I have had an amazing night! I got to engage in Doing
Mathematics! Some of my fondest memories
from college are of a group of guys (yes, unfortunately all guys)
gathered around a coffee table, white board, or chalk board that is filled with
mathematical scratching in a room littered with beer bottles. This is when I came
to love mathematics; the active, energetic, disappointing, and exhilarating
process of Doing Mathematics.
Doing Mathematics is entirely different from high school
mathematics (which I sometimes call mathematish because I am oh, so clever),
though with the implementation of the Math Practice Standards, it’s not
supposed to be all that different. As I mention above, Doing Mathematics is an
active process. Yes, we did a fair amount of sit and get in college lecture
halls (I did less of that than most of my classmates. Oops.), but outside of
the lecture halls there was discussion, there was argument, there was joy,
there was despair, there was surprise. You could run the emotional gamut when
working on a mathematical proof just as much as with a great work of
literature. There is the trope of the single, solitary genius rigidly following
the rules of deduction to a logical conclusion that seems inevitable, but that
view is impoverished. For me, mathematics is a social activity made much more
enjoyable with others.
I am currently at San Diego State University for a
curriculum training to teach AP Computer Science A next year. I am staying in
the dorms with many of the other future AP CSA teachers in my cohort. We were hanging out in the common area of our
suite this evening trying to get some program to install and cooperate and one
of my colleagues brought out this problem:
I’m thinking of a
ten-digit integer whose digits are all distinct. It happens that the number
formed by the first n of them is divisible by n for each n from 1 to 10. What
is my number?
This problem was created by John Conway as part of a Pi Day promotion
with Pizza Hut. I had heard about the promotion, but it didn’t really register
with me. Tonight, it took hold. It started with two of my colleagues sitting on
the couch discussing the problem and trying out little strategies. It escalated
when they said that they needed a whiteboard. I was drawn in. It was such a
joyful experience as we grappled with the problem, burned through scratch
paper, asked each other to explain their thinking, and willingly explained our
thinking. I don’t know how long we spent on this problem, but we got it! The
crazy thing is, I don’t even know what the answer is. I don’t care what the
answer is. The answer is not the important part. The important part is the
process; the messy, energetic process of sense making and problem solving. At
the end, when I boxed our answer, I felt a great wave of calm satisfaction. One
of the other guys in the room who wasn’t working on the problem expected much
more of a commotion, but I wasn’t excited, I was serene. I miss this. I don’t
get this from teaching. I need to be Doing Mathematics! (or maybe statistics or
computer science) In the end our triumph doesn’t actually mean much; we didn’t
uncover some new piece of mathematical knowledge or win the free pizza from
Pizza Hut. Hell, it was a competition for high schoolers. But that’s really not
the point. It was cool and it felt good to Do Mathematics.
There is a great irony in all of this. About nine years ago,
I dropped out/flunked out of a masters program in mathematics at San Diego
State. It was one of my lowest points in
life. I was very depressed and unhappy. I was not doing well in the program as
a result and my depression and my poor performance spiraled into one another.
By November, I had stopped attending classes. I lasted a little over two
months. It feels weird to even be back on this campus. I brought my Systems of Differential
Equations textbook with me (one of the classes that I ended up failing) because
I knew that being back on this campus would eat away at me. Right now it is
sitting on the floor in the corner of the room, which is kind of what I
expected, but I knew if I didn’t bring it, it would eat away at me. It feels
like my redemption. Like I would be OK if I just studied some Differential Equations for two weeks in my spare time. In truth, I am living my redemption. I have a beautiful
wife and daughter, to whom I am a loving husband father, respectively. We have
lovely home and I have a career where I get the opportunity to impact the lives
of amazing people. I still have that fucking albatross hanging around my neck,
though; that little voice that says “You are a failure”, “You failed”, “You’re
not as smart as you think you are”, “you blew your chance”. Man, that guy is a
dick!
Doing Mathematics is awesome!
I need to do it more and I need to share it with my students.
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