A Doubter's Almanac (13 page)

“Here,” he said, reaching. “Let me get the door.”

He didn’t exactly fall, but when he righted himself she was holding him by the elbow.

“Are you all right?”

“Perfectly.”

“Are you sure?”

“Of course I’m sure. However, Assistant Professor Andret regret not delivery today lecture to Downtown Club for Pisa this evening—as I choice, you’re welcome.”

She laughed.

He bent to retrieve his hat, and when he straightened he found himself standing against her again. She moved up one stair.

“All right, Assistant Secretary. Maybe is true that Assistant Professor Leonardo Fibonacci he self—maybe I could just sit down for a second, Helena. I think I need some water.”

“All right. You can come up. But just for a minute.”

As they climbed the stairs to her apartment, she kept turning around, saying, “Are you really sure you’re all right?”

“Yes,” he said, pulling himself up the banister behind her. The staircase went on and on. “But your railing’s loose.” He rattled it, although now it seemed perfectly tight. “Heisenberg,” he mumbled.

Her apartment was on the top floor. When they finally reached it, he removed the fedora and held it against his chest, like a minister at the home of a parishioner. As soon as she’d succeeded in opening the locks, he followed her inside and hung it on the hook.

“Here,” she said, pulling out a chair from the small table. “Sit down. That was a long climb. I’ll get some water.”

“Water is my enemy,” he said solemnly.

This silenced her. He had no idea what he’d meant. But he knew she wouldn’t ask for an explanation. At this point, he could have spoken about Hilbert manifolds and she wouldn’t have asked for an explanation. In the scant kitchen she pulled a glass from the cupboard and rummaged in the freezer until she found an ice tray, then had trouble freeing the cubes from it. He ignored the chair she’d pulled out and sat down on the couch instead. In front of him on the coffee table was an art book. The first few pages were oil paintings—nonsense art or maybe abstract landscapes. He set it down and looked around. The apartment itself was singularly tiny. A couple framed prints propped on the mantel above a bricked-in fireplace. A desk crowded into the hall. Underneath it he noticed some kind of uncombed terrier shivering on a mat. He hated dogs. Through a half-closed doorway, he saw the bed: a single.

“Well,” he said. “What were we saying?”

She came in from the kitchen, handed him the water, and took a seat at a miniature stool—to his surprise, it slid out from the wall like a subway bench. The couch he was on was short but deep, and at the far end of it he felt himself sinking into the cushions. After a few moments, he moved to the center. He spilled some water but moved on top of it. From her spot on the wall, she was saying something about the secretaries in the department, her legs crossed at the thigh and her hands clasped over her knees. He realized that she was afraid to let a silence fall. He himself could think of nothing he’d appreciate more.

Next to the door of the bedroom his eye fell on a crucifix. It hung on a chain from a hook above the light switch.

Well.

He felt a burst of sourness. The illogic of religion had always galled him. It occurred to him that the whole evening was going to be a waste.

At that moment, however, she went to the cabinet and returned with a bottle of wine.

“Would you like me to open that?” he said, struggling up from the couch. At the table he took a closer look at the cross. It was a dime-store thing. The hook was an old nail. This was better. He turned and focused on the wine label, wiping off the dust. It was burgundy.

He’d never actually tasted burgundy.

“All right,” she answered at last, although he’d already ripped off the foil and pushed the opener into the cork. “Go ahead and open it. I doubt it’s very good. But it’s more my speed than what you ordered for me in the bar.” She sat down on the subway seat. A moment later she rose again and went to the record player in the corner. After a short pause, the air was decorated by the first notes of a piano sonata.

—

I
N THE MORNING,
he let himself out early. The sun hadn’t even risen as he closed the apartment door and stepped into his shoes in the hallway. Though he knew nobody else in the town of Princeton, New Jersey, he hurried home with the hat pulled low over his face. At the edge of her neighborhood, he turned and made for the woods. He shouldn’t have taken the crucifix, but it was in his hand now. In the cool shade of the first stand of trees, as dawn was coming through the boughs, he leaned down quickly and dropped it into the mat of rotting leaves.

