This week, math is on trial. Our next charge
against math is being hopelessly abstract. It's
filled with imaginary numbers, with unusual geometries,
and ideas that do not seem to have much connection
to our real world. So the prosecution might ask,
what possible use could any of this math be?
Well, history gives us a surprising answer. For
example, for centuries, Euclidean geometry gave
us the obvious description of space. Parallel
lines never meet, triangles always have 180 degrees,
and of course the shortest distance between two
points is always a straight line. And then something
crazy happened. Mathematicians asked what would
happen if we changed Euclidean's assumptions.
Could there be a geometry where parallel lines
behave differently or the angles of a triangle
do not total 180 degrees? Well, at first, non
-Euclidean geometry looked like an interesting
but not practical thought experiment. And then
Einstein needed a way to describe gravity as
the curvature of space -time. The abstract geometry
that mathematicians had already developed gave
physics the language it needed. Something similar
happened with imaginary numbers. The old square
root of negative one seemed so far removed from
reality. It was even labeled imaginary. But today,
complex numbers are essential to electrical engineering.
We use them in signal processing, in quantum
physics, and really much of modern technology.
How about number theory? When we created number
theory for centuries, we were just exploring
the properties of whole numbers without much
thought about how to use them practically. But
today, those ideas secure our financial transactions,
and they make our communications private using
cryptography. So again and again, math has imagined
possibilities. before the physical world revealed
why they mattered. What appeared useless was
not useless. Reality simply had not caught up
with the idea. Now, to be honest, when I look
back on my life, I can be impatient with anything
that does not have any immediate use. I remember
studying for my actual exams and wondering, when
will I ever use this stuff? When I could not
see the purpose, it was easier for me to lose
interest. Looking back, I can see that I did
not yet understand the bigger picture of math.
Yes, some math is taught in ways that do not
feel useful or even connected to anything important.
But those experiences can distort our view of
what math really is and keep us from seeing its
beauty. In the end, I had to work through a lot
of details. before I could understand how they
fit together and to see something greater. And
what I learned is that I may not yet understand
what today is preparing me to see tomorrow. So,
on the charge of being abstract, mathematics
is guilty. But on the charge of being impractical,
well, the evidence says otherwise. So, our question
to finish, Is there a part of your life that
you may have dismissed because it may not matter
today, but maybe it's possibly going to be important
later?