Hi. Two days ago, I shared how I spent time going
deeper into calculus. And yesterday, I shared
a specific calculus problem and how my perspective
on math changed when I stopped seeing it as a
collection of answers and started seeing it as
a collection of tools. And those tools have helped
me explore the world in new ways. But over time,
I discovered the tools themselves had a story.
They did not appear out of anywhere. Every idea,
every formula and technique that I learned came
from somewhere. Someone discovered it. Someone
developed it and someone passed it on. And that
realization, however obvious, led me to another
perspective that has stayed with me ever since.
The deeper I explored calculus, the more I realized
that calculus is not standing alone. Now, when
students first encounter calculus, it often feels
like a completely new subject. We've got derivatives
and integrals and limits. A whole new world.
But over time, I realized that calculus is built
on ideas that came before it. It depends on the
real numbers, on algebra, geometry, and trig.
and many of its biggest ideas can be traced back
more than 2 ,000 years back to the ancient Greeks.
What first looked like a separate branch of mathematics
began to look more like a tree. Now, calculus
was not the whole tree. It was one branch connected
to roots that ran much deeper than I had imagined.
connections everywhere. One idea leading naturally
to another. One generation building on the work
of another. What seemed like separate subjects
became a connected story. And in a way, I think
people are a bit like calculus. Our lives are
rich in meaning. We're always changing and developing.
We're growing in new directions. But just as
calculus has roots that reach deep into the history
of math, each of us has roots that have helped
us become who we are. We have parents and teachers
and friends and maybe even mentors. People who
have encouraged us, challenged us, and even sacrificed
for us. Now, I know for myself, it is easy to
be so focused on where I am today. that I forget
the roots that helped me get here. So here are
my questions for today. Who are the roots in
your life? Who helped make you who you are? And
is there someone today that you should give a
little thanks? See you tomorrow.