Hi. Let's face it, life is about change, and
mathematics quantifies it beautifully. Calculus
can open our eyes to change at the smallest scales
and shows how finite processes can approach the
infinite. But rather than focus on the mathematics
of change, I want to spend this week reflecting
on how mathematics has changed me. Math has changed
what I notice. It's changed how certain I need
to be. It's changed where I place my effort and
even what I allow myself to hope for. Mathematician
Paul Lockhart describes mathematics as a search
for beauty and understanding that leads us to
a higher ground and a more encompassing view.
I just love that image. When we climb to higher
ground, the world below has not changed, but
our view of it has. We see hidden connections.
We recognize how one path meets another. What
seemed random begins to reveal a pattern. And
this is one way that math has changed me. Before
learning a new mathematical idea, I often cannot
imagine what there is to see. So consider proving
that the square root of two is irrational. Now,
at first, the question may not seem important
or even really interesting. The proof can feel
difficulty and foggy. How can we possibly prove
it? And then something clicks. The contradiction
comes into focus. The waters part. You see that
it must be true. And after seeing it, you cannot
unsee it. This is more than just acquiring information.
Information adds to what we know. Understanding
can change the person doing the knowing. Lockhart
writes that mathematics is a way of constantly
evolving and changing myself. Becoming, get this.
reborn as a person who sees in a new way and
cannot unsee. That is much larger than the vision
of mathematics that many of us encounter in school.
Math is often presented as a collection of procedures,
memorize this formula, follow these steps, and
then find the correct answer. Instead, Lockhart
describes a playground of the mind, a place to
explore patterns. to make connections, and discover
unexpected beauty. I'll be honest, the more mathematics
I learn, the more I understand what he means.
Math invites me to pause and to look more closely.
It makes me curious about structures beneath
the surface. It reminds me that the first view
is rarely the only possible view. It may not
be the most revealing one. So this week, I will
explore how math has taught me to find connections
that enlarge my imagination and change how I
think about abstraction and fairness. How it's
challenged my beliefs about growth and connected
me to a community. And finally, how it's shaped
what I allow myself to hope for. The world is
still the world, and I am still me. But mathematics
keeps leading me to higher ground. Each time
I climb, I return as someone who sees a little
differently.