Occam’s Razor

A
T THE FIRST
meeting of the faculty that year, Knudson Hay, the chairman of the department, introduced all the incoming assistant professors, who were seated in a line of folding chairs across the front wall of his sizable office. Milo’s chair stood in the middle of the group. When his name was called, he nodded briefly, as had everyone before him. But then, from somewhere in the rear, a voice called out, “Congratulations, Andret.”

When he looked up, he couldn’t discern the speaker. But he noticed that a few of his first-year colleagues had reddened.

—

T
HERE WAS A
pause, then in the background the clearing of a throat. The phone had rung while he was fixing dinner. It was six in the evening. He recognized the formality of the old man’s tone.

“Listen, Andret,” Hans Borland said neatly, “I was calling to inform you of something. First, how’s that friend of yours?”

“I don’t know who you mean.”

“The Wells girl. Jim Wells’s daughter. Cleopatra.”

“Oh, that—well, that’s over, Professor.”

“I’m sorry.”

“Don’t be.” Through the window, he watched a girl walk past in shorts. “I’ve moved on.”

“I’m sorry to hear it, all the same.” He paused. “Listen, Andret, I recommended you for this position, you know that, right?”

“I know, Professor. I’m grateful.”

“Comport yourself with dignity there, will you? Do what you’re capable of. It will reflect nicely on both of us.”

“I will.”

“Are you carrying the briefcase?”

Down the hall he could see it, overturned beside his bed, a sheaf of student assignments spilling from the pocket. “I have it right next to me,” he said.

“And you’re managing your affairs as we discussed?”

“Yes.”

“You’re a professor, now. Not a graduate student. People notice.”

“I’m an assistant professor.”

“Well, yes. For the time being.”

Borland coughed then, rather harshly, and covered the mouthpiece. When he came back on, he cleared his throat again. “The Malosz theorem,” he began. “If I’m not mistaken, Andret, you believe it was a fluke. You consider yourself undeserving.”

Andret felt the truth of the words.

“Perhaps you feel like a fraud,” the old man went on. “This is entirely natural. Believe me, I’ve seen it plenty of times before. Lars Hongren was a fraud.” He paused. “You, Milo Andret, are
not
a fraud.”

Outside the window, the girl in the shorts disappeared around the corner, and at that moment exactly, the evening turned into night. Andret became aware of his own figure in the glass, of the twisted white catenary of the phone cord bridging the darkness from his cluttered desk, crossing the bookshelves, and arriving at the pale moon of his face.

“Yes, I see,” said Borland. “Well, listen now, Andret. You have a limited amount of time. That’s what I called to tell you. To
warn
you about. I’d hazard ten years, on the odds. Then things will begin to cloud over. I was at the doctor’s yesterday. I’m sixty-two years old now, did you know that? I guess one can’t expect a clean slate forever.”

Milo heard the clink of a glass.

“Is everything all right, Professor?”

“Well—thankfully—yes, it is. But I did have a scare. I jog five kilometers every day, you know. Have for more than twenty years.”

“You’ve nearly run around the world, then.”

The old man laughed. “At the equator, that’s correct. At Berkeley’s latitude, I’m actually on my second lap. But I mention it because it’s set me to thinking. How old are you now, Andret? May I ask?”

“Thirty-two.”

“Well, you have five or ten years then, in all probability, and then perhaps a standard deviation. Two at the outside.”

“Yes, sir.”

“To finish your work.”

“I understand.”

“Your
life’s
work, Andret. You need to start something new. Something as great as what you’ve already done. Preferably,
greater.
”

Andret paused. “I’m already working on something.”

He could hear the old man breathing.

“What I’m trying to tell you,” Borland said, “is that the Malosz theorem was merely the beginning of what Milo Andret can do. Of what he
will
do.”

Andret couldn’t speak.

“Just the beginning,” Borland repeated.

“Yes, I heard you.”

He hadn’t intended to sound so sharp.

“I see,” said the professor. After a time, he added, rather clumsily, “Well, that’s all I wanted to say. Goodbye then, Milo.”

—

A
T THE OFFICE
now, he had difficulty facing Helena Pierce. He quickly discovered that she had the same difficulty facing him.

