WEBVTT

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Hi. More than 2 ,000 years ago, Euclid organized

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geometry around a small collection of starting

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assumptions called postulates. Most of these

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seemed simple. A straight line can be drawn between

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any two points. We can draw a circle with any

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center at any radius. But one assumption was

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different. Eventually, we named it the parallel

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postulate. In short, it says that if you have

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a line and a point outside that line, exactly

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one line can pass through the point without ever

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intersecting the original line. Now, unlike Hewlett's

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other assumptions, this one seemed complicated.

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It did not feel as obvious or even fundamental.

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So, mathematicians wondered whether it was really

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necessary. Perhaps the parallel postulate was

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not an assumption at all. Perhaps we could prove

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it from the other postulates. So, for roughly

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2 ,000 years, mathematicians tried. Again and

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again, they constructed proofs. Again and again,

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their reasoning failed. Now, by the usual definition,

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they failed. But then, something remarkable happened.

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Mathematicians began asking a different question.

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What if the parallel postulate could not be proven

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because it was truly independent of the others?

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And what if they replaced it with something else?

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Suppose there were no parallel lines through

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the point. Or, suppose there were many. Now,

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at first, these possibilities seemed absurd.

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Surely, changing the parallel postulate would

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produce a geometry filled with contradictions.

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But, it did not. Instead, mathematicians discovered

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entirely new geometries. For example, on a curved

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surface, the angles of a triangle do not necessarily

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sum to 180 degrees. Parallel lines may behave

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very differently from what we learned in school.

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The geometry of a flat surface is only one geometry

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among several possibilities. Eventually, these

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new ways of thinking gave Albert Einstein the

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mathematical language he needed to describe curve

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space and the theory of relativity. Wow! So what's

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the big idea here? 2 ,000 years of unsuccessful

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proofs open the door to a larger understanding

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of reality. Those mathematicians did not solve

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the problem that they originally wanted to solve,

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but they discovered that their question was pointing

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towards something far greater. And I find that

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encouraging, because many of my small ideas or

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small problems often are part of something bigger

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than I ever imagined. if I'm open to see it.

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Many of my failures and struggles were not dead

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ends, but they were invitations to question the

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path itself and to discover an entirely new world

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of possibilities. So, how about you? What problem

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are you trying to solve that you are ready to

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quit? problem important and if it is it is likely

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worth persisting