WEBVTT

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Hi, yesterday we talked about how truth and math

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is not just something that we are told. It is

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something we can discover, something we can see.

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And once we see it, we're convinced. But once

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we begin to see truth clearly, sometimes we are

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shocked. Because sometimes the truth we discover

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is not what we expected. This is absolutely one

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of the most delightful things about math. Even

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when we follow the logic carefully, even when

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we ask good questions, the answer can still surprise

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us. A simple example is with prime numbers. Prime

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numbers are numbers like 2, 3, 5, 7, numbers

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that are only divisible by 1 and themselves.

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If you start listing them in order, they begin

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to spread out. They appear less often. And it's

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natural to wonder, do they eventually run out?

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Do we reach a point where there are no more primes?

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Well, over 2 ,000 years ago, Euclid asked that

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same question. What he discovered was that no

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matter how many prime numbers you find, there

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is always another one. always another, then another.

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When you think about it, this is amazing because

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how do you prove that a list of numbers is infinite

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if you cannot list an infinite set of numbers?

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But just because we cannot list the infinite

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set, we can prove that the set is infinite. And

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the proof is surprisingly simple. It is such

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a thing of beauty that we will discuss in detail

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on a later day. For now, the key idea is that

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the proof shows that even if you tried to gather

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all the prime numbers together, you could always

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construct a new number that leads you to another

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one. And when you see it, really see it, it changes

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how you think. Because the truth is bigger than

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you expected. And I think that is the part of

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what makes truth so compelling. It does not just

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confirm what we already believe. Sometimes it

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stretches us. Sometimes it expands what we thought

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was possible. And when that happens, we have

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a choice. We can hold on to what feels familiar,

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or we can stay open. to what we are discovering.

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Because truth is not always comfortable, but

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it is worth following. Truth does not just answer

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our questions, it reshapes them. So my question

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today is, am I open to discovering what is true,

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even when it stretches what I expect?