Why I Love Mathematics

Friends,

People sometimes ask me if I miss math (note: I left math grad school to do college ministry).  The answer is usually "Eh. Not really."  But when I say that, what I mean is that I don't really miss math grad school.  Do I miss math?  Of course.  It's awesome.  And, for the record, here's why...


1. The thrill of strategic victory

I love strategy.  As a (twenty-five year old) kid, I loved Connect Four.  When I got older I loved Risk and Stratego.  But, as strategic as those games are, they don't compare to tackling a math proof.

I'll try to explain how proving some mathematical fact is the ultimate strategy game.  The object of the game is to prove that something is true.  The rules are the laws of logic.  The pieces you can use are the axioms of mathematics and any sufficiently well-known result from any mathematician in history.  Your opponents are your ignorance and the limits of your brain.

The satisfaction of solving a difficult problem far outweighs the thrill of trading in three ores and two wheats for your tenth victory point.


2. The majesty (and usefulness) of correspondence

The thing that always awed me about math was that certain abstract things (numbers, sets, mathematical structures) correspond perfectly with other things, both abstract (different sets and structures) and physical (atomic spin, the relationship between space and time, data storage).  So many times, when you want an answer about one of these things, you are forced to turn to some equivalent abstract thing and you can find the solution there.

In fact, just today I was talking to an old friend about his math Ph.D. thesis and it consisted entirely of this sort of thing.  Here's my misquoting of his explanation of his research. I've put math jargon in brackets so you can ignore it.

"I'm looking at certain examples of [directed graphs] which have special properties (e.g., that [each edge is assigned a group element] and that [there are cycles within the graph upon which the group operation yields the identity element]).  We call these [matroids].  You can also define a [matroid] as anything that has three such-and-such properties.

This serves as a generalization of the idea of [linear independence] from linear algebra.  What I'm specifically doing is looking at the matrix form of these graphs to answer questions about the graphs/matroids."

(He should totally title his dissertation "Super Matroid".)

If that was stressful, nauseating, and/or another language to you, I apologize.  My point is that in math, we're always switching back and forth between equivalent versions of the same thing, and picking up useful information as we go.  In that sense, correspondence is useful.

It's when you think about real-world correspondences that it becomes beautiful.  Our understanding of the arts, financial markets, architecture, chemistry, and (insert just about anything) relies so heavily on mathematics, and this is made possible because the numbers, ideas, and structures of mathematics truly correspond to realities in the world.

It's really astonishing.

How much of a nerd are you?

What are your thoughts and feelings about math?

Jon