Hi, more than 20 years ago, I climbed Longs Peak
in Colorado. It was the most difficult and likely
the most rewarding hike of my life. The hike
starts before sunrise and then it takes you high
above the tree line. Now, one of the coolest
parts of the climb is passing through a narrow
opening in the rocks called the Keyhole. And
I remember it as if it happened yesterday. As
I stepped through that keyhole, the view suddenly
changed. Before the keyhole, I was focused on
the trail immediately in front of me, like where
to place my feet or how much further I had to
go, and my body telling me to stop. But through
the keyhole, an entirely new landscape opened
up. The view on the other side was breathtaking.
If you think about it, That landscape had been
there all along. I just could not see it from
where I was standing. The mountain had not changed.
My perspective did. And that experience reminds
me of something that the mathematician Paul Lockhart
once said. Paul compares mathematics to climbing
a mountain. Many people think mathematics is
about getting answers. You know, finding X. Computing
a derivative, calculating an area, all good things
for sure. But Lockhart argues that the real purpose
of climbing a mountain is not simply to reach
the summit. It is seeing from a higher perspective.
And as we climb higher, we begin to notice patterns
and connections that were invisible from below.
And mathematics can work the same way. Sometimes
the greatest reward is not the answer. It is
seeing something in a new way. And I can relate
to that idea because over the years, my perspective
on math has changed. When I was younger, math
was mostly about facts and formulas and answers.
But then I began reading books about the history
of math. I discovered that calculus did not simply
appear in a textbook one day. It emerged through
centuries of people. wrestling with questions
about motion and change and area and infinity.
Suddenly, calculus felt different. It was no
longer just a collection of rules. It was a human
story, a story of curiosity, of creativity, persistence,
and surely discovery. Reading about the history
of calculus was a keyhole experience for me.
It helped me see math from a higher ground. And
from that perspective, I began noticing beauty
and connections that I had completely missed
before. So, this week, we're going to explore
the idea of perspective. And together, we will
walk through different keyholes of math. We will
discover some beautiful ideas that may have been
there all along, but hidden in plain sight. Our
goal is not to change the world, but to see it
from a different perspective. And perhaps that
different perspective will change us. Before
we start, here's a question to consider. How
do you view mathematics? And more specifically,
what is your perspective on what math is? Hope
to see you tomorrow.