It happens all the time. I'm at a social gathering, I meet someone new,
and the standard question comes up: ``So, what do you do?'' I'm tempted
to limit my reply to ``I'm a professor at the university'', but this
only postpones the inevitable. It's better to just get it over with:
``I'm a math professor at the university''.
At this point there are several common responses:
1. The person steps back in horror, as though I had just announced I had
the bubonic plague. Then, perhaps recalling that mathematics is not
contagious, or at least not fatal, they recover and reply: ``I was never
any good at math.''
I've never understood this. If I'd said I was a biology professor, would
the response be ``I was never any good at biology''? If I played the
bassoon in the orchestra, would they reply ``I was never any good at the
bassoon''? I doubt it. Yet a surprising number of people seem compelled to
immediately proclaim their incompetence in mathematics. I myself am
hopeless at any form of visual art, but I don't feel the need to
announce this every time I meet an artist. But what I really want to say to
the person, and sometimes do, is this: ``What makes you think you're no good
at math? I don't believe it!'' The same goes for any reader of this blog
who thinks they are ``no good at math'' or claims not to like math. In
this series of posts, I'm going to try to prove you're wrong.
2. ``oh, you must balance the checkbook in your family''. That's
hilarious, especially for Wendy. Even worse:
``So do you know Professor so-and-so in the Accounting Department?''
Huh? No, I don't know Professor so-and-so, nor do I know Professor
Whatshername in the Department of Finnish Literature. Well, I don't
actually say that, recognizing all too well what prompts the question:
For many people, ``math'' is the same thing as ``arithmetic''. I was
astonished to find a website asserting that ``there is no math in
Sudoku''. On the contrary, this popular game is PURE mathematics. What
the website author meant is that there is no arithmetic in Sudoku, which is
true, but the unfortunate choice of language insinuates that if there
was math in it, it couldn't be fun. On the contrary, if you like Sudoku
then you are a mathematician! I'll explain this in a later post.
In any case, I have nothing against accounting, but it has nothing to do
with the mathematics I love. Music would be much closer.
3. ``So you teach math?'' Well, yes. Often I leave it at that, which
leads to an easier, more pleasant conversation in which I can talk about
the courses I teach, what the students are like, and so on. Only in my
more optimistic moods do I venture to add: ``And I do research, which in
fact is about half of my job.''
This statement is often met with outright incredulity. ``You can do
research in MATH???'' A cousin of my wife's, in his early 20's at the
time, found the idea so absurd that he literally burst out laughing,
and asked: ``What do you do, look for new ways to find...[here he
paused, evidently searching for the most advanced, esoteric mathematical
concept he'd heard tell of]...square roots?''
I can understand why it comes as a surprise to most people that there is
such a thing as mathematical research. We mathematicians have to take
some of the blame for this state of affairs; evidently we've done a bad
job of explaining ourselves to the general public. What I don't
understand is this attitude of willful ignorance, all too common in our
country: ``If I can't imagine it, then it doesn't exist''.
Yes, you can do research in mathematics. People have been doing it for
three thousand years, and tens of thousands of people around the world
are doing it at this moment. And when I say you, I mean YOU! In the
course of these posts I'll mention some unsolved problems that anyone
can work on, or at least play around with.
4. ``Does it (mathematical research) have any practical applications?''
This is certainly a reasonable question, but a very frustrating one to
answer. On the one hand, there is no field of knowledge that has more
practical applications than mathematics. It has been pervasive for
centuries, and especially since the advent of computers. In fact, a
striking trend over the last fifty years or so is that EVERY branch of
pure mathematics, no matter how abstract or esoteric it might appear,
finds applications sooner or later. On the other hand, this is not why I
love mathematics, and therein lies the frustrating point. I love
mathematics for its intrinsic beauty; the applications are just a bonus.
I could talk about practical applications, many of which are quite
amazing, but that's not what I personally think about. So in these essays
I'll mention an application or two when I can, but my main goal is to
give some inkling at least of why mathematics in and of itself is so
fascinating. And fun!
The fun will begin in the next post. Meanwhile, if you had any bad
experiences with math in school, banish all such memories from your
brain. Did you find it boring to recite multiplication tables, solve
long lists of algebra equations, analyze equilateral triangles or memorize
trig identities? Excellent! This indicates good taste, and that you have
a future as a mathematician. Or perhaps you enjoyed geometry but not
algebra, or vice-versa. This too is excellent; mathematics is a vast
subject and there is nothing wrong with preferring one branch over
another. Most important of all, get rid of the idea that mathematics was
all written in stone a thousand years ago, and the Big Mathematical
Cheese in the Sky handed it down to a few select prophets on the
mountaintop. Mathematics is a vibrant, living, human enterprise. WE are
the mathematicians, and this includes YOU. Relax your mind. Return to
the innocent, unfettered curiosity that all children have. And enjoy!