By the end of his first month, they hadn’t even spoken again. Was she angry? He didn’t know. Wounded? Was it a triviality to her? He had no idea. Could it have been the crucifix? No—if that was what was bothering her, she would have mentioned something. It could have been that she was merely shy. Certainly she was inexperienced, and more than likely she’d been drunk. They’d both been.

Whenever he appeared in the mathematics offices now, she was there at her desk, but always at the rear, her head lowered over her typewriter. It was as though she could sense him through the two concrete walls, the carpeted anteroom, and the pair of frosted-glass doors that led from the hallway. When he entered, the blonde secretaries in front continued their noisy laughter and their cheeky asides, but Helena Pierce no longer rose to defend him.

—

H
E COULD WORK
on something related to the Malosz, as plenty of other mathematicians would have done in his situation. But Hans Borland was right: there would need to be something greater.

That winter, as he perused the journals, his attention landed on the work of a man named Ulrich Abendroth, a midcentury Austrian who at nineteen had proposed an eminent problem. Abendroth’s precociousness itself had been the stuff of legend: at sixteen he’d been appointed to the faculty of both Cambridge and the École Polytechnique; at eighteen he’d fathered two sets of twins with two different women on two sides of the English Channel; and at twenty, a month after he’d proposed his conjecture, he’d been found dead in a coffeehouse. His problem had entered the canon with a flourish of intrigue. In fact, if mathematicians had believed in any sort of superstition, they might even have considered it cursed. It was famously difficult—very likely as difficult as the Malosz—and in the years since its appearance it had resisted every advance.

All of this sat fine with Andret. He
was,
in fact, superstitious—but in reverse: what was supposed to be cursed attracted him.

The central puzzle of the Abendroth conjecture concerned a subset of Whitehead’s CW-complexes that were infinite yet finite-dimensional. Clear enough. Though it was considered part of algebraic topology, Andret had a feeling that its solution—if it was going to be solved at all—would come not through equation but through the ability to visualize strange and unearthly shapes.

At this he was quite adept.

In those days, as it happened, the broader discipline of topology was at the apex of its ascendance. The field had become prominent at the turn of the century with the publication of “Analysis Situs,” and in the following decades it had only grown in eminence, not just among mathematicians but among scholars of every branch of the natural sciences. The years leading up to his arrival at Princeton had charted themselves perfectly for the wave of new thinkers who were beginning to populate the upper levels of the universities. These men were no longer bound by symbology but instead spent their days constructing complicated hypothetical shapes that had never before been seen—nor likely imagined—by the human mind. Topologists built undrawable figures in their imaginations, then twisted and folded them. They devoted their time to inventing a cosmology in which the world as it was known—the world of earth and sea and sky—was no more than the three-dimensional rendering of an infinitely higher-dimensional space, much as a two-dimensional movie screen might appear to hold a three-dimensional tableau. In the new paradigm, sensory experience counted for nothing. Pure mathematical ingenuity—the ability to ignore common understanding, to construct a world solely from derived principles—had begun to supersede empiricism.

The field itself required a particular mode of thinking. Not merely the standard mathematical skills but a visual dexterity that could retain complex constructions in the mind for long periods of time, transforming certain parameters while leaving others intact. It was a strenuous and disobliging intellectual endeavor, a sea change of thought in which the brain performed multidimensional mapping. There were topologists who could build architectural structures in their imaginations, then turn them over, then flip them inside out, then spin them around, then open them up and go inside them.

Andret’s own gift for such internal rendering seemed to him to be a derivative of the old positional sense that had once located him in the woods. And not only did it guide him now when he pictured objects in his mind, but also when he drew them with his pencil. He found that he could begin any topological rendering at the upper corner of a sheet of paper and proceed diagonally down to its opposite. No matter how complex the figure, no matter how many layerings of foreground and middleground and background interceded, he could steadily bring to life an entire theoretical construction, with all its dapplings and stipplings, depicting shadow and volume and transformation, in a single, angled pass. It was an astonishing aptitude, really. As far as he knew, nobody else in the department possessed it.