Hi, I absolutely enjoy running. Now, that does
not mean every run is easy. Some mornings I'm
tired. Some miles feel longer than others. And
sometimes I have to persuade myself just to put
on my shoes and walk out the door. Running still
requires perseverance. But it helps that I enjoy
it. I like the movement. I like to be outside.
I like the quiet time to think. And I enjoy the
feeling of accomplishing something difficult.
Perseverance and enjoyment are not opposites.
In some ways, they depend on each other. Part
of what makes running satisfying is that it requires
effort. I think the same thing is true of mathematics.
We sometimes talk about perseverance as though
it means forcing ourselves to continue to do
something we do not like. Just keep going. Try
harder. Do not quit. Now, there may be times
when that kind of determination is good, but
I'm not sure that it can sustain us forever.
Joy gives perseverance a reason. Think about
people who are wonderful musicians or artists.
They may practice for thousands of hours. They
repeat scales and they revise sketches. They
create work that no one else will ever see. They
persevere, but usually there is also something
they love. Perhaps it is the sound of the instrument,
the pleasure of creating. or the possibility
of expressing something that they cannot communicate
in any other way. I experience mathematics in
a similar way, and so do many other people. We
explore patterns because they are beautiful.
I solve problems because they are interesting.
Some problems are deeply interesting. And we
continue even when no one is grading us and there
is no practical reward. We do mathematics simply
for the pleasure of doing mathematics. And this
makes me wonder whether we sometimes begin in
the wrong place when we're teaching math. We
may focus on performance or emphasize speed or
accuracy or grades. or even just avoiding mistakes.
And then when students lose interest, we search
for external rewards to motivate them. I believe
the deeper opportunity is to help people discover
that mathematics itself is beautiful and can
bring great joy. That does not mean removing
all the difficulty. If we remove every challenge,
We may also remove the satisfaction of discovery.
The moment of understanding feels meaningful
partly because understanding did not come easily.
A difficult problem invites us to wonder, to
experiment, to struggle, and eventually to see
something that we would not see before. So perhaps
our goal is not to make mathematics effortless.
Maybe it is to help people find that mathematics
is worth the effort. Because fear of failure
may keep us working for a while, but joy can
keep us exploring for a lifetime.