WEBVTT

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Hi, what if there were numbers smaller than zero?

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Now, today that question seems ordinary. We talk

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about temperatures below zero, bank accounts

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with negative balances, and elevations below

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sea level. But there was a time when negative

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numbers seemed absurd. How could you possibly

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have less than nothing? Yet, someone was curious

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enough to ask the question. And mathematics?

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Then another question appeared. What if we could

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undo the squaring process? If 3 squared equals

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9, could we find a number whose square is 2?

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And that question led mathematicians to discover

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irrational numbers, numbers that cannot be written

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as fractions. Well, then came an even stranger

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question. What if the square root of negative

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1 existed? Now, at first, this seemed completely

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impossible. After all, no positive number multiplied

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by itself gives a negative result. And yet, mathematicians

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explored the idea anyway. And that curiosity

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eventually led to complex numbers, which today

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helps to describe electricity and sound waves

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in modern physics. So again and again, mathematics

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has grown because someone asked a question. What

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if? What if there is another kind of number?

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What if this pattern continues? What if geometry

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worked differently? What if infinity behaves

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different than we expect? It is easy to think

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about mathematics as being about certainty. And

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in some ways it can be. But before there was

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certainty, there was curiosity. Before there

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were theorems, there were questions. And before

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there were answers, there were people willing

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to explore. I've come to believe that curiosity

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is one of the most powerful forces in human history.

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It expands mathematics, it expands science, and

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it expands us. Because every new discovery begins

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the same way. someone becomes curious enough

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to ask, what if? And maybe the curiosity you

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need today is not about discovering a new kind

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of number. Maybe it's simply asking, is there

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a different way to solve my algebra problem?

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Is there another perspective I have not considered?

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Could there be more here than I currently see?

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Because every meaningful discovery begins with

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those same two words. What if?