Why Math?
"A mathematician is a machine for turning coffee into theorems."--Paul Erdös
If you're an engineer or math professor about to protest it's obvious why math, let me explain. (Forgive the generalizations in what follows; tacking on modifiers every sentence becomes tiresome.)
When I tell other people that I was a math major, their most common responses are: "Yuck! I could never do that," or "I hate math." Reassuring, isn't it?
Well, no. I've listened to the gripes of many intelligent people who don't "get" math, or hated their 9th grade geometry teacher. They don't understand why anyone would volunteer for more hours of killer calculations and pointless proofs. Of course addition works for the real numbers the way it does for the integers! Why do you have to prove it? For that matter, of course there are real numbers!
On the other hand, when I tutored writing, a tutee sometimes asked at the session's end, "Are you a grad student?" No. Well, that wasn't so disappointing. "Are you an English major?" No, I'm a math major. At which point they looked at me as if I admitted to eating students for fun and profit. (The exception was an engineering student who gave me a profoundly relieved look and began telling me how he couldn't make sense of this "fuzzy" language business, and would rather everyone spoke in predicate logic.)
What's going on?
After such encounters, I've concluded that it isn't math so much as how it's often taught. Granted, there are people who don't get along with the topic, the same way some people hate modern art and others dislike chemistry. Others go to math classes willing to see what it's about and come away disillusioned, sometimes for life.
Maybe it's because the beginnings of math--the basics--involve hours of drill. Maybe it's because it isn't clear what the drill is for ("Can't I just use a calculator?"--and never mind that some circumstances render the calculator's magic answer useless). Maybe--and this is hardly unique to math--the teacher is a favoritist twerp.
I've gotten math-haters to show a flicker of interest when I describe a Sierpinski gasket [Mathworld], or discuss my sketchy understanding of Gödel's incompleteness theorems. I got an "artsy" acquaintance to look at color plates of fractally-generated flowers in wonder. If these people can appreciate the "neat" parts of math, why shouldn't the "neat" parts be incorporated and tied to the "boring" topics?
Math is beautiful. But try to show your average high school/college class the elegance of the Fundamental Theorem of Calculus, and they'll think only of the integration formulae they have to memorize for their next exam. The people who "see it" are people who will go on to become mathematicians or math teachers or scientists.
Even so, I explained Euclid's proof that there exists an infinite number of primes to my fidgeting sister, and after some minutes of finger-tapping, her eyes lit in a "eureka" as she deciphered my words. I felt that "eureka" for the first time when I read Cantor's diagonal slash proof in Roger Penrose's The Emperor's New Mind (in a footnote, no less). I stared at it for fifteen minutes, growing steadily more irritated--and the idea burst clear. Maybe that should have warned me that I wouldn't end up as a history major, but in math. (Not that I don't appreciate history, but that's another essay.)
Then, too, there's the history of math, the sense of mathematics as a process started by various cultures and various times and continued today. Most people I know don't think of mathematicians, dead or alive, as people. They must drink equations for breakfast (Erdös' coffee quote notwithstanding) and chew on theorems for dinner. If Evariste Galois wasn't human in his misfortune, if Newton and Leibniz in their quarrels weren't human, I don't know what to tell you.
In the sciences you have this sense of history, however obscured by neat textbook organization (my exposure to the history of science tells me it was downright messy): Watson and Crick discovered DNA, Einstein's "E = mc2" (which I've heard from people who couldn't define "energy" in the physics sense to save their lives), Darwin's voyage on the Beagle. You have a sense of the progression of ideas, the tortured paths of proofs, the concerns that surrounded scientists. (Kepler's original model of the solar system, anyone?)
Where's this sense of history in math? Other than the oft-ignored biographical sidebar, nowhere. I learned math, as a child, as though an angel had come down to the world with Tablets of Everything You Need to Know About Math. It didn't happen that way, but I only discovered that years later. If students can think of math as something in development, a development whose tracks they can begin to follow, perhaps they'll receive it more willingly.
And me? What am I doing here? I am more of a "humanities person," and while I'm competent at undergraduate-level math, I'm no genius. I'll never be a Galois (thank goodness) or a Gauss, but I'm a small anomaly: someone who likes math even so, and can try to put it in words. I don't expect others to fall in love with the subject, but surely a working relationship is worth trying for?
Go forth and spread the math!
For Ms. Sharon Widdekind.
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