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“Good.”

I whistled nonchalantly and finished packing up. But underneath all the pleasant sounds I was making, I could hear that she was still thinking. Emmy thinks the way my father used to — silently, for long periods, and in the midst of others.

Finally, I had no choice but to turn and look at her.

“You could have figured that out, too,” she said.

ONE AUTUMN EVENING, not long after I’d noticed my father’s belly at the pool, he leaned back at dinner and said to my mother, “Temptation sell everything, force ’em forward till the nigger strains.”

“Pardon?” she answered. In those days, my mother was somewhat conservative politically, but my father had always been a wild liberal, a man who ranted at the car radio about all the various strains of bigots who lived around us in southern Ohio.

“All the curlings,” he said (or something like that — he wasn’t speaking clearly), “sky, bit-grass. Feed of it, for all know — to the nigger strains.”

My mother’s eyes went to his glass: about half full.

He stood up. His evening gait had always been distinct — getting up from dinner, he tended to walk like a man on a ship, his head lowered and his eyes pinned to the spot where he was heading — the liquor cabinet, usually, or the reading chair. Now we watched him totter to the kitchen door. “Front, back, front,” he said, though I’m not sure any of us could understand him.

My mother rose halfway from her seat.

At the threshold of the room, he coughed once, harshly, without bringing his hand to his mouth. It took me a moment to connect this action with what I saw a moment later on the doorframe — a dark purple blotch the size of my fist, as though someone had smashed a pomegranate against the wood. I watched it slide slowly to the floor.

As it turned out, he’d caught hepatitis from some contaminated seafood, exacerbating what must have been, for some time by then, his hidden condition.

He recovered quickly — after only two nights in the hospital. But it gave our family the first glimpse of what would one day come home with him to stay.

A WEEK LATER he was back teaching his classes, churning out another generation of Fabricus baccalaureates to the nursing schools, secretarial corps, and real-estate agencies of the upper Midwest. And his belly, just like that, had receded — the integral had gone to zero. Yet I couldn’t help remembering the blotch of dusky purple on the wall, which I’d cleaned up later that night, after he’d been admitted to the GI ward at Southern Ohio Lutheran. By then the color had faded to an unremarkable brown against the white linoleum floor, and the surface had hardened to a dry, stretchable crust, like the skin inside an old can of paint. But from underneath it when I scraped — also like the old can of paint — an eruption emerged of brilliant crimson. I allowed the blood to spread onto my fingers and then forced myself to examine it: my father was coming undone in my hands.

The Great War of the Calculus

AT THE AGE of eleven, I entered Tapington North High School. By that point, of course, I’d already been tutored for several years by my father in serious mathematics and encouraged by my mother in various aspects of English, civics, and the arts. But for my first year at Tapington North (there was no Tapington South, just fading hopes for one) I worked diligently all the same, not because I needed to study but because I knew of nothing else. There were no woods to explore behind our house.

What there was was Old Blair Creek, a narrow depression at the bottom of a low ravine that rose with runoff in April and was mud by the end of July. Our yard lay downstream from a Ford light-truck factory that had been shuttered a decade before, but a scattering of chemical and manufacturing plants still thrived in the county and accounted for a good part of my backyard entertainment. At certain times in the spring, I could sit on our porch and watch sluggish continents of brownish foam drift past the property. Sofa-sized icebergs of leaf-flecked suds would slide along, rotating in the eddies, until they either made it around the bend or were caught by the branches of the willows. It was a game of mine, betting on how far each one would reach. It’s a complicated problem — wind, current, and angular velocity, to name a few — but even at that age I was convinced that the outcome wasn’t exactly random.

I should add that I had no friends in the neighborhood and only a few friends at school. Midway through my freshman year, Tapington North’s principal, Mr. Dowater, had called me into his office. By then, I’d already made my way through calculus and differential equations and had recently coregistered for a night course in Fourier analysis at OSU.

“So,” Principal Dowater said. “Tell me your name.”

“Hans Andret.”

Obviously he knew my name. How could he not know the name of a boy like me in a school like North? And anyway, he’d called me Hans when he’d first beckoned me in from the secretary’s office. He was just trying to see whether I could speak. But I could speak. Like my father, I could speak well.

“Hans Euler Andret,” he said, reading from his roll book.

“The middle name rhymes with toiler, actually.”

He laughed.

“It really does, Mr. Dowater. Most people think it rhymes with ruler. But it rhymes with oiler. As in Leonhard Oy-ler.”

“You’re named after a mathematician, then.”

“After three of them, in fact.”

“I see.” He didn’t waste any time thinking about it. “Tell me, Hans, how do you expect to take a night course at the university while you’re enrolled during the day at North?”

His question wasn’t logical. I answered anyway. “My mother drives me.”

“Well, that’s awfully nice of her.”

“She’s taking classes, too.”

This seemed to catch his interest. “In what, may I ask?”

“Nursing.”

“She wants to go into the healing professions, then?”

I couldn’t decide on a response. It seemed to me that in reality she didn’t want anything of the sort, that in fact she’d enrolled in nursing school only so that she could drive me to my course in Fourier analysis. But this didn’t fully make sense to me, either, since her goal had always seemed to be to extend her children’s education beyond mathematics. In fact, what I secretly suspected was that she was driving me to Columbus every Tuesday and Thursday evening because she hoped that while I was there I would sign up for a course in art history.

“I suppose she does,” I said.

He nodded. “And tell me, Hans, how’s it here for you?”

“It’s good, Mr. Dowater.”

“Excellent, then.” He looked up wryly. “And the other inmates,” he continued, “they treating you okay?”

“I don’t really notice.”

He picked up the Panthers calendar from his desk and flipped the page. “There’s a math competition that our seniors go to every year,” he said. “Has Mr. Kirpes told you about it?”

“I don’t like competitions.”

“I agree. I agree — but now, this is a statewide event. Even at your age, you’d probably have a good chance at taking the prize. For North, I mean. I think it would bring a few hours of glory to this old place. Glory to you, glory to our untiring Mr. Kirpes, and glory to the Panthers. It’s only in Dayton, you know.”

I didn’t answer. Mr. Dowater had a reputation for deadpan humor, a humor that was strangely similar to the low-level, sarcastic sniper fire offered by the school’s underbleacher population of stoners and class-cutters. It didn’t really pay to engage it. After a moment, he set down the calendar and dropped the cheer from his voice.