WEBVTT

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Hello. Imagine you run a five mile race where

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you start slowly and gradually increase your

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speed. At the one mile mark, you're running exactly

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one mile per hour. At the two mile mark, you're

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running exactly two miles per hour. And at the

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three mile mark, you're running exactly three

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miles per hour. In fact, at any distance X, you're

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running exactly X miles per hour. This is one

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of the ways a beautiful number. enters mathematics.

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Whenever the rate of change matches the amount

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you already have, whether it's speed matching

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distance, or money growing according to how much

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money you have, or a population growing according

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to its size, a specific number appears. And mathematicians

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call this number E. Like pi, E is irrational.

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That means its digits continue forever without

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repeating. What fascinates me about E is its

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unusual combination of beauty and mystery. If

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you study to become an actuary, you will find

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E everywhere. In interest theory, probability,

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risk models, survival models. We see it so often.

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we stop asking what it is. It's a bit like gravity,

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always there, always doing its thing, part of

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the fabric of the world. But when I stop using

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E to solve problems and start asking what E actually

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is, I realize how remarkable this number really

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is. Now one reason I find Pi beautiful is that

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it comes from a perfect curve, a circle. Yet,

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we can express it exactly through beautiful patterns

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built from whole numbers. And in a similar way,

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E emerges from the idea of continuous change.

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And yet, mathematicians have discovered countless

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beautiful ways to express E using simple patterns

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of integers and sums. and products and fractions.

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If you're interested, I encourage you to look

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up formulas for E just to notice a few. Why these

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patterns exist feels like a mystery. Michelangelo

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once said, David was already in the marble and

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he simply removed what was not David. And to

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me, Beautiful math can feel the same way. Mathematicians

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do not set out looking for E. Yet, as they explore

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new ideas, E just keeps showing up. Almost as

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if it had been there all along. Here's just one

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example that I recently encountered. Generate

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random numbers between 0 and 1. Keep adding them

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until the total exceeds 1. And then start over

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and count how many numbers it took. Repeat the

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experiment thousands of times. And here is the

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kicker. The average count approaches E. Now,

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I find that interesting because why should a

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number connected to growth and change suddenly

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appear in a game of random numbers? And yet,

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there it is. tip of the iceberg of what we call

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E. Just as pi is the mysterious number behind

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circles, and the sine curve is the beautiful

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pattern behind waves, E is the mysterious number

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behind growth and change. And the more time I

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take to slow down and notice where E appears,

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the more I find myself wondering why this one

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number keeps showing up and the more I wonder

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the more I am drawn to the beauty of it all