Hi, this week has been about how math has changed
me. And to be honest, I rarely like change as
it is happening because it is usually difficult.
But when I look back in retrospect, I appreciate
how I have been changed. And this all leads to
our final idea this week that is a beautiful
paradox at the heart of mathematics. Amidst all
our discussion of change, consider this. Mathematical
truth can remain stable while mathematics continually
changes the people who encounter it. A proof
does not become false because a civilization
disappears or a century ends. Once a relationship
has been established from its definitions and
assumptions, it remains available for someone
else to discover. Languages change, empires rise
and fall, cultures meet, conflict and influence
one another, and yet mathematical ideas pass
through time, carried from one human mind to
another. The ideas endure, but we are changed
by them. This week I have reflected on some of
those changes in me. Mathematics has led me to
higher ground and has given me a more encompassing
view. It has taught me to search for connections
between things that appear separate. It has enlarged
my imagination through infinities I cannot picture.
And it has shown me the power and danger of abstraction.
It has challenged fixed beliefs about my own
abilities. And it has welcomed me into a human
conversation that began long before I arrived.
All of this has changed what I allow myself to
hope for. Reasonable Hope It is not the belief
that everything will work out exactly as I want.
Mathematics does not promise that kind of certainty.
It reminds me that constraints are real, assumptions
matter, and some outcomes are more likely than
others. But mathematics also warns me not to
confuse what I have previously seen with all
that is possible. My intuition can be incomplete.
Problems can have an approach that I have not
yet considered. Two disconnected ideas can suddenly
meet. A small change, repeated and shared, can
alter an entire pattern. Again, back to Francis
Hsu. He argues that mathematics can serve basic
human desires for play, beauty, freedom, justice,
love, and belonging, and cultivate virtues that
help us flourish. That vision moves mathematics
far beyond calculation. Mathematics becomes one
of the ways that we practice being fully human.
And perhaps that is why math has survived across
cultures and centuries. We preserve it not only
because it is useful, but because human beings
continue to find wonder in patterns, satisfaction
in understanding, and joy in discovering that
the world is richer than we thought. Mathematics
has not taught me that change is easy or inevitable.
It has taught me that change is possible. It
has taught me to look again, to try another representation,
or to question the boundaries of my imagination,
to learn from others, and to remain open to becoming
someone who sees differently. Math has changed
more than the way I solve problems. It has changed
me. And from this higher ground, I can see farther.
than I could before. And that is where my reasonable
hope begins. So how about you? Are you open to
be changed? To see a different reality than you
currently see? Doing math will take you to a
larger landscape.