Ethan Canin - A Doubter's Almanac

“Your work is quite mysterious to someone in a field like mine. That’s all. I was just wondering what a person like you does all day. As a historian, I know what I do.”

“Which is what?”

“Travel and search out sources and make notes. I teach. I write. At the moment I’m stuck in a little skirmish over Sigismund the Third, of Poland. But I don’t imagine you spend your days fretting over anything quite like that.” She rose. “Well, you’re obviously busy. I can come back another time.”

Beneath the dowdy clothes, he glimpsed a body that, like the laugh, wasn’t dowdy in the least. “No, no,” he said. “In fact, I welcome the interruption, and I’ll almost certainly be busier next time. As it so happens, I was just trying to figure out the same thing myself.”

“The same thing?”

He leaned back in his chair. “What someone like me does all day,” he said.

—

SHE WAS A farm girl. Had spent her childhood on a cattle ranch half a day’s drive from a library and now found it ceaselessly amusing to be teaching seventeenth-century history in the Ivy League.

In a way, then, she was like him.

She told him all of this the next afternoon, when they met for a drink on the patio of a place on Chambers Street. She ordered a glass of wine. Spring had appeared. They sat along the sidewalk, where bikes and baby strollers and students on roller skates ambled past. The peak of the afternoon in the peak of the season. As they talked, she greeted a number of professors who stopped at the table to talk. Most of them looked quite senior — cuff links and bow ties — and all of them forwarded their regards to her husband.

When another of them had walked away, Andret lifted his bourbon and examined her over the top of it. “Your husband is evidently quite an important man,” he said.

“Yes, indeed he is.” She glanced to the side, then brushed at her hair. Then she took a swallow of wine.

“Ah, yes,” said Andret. They were silent for a few moments, during which the air seemed to grow warmer. “Why don’t we go someplace a little less public,” he finally suggested.

—

ONE DAY, ALMOST three years along in the task, he happened upon a paper by Paul Erdős. There was an older theorem of combinatorial topology that Erdős and a colleague named George Breville had proven rather magnificently, but also rather whimsically, by modeling their analysis on a children’s game. The game was called Kutyák és Lovak, or, loosely translated, Apples and Oranges. Erdős had played it as a young boy in Budapest.

In the game, one child named an object — a lemon, say, which was sour — and the other child countered with an object that possessed some antithetical quality: a cube of sugar, say, which was sweet. The first child then had to do the same for the cube of sugar, but in relation to another quality — it was orthogonal, for example, while a sheet of paper was flat. And so on, until one of them accidentally named an item that shared one of the previously named qualities with the lemon. The game, as Erdős and Breville pointed out, was simple enough for children; but if one began with multiple objects and multiple players, it became more difficult. There were other permutations, too. If after a certain number of moves, for example, the players were allowed to secretly change direction, so that one group might be racing away from the lemon at the same time that the other group raced toward it, it became devilishly complex. This last incarnation was the drinking game that Erdős and his friends had played for bar money at university.

The paper was printed toward the rear of the Journal of Combinatorics, spring 1978. Andret read it late on a Monday afternoon. He stared at the poorly printed page in the small lounge where the department shelved its literature. A steeple bell chimed the hour; but he hardly heard. Someone entered the room, poured a cup of coffee, and left. Andret turned back the page and reread the paragraph.

Erdős had cited a method he’d developed to discern the probability that one of his opponents had changed direction in the game. Andret closed his eyes for a moment, then went back and read the paragraph again.

This was it. This was the way to breach the Abendroth.

He shut the journal, set it back in its place on the shelf, and looked around, as though he’d been caught at something.

NOW HE BEGAN a search. The instructive theoretical instance was the prize he sought. When he arrived at the office, he would clear the desk of yesterday’s notes, then spend the morning in thought — it might take three or four hours to assemble a single figure in his mind. In the afternoons, he would sketch, committing what he’d composed to memory. At first he tried to conceive of a figure that might invalidate the approach he’d picked up from Erdős; but then, as such figures one by one proved assailable, he began to work on examples that might support it. At home on his bed table, he kept a pen and paper, in case something came to him at night.

For months, he pushed on. The proof might require another three years of work, maybe four — but so what? To solve two great problems in a lifetime would bring him to the pinnacle of his profession. He asked one of the secretaries to buy a half-dozen cartons of laboratory notebooks. When they arrived, he numbered their bindings, then filled the pages with variations on certain theoretical shapes—3-manifolds parsed into every sort of Heegaard Splitting and torus decomposition that he could imagine.

Then he began, slowly and at first by negation, to bridge the moat around the problem. It was tedious work, but the moat needed to be crossed before he could scale the walls. In a day he could fill an entire pad with drawings. As he worked, he felt warmed through his body, down to his hands and feet, as though it were vigorous physical exercise he was performing and not a motionless feat of endurance, sitting still at his desk for hours. He kept a window open for air. Sometimes he grew breathless nonetheless, as first he sensed himself moving to the edge of the moat, then starting across it. On he went. Into numbered file boxes he laid numbered notebooks, which in turn he stacked in numbered sequence along the bare walls of the office. He didn’t need his own drawings in order to think, as did some of his lesser colleagues; but he knew that he would need them later for reference — a year from now, five years from now — when he went over the wall into the castle.

—

IN OLGA PETRINOVA’S basement apartment, the radiator was set so low that she kept a sweater on indoors. But underneath the sweater was always a dress, pleasingly stretched, and underneath the dress a queerly sewn, Bolshevik-style undergarment that he grew to crave. Between the knees and breasts it was a thick gray wool, but around the hems ran lacy sinuations of black silk that might have come from a shop in Paris.

The revived state of his work made him ravenous.

Afternoons, he visited. At the door, which was down a flight of stairs, she would greet him with her hands on her hips, her breasts thrust forward through the sweater in a way that was both flirtatious and accusatory. Was this only in his mind? At the small thrift-store table by the refrigerator they would drink a pair of bourbons, then slide the chairs across the room to wait for the sun. Her hands smelled of fennel, and there was something not quite real about the color of her hair, but her bony beauty never failed to catch him. By 2:30 or so, when the sun and the bourbon had warmed her enough, she would narrow her eyes.

In bed she liked to talk, a little before and a little after, both of which were courtesies that the drink allowed him. Before she would let him touch her, she would converse with him solemnly for a few minutes, about Soviet politics or academic mathematics, the way other women might talk about the roses or the house. She seemed to regard these moments as a test of her character. As she talked, Andret would make gentle, two-fingered tugs all the way around the hem of her dress to expose the lacy parts of her undersuit, like a child pulling candles from the rim of a birthday cake. Then he would begin kissing the frills. This she found beguiling. During sex she would quiet, moving suddenly on top of him like a lion over its prey. Her eyes stayed wide. Andret liked to keep his own closed; but whenever he opened them, there she would be, staring down at him, her black pupils gyroscopically inert. Again: leonine. He couldn’t help thinking that her gaze, even as she bent over him and strained her shoulders like a collared beast, was in fact an indictment.