Confessions of a Luddite mathematician. – Math with Bad Drawings

This summer I’ll be completing an M.S. in Data Analytics. Yet it’s weird to think of myself as someone with technical skills, no matter how meager. I present this essay, which I wrote four years ago, as a peculiar and unedited capsule of my past self.

In 2004, the week before the AP exam, I gathered my graphing calculator and sought out my calculus teacher. “How,” I asked, holding the device like an enchanted egg that might hatch at any moment, “do you use this thing?”

He looked at me. He sighed. Then, with the infinite patience of a veteran teacher, he took the calculator from my hands, flipped it right-side-up, and put it back in my grasp.

“That’s a start,” he said.

Today, although I am a math teacher myself, my technological knowledge remains full of craters and chasms. I learn a lot about graphing calculators from my students. My programming skill, in every language, is worse than my Italian. (I don’t speak Italian.) What any self-respecting coder can accomplish in one minute, I accomplish in ten or fifteen, maybe, and even then, only via a jerry-rigged Excel spreadsheet that would make my high school CS teacher doubt God’s mercy.

I’d love to believe that my technological innocence is a virtue. But I know better. I know that I am typing these words on a device of staggering computational power; a device such as Lovelace dreamt of, such as Leibniz thirsted for, such as Poincaré would have chainsawed his thumbs to possess; a device that promises to transform mathematics and the world.

A device that I use mostly for word processing.

I’m not alone. In fact, I am a prototypical product of a certain kind of secondary and postsecondary mathematics education: a theory-heavy kind, practiced at elite universities and their many imitators, well-suited to graduate work in pure mathematics and proudly unsuited to most other human endeavors. It prizes proof and rigor, and it regards digital technology with reptilian suspicion. Centuries change faster than this species of education has.

After years of advocating fiercely for its merits, I have begun to question the whole enterprise. I was born into the computer age: an apotheosis of human technology. A time, it’s little exaggeration to say, of magic. Then I spent my education learning the abstract principles of magic, without ever becoming a magician myself.

What’s the point of a sorcerer who knows no spells, a wizard who can’t use wands?

I was feeling my inadequacy acutely this week, as I read a collection of essays by Cory Doctorow. He is a hypercompetent polymath technologist, and a great writer to boot. Check out this meditation on some old technologies he keeps around his office:

Which brings me back to these beautiful old machines I’ve got around my office, from the 300,000-year-old stone axe-head to the rusting, nonfunctional wind-up bank. I don’t have these here because they’re inherently well-made or beautiful. I have them here because they are uproarious, the best joke we have. They are the continuous, ever-delightful reminder that we inhabit a future that rushes past us so loudly we can barely hear the ticking of our watches as they are subsumed into our phones, which are subsumed into our PCs, which are presently doing their damnedest to burrow under our skin.

The poets of yore kept human skulls on their desks as mementos mori, reminders of humanity’s fragility. I keep these old fossil machines around for the opposite reason: to remind me, again and again, of the vertiginous hilarity of our age of wonders.

Reading this, it struck me that the mathematical mindset is almost precisely the opposite.

From mathematics we learn that history is full of treasures. Brilliant minds inhabit every age. I’ve got tools that, in their wildest fancies, Archimedes and Liu Hui would never have guessed, but they’ve got insights that, in my wildest inspiration, I would never have guessed, either.

Technology charges us pennies for miracles. Math, meanwhile, demands hours of toil, and pays out tiny increments of truth, each of which feels obvious the moment that it’s in hand. And yet those truths accrue, over time, into miracles.

Technology teaches us the contingency of matter. Math teaches us the universality of minds.

I don’t mean to excuse the Luddites like me. Our abstinence from technology cannot redeem us. But I’m newly hopeful that, while the CS majors were racing ahead to fancier job prospects, we were learning something of true value, too. Computers are magic wands, but so, in their own way, are mathematical ideas. An older magic, yes, but I can settle for that.