest, the more mathematics

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I learn, the more I understand what he means.

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Math invites me to pause and to look more closely.

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It makes me curious about structures beneath

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the surface. It reminds me that the first view

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is rarely the only possible view. It may not

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be the most revealing one. So this week, I will

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explore how math has taught me to find connections

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that enlarge my imagination and change how I

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think about abstraction and fairness. How it's

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challenged my beliefs about growth and connected

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me to a community. And finally, how it's shaped

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what I allow myself to hope for. The world is

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still the world, and I am still me. But mathematics

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keeps leading me to higher ground. Each time

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I climb, I return as someone who sees a little

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differently.