the paper I’d assign to a calculus class if everyone shared my slightly skewed sense of intellectual fun and my excessive fondness for mathematical metaphors
Forget the history of calculus. Write me a paper on the calculus of history.
You won’t be the first. In War and Peace, Tolstoy compared civilization to a vast integral. Only by summing all “the individual tendencies of men,” Tolstoy wrote, “can we hope to arrive at the laws of history.” His was a true people’s history. Each peasant and prince gets the same weight in Tolstoy’s great Riemann sum. To give the monarchs disproportionate weight (thereby silencing the masses) would be a perversity, a paradox. No delta functions in Tolstoy’s mathematics.
History as an integral. That’s one way to see it. Continue reading
Last April 13th, I emailed a few friends to let them know I was starting a blog. “I’m a little afraid it will land with a dull thud against the hard pavement of the internet,” I wrote.
Two weeks later, I posted an essay called What It Feels Like to Be Bad at Math, about my struggles with topology. It was stubbornly hard to write. I spat out 500 words of excuses and hedges (which I later deleted) before I could bring my fingers to type the truth.
Then the post started getting passed around. Continue reading
I’ve always dreaded being asked for my “teaching philosophy.”
For years, I gave nonsense or scattershot answers. “Logic and critical thinking are paramount.” “I care more about conceptual understanding than computational skill.” “A balanced, student-centered approach is always best.” “We buzzword to buzzword, not for the buzzword, but for the buzzword.” At best, each of my disjointed half-theories captured only a piece of the puzzle.
Worse still, none of my replies explained why I devote so much class time to plain old practice. Continue reading