Hello. Imagine you run a five mile race where
you start slowly and gradually increase your
speed. At the one mile mark, you're running exactly
one mile per hour. At the two mile mark, you're
running exactly two miles per hour. And at the
three mile mark, you're running exactly three
miles per hour. In fact, at any distance X, you're
running exactly X miles per hour. This is one
of the ways a beautiful number. enters mathematics.
Whenever the rate of change matches the amount
you already have, whether it's speed matching
distance, or money growing according to how much
money you have, or a population growing according
to its size, a specific number appears. And mathematicians
call this number E. Like pi, E is irrational.
That means its digits continue forever without
repeating. What fascinates me about E is its
unusual combination of beauty and mystery. If
you study to become an actuary, you will find
E everywhere. In interest theory, probability,
risk models, survival models. We see it so often.
we stop asking what it is. It's a bit like gravity,
always there, always doing its thing, part of
the fabric of the world. But when I stop using
E to solve problems and start asking what E actually
is, I realize how remarkable this number really
is. Now one reason I find Pi beautiful is that
it comes from a perfect curve, a circle. Yet,
we can express it exactly through beautiful patterns
built from whole numbers. And in a similar way,
E emerges from the idea of continuous change.
And yet, mathematicians have discovered countless
beautiful ways to express E using simple patterns
of integers and sums. and products and fractions.
If you're interested, I encourage you to look
up formulas for E just to notice a few. Why these
patterns exist feels like a mystery. Michelangelo
once said, David was already in the marble and
he simply removed what was not David. And to
me, Beautiful math can feel the same way. Mathematicians
do not set out looking for E. Yet, as they explore
new ideas, E just keeps showing up. Almost as
if it had been there all along. Here's just one
example that I recently encountered. Generate
random numbers between 0 and 1. Keep adding them
until the total exceeds 1. And then start over
and count how many numbers it took. Repeat the
experiment thousands of times. And here is the
kicker. The average count approaches E. Now,
I find that interesting because why should a
number connected to growth and change suddenly
appear in a game of random numbers? And yet,
there it is. tip of the iceberg of what we call
E. Just as pi is the mysterious number behind
circles, and the sine curve is the beautiful
pattern behind waves, E is the mysterious number
behind growth and change. And the more time I
take to slow down and notice where E appears,
the more I find myself wondering why this one
number keeps showing up and the more I wonder
the more I am drawn to the beauty of it all