—
AT THE BACK of his mailbox one morning, a sealed envelope with his name on it.
I was buying a humidifier for the office. (I never shop there myself, the prices are ridiculous.) If you need anything related to the department I’m available and hope you will ask. I’m not ashamed about what happened but I’m not proud on the other hand, and it’s better if we just ignore whatever it was and pretend it didn’t occur. (Of course I mean better for both of us.)
Dogs and Horses
THERE WAS NO denying it: time had passed, yet he’d made almost no progress on the Abendroth. He wouldn’t be able to overpower it the way he’d overpowered the Malosz.
Tactic rather than force: that’s what he would need.
At first consideration, the problem appeared almost facile; but the essentials quickly hid themselves. He’d begun to conceive of the proof as a fortified castle pierced by ten thousand brightly painted doors, each of which was designed to deceive him. All ten thousand would open — this wasn’t the issue — but so far, none of them had allowed him entrance.
Perhaps none ever would.
After a year and a half of effort, he realized that it made sense to limit his aspirations. Perhaps it would help to give up on a solution altogether and focus instead on merely locating the proper vulnerability.
He also understood with a dull sense of foreboding why so many gifted men had been circling the problem for most of a century. The work to all of them must have seemed a seductive lover. By now he’d grown accustomed to waking in the middle of the night with some electrifying premonition, to hurrying through the dark to the mathematics building, to laboring alone in the predawn hours while the radiators clanged around him, as though being hammered by Ulrich Abendroth’s own imperious ghost. But over the course of the pale, tree-obscured sunrises, which turned his office from blue-gray to dusky orange to a brightly nauseating yellow, his thrilling premonitions uniformly faded. He could find no passage in.
—
ONE AFTERNOON NEAR the end of his second year at Princeton, there was a knock at his office. He ignored the interruption; but a moment later it came again. When he opened the door, a woman said, “Oh! You’re here then.”
“Forgive me,” said Andret.
She was well dressed, almost prim — his own age or slightly younger. Dark red heels and a somewhat-dowdy outfit of a related color. Although he never trusted his memory of people, he was fairly sure he’d never seen her before. “I must have been lost in my work,” he said.
“I’d give anything for that.”
He looked again. A rather pretty face. Maybe a little rebellion in the eyes. No: they’d certainly never met. “Would you?” he said.
“You must be busy. I just wanted to see if I could make an appointment. But I can come back another time.”
For a woman who’d arrived uninvited she seemed insistently timid. Yet on the other hand she made no move to leave. In fact, she appeared to keep herself before him by some calm demonstration of will, like a mystic holding a finger in a flame.
He lifted a box of work off the visitor’s chair and gestured her in. “The problem,” he said, taking the seat at his desk, “is that I might be even busier the next time. You’d have to estimate those odds, too. What may I do for you?”
“You’re absolutely sure?”
“No.” He shook his head. “Nothing is absolutely sure.” He smiled. “But now’s as good as ever.”
She sat down across from him and returned his gaze. Her name was Annabelle Detmeyer, and she was an associate professor in history. “My husband, Yevgeny Detmeyer”—she paused—“my husband is the chair of economics and the co-chair in political science.”
“Ah. A double threat.”
She laughed, pleasingly. Her laugh wasn’t so dowdy.
“How can I help you?”
“I just wanted to learn what a mathematician does,” she said. “It’s so different from what I do, and I’d heard so much about you. I read an article about the Malosz theorem, and I was intrigued. I actually tried to read it. The proof itself, I mean.” She laughed. “I got about a half a sentence in.”
“Well, history might be beyond me, too.”
“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.