Hi, do you picture mathematics as a solitary
activity where one person is sitting alone with
a pencil, a sheet of paper, and a difficult problem?
Yeah, there is some truth in that image because
mathematical thinking sometimes requires long
stretches of quiet concentration. But learning
mathematics has shown me that even when I am
working alone, I am participating in a much larger
conversation. For example, the symbols I use
were developed by other people. The questions
that I explore began long before I encountered
them. Every theorem rests on definitions, insights,
and arguments that were built across generations.
And when I learn math, I enter a structure. that
countless people have helped to create. And I
find something humbling and hopeful in all this.
No one invented mathematics in isolation. People
from different cultures and periods observed
patterns. They've created ways of representing
them. They've posed questions. They've made mistakes.
and have even extended one another's ideas. Some
names have been preserved and celebrated, but
many others have been forgotten. And yet, their
thinking remains present in the mathematics we
inherit. The work continues throughout the math
community today. We understand more when we explain
our reasoning. or listen to another approach,
or let someone question an assumption that we
did not realize that we were making. A solution
may begin in one mind, but it becomes more reliable
when others can examine it and challenge it and
build upon it. A proof is not merely an answer.
It is an explanation offered to other people.
And this has changed the way I think about asking
for help. If mathematics were only a measure
of my ability, needing another person might feel
like failure. But if mathematics is a shared
pursuit of understanding, well then, asking,
explaining, listening, and revising are all part
of the work. Mathematician and author Francis
Hsu, definitely one of my favorite. writes about
mathematics as a practice that can satisfy deep
human desires and cultivate virtues that are
necessary for flourishing. And one of those desires
is belonging. We want to know that there is a
place for us and that our contributions matter.
Mathematics can become that kind of place when
it is practiced congressively, not as a contest
to determine who is smartest. but as an invitation
to understand something together. Now, I may
solve some problems by myself, but I never do
mathematics entirely by myself. I am learning
from people I will never meet, choosing ideas
I did not create, and adding my small questions
to a conversation larger than any one life. mathematics
has changed my understanding of what achievement
is about. The goal is not only to reach the answer,
it is also to bring others with us and to continue
a human conversation that began long before we
arrived.