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About mathematics Annabelle herself knew nothing. She liked bourbon, though, and after their first meeting in town they’d been drinking it regularly at the house. With the children in school they could lounge together on the plush European mattresses upstairs. There were three guest bedrooms on that floor alone, but to his surprise she preferred the master suite, despite the bowl of cuff links on the dresser there. He indulged her preference. The room took up the full width of the house and on two sides looked out on nothing but forest, which allowed him to rise when they were done and gaze out the window like a baron.

His mind in those moments was suffused with calm, the work gone for a few moments of a day. He found Annabelle a refuge and partook of this refuge on every weekday morning that he could. She was strongheaded and not particularly bright — for Princeton, anyway — but unfailingly generous.

As a lover she was somewhat demure — maybe this was her prairie upbringing — and like Olga, she required conversation. With Annabelle, though, it was always about him. His work. His plans. The detailed narration of his endeavors, both professional and quotidian. In this way she reminded him of Cle Wells, constantly fitting him to an ambition that seemed somehow to have become her own.

In bed, she liked to start out prone. He would begin by kissing her spine through her dress as he answered queries about his life, moving slowly to the neighboring regions — her smooth shoulder blades, the moist rise of her neck, the hot sides of her breasts as he released them from the fabric. Her skin smelled of mint. As he moved, she continued to question him, her eyes closing finally as he began to answer only in grunts, her hand reaching for his hair. When she was sufficiently aroused a hush would finally settle and then with a sigh she would roll over gently onto her back, like a doe turning in leaves.

How he loved that bed! Yevgeny Detmeyer, as it turned out, spent an inordinate amount of time abroad, in Tokyo and Zurich and London and Berlin and Zagreb. He was an extroverted and unstoppable public personality, a highly regarded macroeconomist, and an avidly sought consultant on international politics. And as Andret discovered one afternoon while thumbing through the Princetonian in the man’s own kitchen, he was also regularly mentioned as a candidate for the Nobel Prize.

The Nobel Prize!

That was Princeton for you. The fact revved his libido.

One day near lunchtime, from the side window of the bedroom, he watched the two Detmeyer girls clomp up the porch steps with their bookbags. Annabelle sat up in bed and gasped at the sound: she’d forgotten that they’d been let out early from a field trip. As she rummaged in the closet for an outfit, he made for the door, pulling on his clothes and hurrying down the back set of stairs.

After that, she wouldn’t see him past eleven in the morning. But this wasn’t a problem. In fact it made things simpler. He learned that day that if he took a diagonal through the woods and came out of the trees alongside the soccer fields, he had time to stop at Clip’s for a pick-me-up and still be at Olga Petrinova’s before the afternoon sun came through the window.

Time and Chance

IN KEEPING WITH the fickle nature of the work, however, his optimism soon began to wane. On most mornings, he woke with a vivid idea of the day’s endeavor, but he’d also begun to recognize that his new state of hope was also a state of agitation. And the agitation wearied him.

He’d been at Princeton now longer than he’d been at Berkeley. At the mixers every September, the new hires were already in the habit of asking him to draw their portraits, a practice that had grown to become something of a welcoming rite into the department of mathematics. He’d taken to performing it as a kind of joke: he’d look at the face of whichever new assistant professor had approached him, then look down at the paper, then back up at the face, then back down at the paper, drawing steadily until at last he presented the recipient with a perfect rendering, depending on the man’s subject, of Descartes, or Pascal, or Grothendieck. The likenesses were framed in half-a-dozen offices around Fine Hall.

On and on he worked. He walked around campus worrying the lessons of the Erdős paper like a man fingering a wound in his side. It seemed possible now that the paper’s conclusion would be no more crucial to his final push against the Abendroth than any of a dozen others he’d read. Yet still it battered him. He was certain there was a clue there, even if he’d not been able to name it. That was the nature of mathematics. You mined a hunch until the hunch was proved either right or wrong. So far, he’d proved it neither.

In the meantime, he’d befriended a man at Clip’s. DeWitt Tread was a former member of the mathematics department who’d either been denied tenure or resigned it and now worked as a fabricator for the School of Engineering. This mattered nothing to Andret. What mattered, at least at the start, was that Tread liked to drink. He was from an aristocratic East Coast family and had the facial features of a white-wigged colonial governor, but his life had been one long rowdy procession of drugs and booze and shady business deals that had left him with two teeth broken at the front of his mouth. Like Andret, he wore suits at Clip’s; but Tread’s, unlike Andret’s, were worn to a shine. He owned a huge, ruined house in Princeton Junction and filled it with all kinds of junk that he was always either buying or selling. Most nights, he closed the bar. They began spending time together.

The thing was, Andret could talk to Tread about the Abendroth. There were probably no more than a dozen people in the world who were even capable of understanding the question that the problem necessitated solving; yet Tread, a nodding drunk who had to pay for his drinks before the bartender would pour them, turned out to be one of them. It was preposterous. A derelict in a workingman’s dive a half mile from Andret’s office. Yes, a mathematician; yes, a former member of the department; yes, a man reputed to have an Erdős number of 2—which, in a manner of speaking, gave Andret an Erdős number of 3—but still, a disheveled, nearly wordless man who’d sat down next to him by chance one day in a cocktail lounge.

At Clip’s, Andret would begin a summary of his day’s work, sometimes drawing shapes on the tiny napkins, and Tread would listen, noting any unwarranted assumptions that might have been made. All this over doubles, no ice. Andret’s tab. Tread could outdrink him 2:1, but Andret paid because he found his friend’s analysis so helpful. Sometimes acutely so. Reading a mathematical paper was difficult under any circumstances, but analyzing at speed another mathematician’s thoughts was next to impossible. Yet Tread could do it. He was, Andret sometimes thought, a genius.

He also appeared to have no instinct at all for his own advancement. Mathematicians were always celebrating their efforts as communal — and great collaborators like Erdős were beloved all over the world — but Andret himself had never wished to take part in any type of cooperation. He was going to vanquish Ulrich Abendroth entirely on his own. And when he did, he was going to share the credit with nobody.

As Andret talked about the problem, Tread would slump in the stool next to him, his lips parted to show one of the broken teeth, and stare at the rail of the bar. He appeared not to be listening at all. But if even the tiniest increment of mathematical rigor was evaded, he’d look up immediately, his veiny eyes brandishing a glitter. He didn’t even have to speak; his expression alone — combined with the fact that Andret, too, possessed an inborn sensor for even the most trivial lapse of logic — was enough to point out the error that, by the following meeting, Andret would have carefully readdressed.

Yet Tread never spoke of collaboration. He never spoke of working on a paper together.