Hi, let's recap this week. We have explored failure
and perseverance. We've seen that failing an
exam is not the same as failing at mathematics.
We've considered how joy can sustain perseverance
and why not knowing can be a gift and how mathematical
struggle can resemble climbing a mountain. We've
also seen that 2 ,000 years of failing to prove
the parallel postulate opened the door to new
geometries. And we've seen how an error in Andrew
Weil's proof became part of one of mathematics'
greatest stories. All these stories have a common
idea. The people were willing to work on questions.
where the answer was not easily seen. Now this
seems obvious, but it does run against much of
what we learn in school. In school, we are often
given problems that someone else has already
solved. We already know the method. The answer
is in the back of the book. And our job is to
just reproduce it. And if we can't, We conclude
we are not good at math. But mathematicians work
differently. They look for questions difficult
enough that they do not know what to do next.
They expect false starts. They make conjectures
that turn out to be wrong. Nowhere. Their unsuccessful
attempts are not evidence that they cannot do
mathematics. They are evidence that they are
doing mathematics. So never confuse an unsuccessful
result with an unsuccessful person. A test score
may describe your performance on a particular
set of questions on a particular day. But it
cannot measure your curiosity, your creativity,
your potential, or your capacity to understand.
Yes, doing math is difficult. And that is part
of its beauty. The most interesting problems
rarely surrender their secrets immediately. They
ask us to experiment. to become confused, and
to reconsider our assumptions, and then to try
again. So, I want to encourage you to find a
question that awakens your curiosity. It does
not need to be famous. It only needs to matter
to you. So pursue it with your best effort. Give
yourself permission. to move slowly. Let every
false start teach you something. And when you
are stuck, remember being stuck is not the end
of the journey. It may be the exact place where
deeper understanding begins. I have seen this
over and over again in my life. Perseverance
is not simply refusing to quit. It is learning
to see each failure as part of the search. So,
what we'll learn this week is the greatest failure
is not arriving at the wrong answer, but it's
allowing the fear of being wrong to keep us from
exploring at all.