WEBVTT

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Hi, have you ever seen a flower you thought was

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beautiful? Or a sunset that took your breath

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away? Or listened to a piece of music that moved

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something deep inside you? The answer to at least

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one of these questions is likely yes. But have

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you ever seen math that you thought was beautiful?

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So how do we go from math to beauty? Let's start

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with one of those funny fishing pictures where

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someone holds a fish towards the camera and suddenly

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the fish looks enormous. Now, the fish isn't

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actually bigger. The mathematics has not changed,

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but perspective changes what we see. And artists

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have understood this idea for centuries. Perspective

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shapes how we experience beauty. And hidden underneath

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perspective, is mathematics. And this week, our

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focus is on beautiful math. Now, most people

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do not think of math that way. I know I did not.

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For many years, I considered math as formulas,

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homework, calculations, or just getting the correct

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answer. Something useful, perhaps, but not beautiful.

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Yet, many mathematicians describe math as the

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purest form of art. So my obvious challenge this

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week is that I cannot use pictures or diagrams

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and only words. So I will have to be creative

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while talking about how mathematics itself can

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be creative. Math is not just about patterns,

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but about perspectives. One of my favorite math

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authors, Paul Lockhart, compares doing mathematics

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to climbing a mountain. Yes, climbing takes effort,

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you get tired, and you struggle. But the goal

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is not merely exercise. The goal is the view.

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To stand somewhere higher and suddenly see something

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you could not see before. The vastness of the

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landscape. The surprising details of a flower.

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The beauty that was always there, waiting to

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be noticed. And I think mathematics is like that.

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One of my favorite examples comes from over 2

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,000 years ago. In an example we've discussed

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before, the Greek mathematician Euclid wanted

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to understand prime numbers, you know, 2, 3,

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5, 7, 11, so on. And he asked a simple question,

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are there infinitely many prime numbers? Now,

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what amazes me is that he did not answer the

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question by listing all the primes. That would

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be impossible. Instead, Euclid had a unique perspective.

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He had a beautiful idea. He showed that no matter

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how many prime numbers you collect, there must

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always be another prime beyond the previous.

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In other words, prime numbers can never be contained.

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And I find that perspective breathtaking. Not

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because it helps me calculate something, but

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because it reveals something unexpected and true.

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Euclid transformed a question about infinity

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into a question about containment. And with that

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simple shift in perspective, he revealed something

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beautiful. So this week, we will explore creative

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and beautiful ideas for mathematics. And I want

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to share some of that beauty that keeps drawing

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me back. to behold.