WEBVTT

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Hi, more than 20 years ago, I climbed Longs Peak

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in Colorado. It was the most difficult and likely

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the most rewarding hike of my life. The hike

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starts before sunrise and then it takes you high

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above the tree line. Now, one of the coolest

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parts of the climb is passing through a narrow

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opening in the rocks called the Keyhole. And

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I remember it as if it happened yesterday. As

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I stepped through that keyhole, the view suddenly

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changed. Before the keyhole, I was focused on

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the trail immediately in front of me, like where

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to place my feet or how much further I had to

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go, and my body telling me to stop. But through

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the keyhole, an entirely new landscape opened

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up. The view on the other side was breathtaking.

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If you think about it, That landscape had been

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there all along. I just could not see it from

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where I was standing. The mountain had not changed.

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My perspective did. And that experience reminds

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me of something that the mathematician Paul Lockhart

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once said. Paul compares mathematics to climbing

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a mountain. Many people think mathematics is

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about getting answers. You know, finding X. Computing

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a derivative, calculating an area, all good things

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for sure. But Lockhart argues that the real purpose

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of climbing a mountain is not simply to reach

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the summit. It is seeing from a higher perspective.

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And as we climb higher, we begin to notice patterns

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and connections that were invisible from below.

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And mathematics can work the same way. Sometimes

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the greatest reward is not the answer. It is

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seeing something in a new way. And I can relate

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to that idea because over the years, my perspective

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on math has changed. When I was younger, math

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was mostly about facts and formulas and answers.

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But then I began reading books about the history

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of math. I discovered that calculus did not simply

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appear in a textbook one day. It emerged through

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centuries of people. wrestling with questions

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about motion and change and area and infinity.

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Suddenly, calculus felt different. It was no

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longer just a collection of rules. It was a human

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story, a story of curiosity, of creativity, persistence,

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and surely discovery. Reading about the history

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of calculus was a keyhole experience for me.

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It helped me see math from a higher ground. And

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from that perspective, I began noticing beauty

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and connections that I had completely missed

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before. So, this week, we're going to explore

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the idea of perspective. And together, we will

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walk through different keyholes of math. We will

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discover some beautiful ideas that may have been

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there all along, but hidden in plain sight. Our

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goal is not to change the world, but to see it

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from a different perspective. And perhaps that

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different perspective will change us. Before

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we start, here's a question to consider. How

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do you view mathematics? And more specifically,

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what is your perspective on what math is? Hope

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to see you tomorrow.