The year is 1505. You pull up to your daughter’s new school in your creaking old oxcart, your arms aching from swinging a scythe all day. Eying the other parents’ brand new carts, the fancy kind with the ostentatious leather seats, you wonder, for the umpteenth time, whether it was a good idea to enroll your daughter in the Royal High School. You’re not even sure what a “High School” is. Some newfangled invention. Probably French.

The commute to Edinburgh twice a day from your estate is a huge pain. Still, it sounds impressive: “high school.” You did all right with your primary school education, but these days, a primary education isn’t good enough. Not according to your wife, anyway, whose idea it was to enroll the kid in a fancy private school. The Royal High School, no less. You know it’s only a matter of time before your precious little bundle starts lording her education over you.

But all the grumbling ceases when she hops into the oxcart in her cute school uniform, her cheeks glowing with excitement. “Okay, Dad, let’s go!” she says. You give the old ox a touch of the whip, and soon you’re out of traffic and on the open road.

The warmth of the cart blanket and the clatter of the wheels on the cobbles makes your daughter sleepy, so to keep her awake you ask her what she learned that day. She looks over at you with the narrow eyes that mean, “Really, Dad? Really? I was just getting comfortable,” but she plays along.

“Oh, it was kind of boring, but we learned some mathematics.” She says it casually enough, but you can tell she’s testing you. “Hey, that’s great,” you say. “I studied mathematics in school. I used to love the animal signs. I’m a Capricorn myself. Did you cover Capricorn?”

She rolls her eyes and says, “Dad! Astrology is so 15th century. That’s not what ‘mathematics’ means anymore. Now, it means this…” With her finger, she draws two symbols on the dusty plank at your feet: a “+” and a “-”.

“Is it religion?” you ask hopefully. After all, one of the symbols does look reassuringly like a cross.

“Duh!” she says. “It’s addition and subtraction. You know. Pluses and minuses. Those are the new symbols for it. Invented by some German dude called Johannes Widman. Like, fifteen years ago.”

“Oh, right, pluses and minuses,” you say. Fifteen years ago, you were busy starting a family — and already ten years out of school.

You drive for a while in silence, fuming. It’s not that she’s already outstripping you — that’s the whole point of high school, right? You’re irritated because your own education, which cost you so much time and effort, is obsolete.

Fast forward to September, 2012.

Your daughter hops in the car, her cheeks glowing with excitement, and directs the a/c vent at her green-streaked hair. She gives you a peck on the cheek and starts talking about her day.

“In math we did graph theory,” she says.

“What’s that?” you say. “Like, graphs?”

“Not really,” she says. “You know, like, ‘vertices,’ connected by ‘edges.’”

“Oh, right,” you say, hoping she’ll elaborate so you’ll have the faintest idea what she’s talking about.

“So it’s a way of mapping data. Seeing the connection between things as a form of problem-solving.”

“Give me an example,” you say, hanging onto the conversation by the merest thread of understanding.

She gives you several examples. You nod sagely, but it’s only later that night, when you’ve looked it up on Wikipedia, that you begin to understand a thing or two about graph theory. Apparently it’s the study of graphs. That part seems simple enough. But these aren’t your grandfather’s graphs. These are newfangled graphs that model extremely complex problems; like, for instance, how to coordinate the class schedules of four hundred squirming high-schoolers.

Since ancient times, mathematics has been playing catch-up with the world. The earliest math — counting — was based on an extremely useful abstraction: two apples and two oranges had something in common, their “two-ness.” Why not create a symbolic category called “two,” and use it to help keep track of how many apples and oranges you had in your cart?

Advances in addition and subtraction were well and good, but as human beings organized and built cities, armies, and empires, new abstractions were needed to meet the challenges of the day. Consider for a moment the kind of math needed to implement taxes across a population, the geometry required to build a domed cathedral.

Each generation inherits a world more complex and faster paced than the world of its fathers. Sometimes, the old way of looking at things isn’t up to the challenge. Sir Isaac Newton realized that the math he learned in school didn’t describe what he observed in his physics lab. Traditional math couldn’t express the changes in speed of an object as it fell. In the 1660s, there was no mathematics of “acceleration.” So in order to create a more accurate science of physics, Newton was forced to invent a new kind of math: “calculus.”

Today’s high schoolers face all kinds of new challenges, including a strange and beautiful problem, courtesy of the Internet: too much information. The future belongs to those who can tame the noise and find the hidden patterns. That’s what graph theory is all about, and why it has become such a crucial discipline.

I’m all for the new math. Even if it makes me feel like a dope on the drive home from school.

This column was published in the Perry Co Times on 20 September 2012

For more information, please contact Mr. Olshan at writing@matthewolshan.com