A Doubter's Almanac (57 page)

—

C
LE HAD ROASTED
a chicken. I’d made a salad, from carrots and lettuce and the pink, box-cornered balls of wax that were sold by the Felt City General Store as tomatoes. The afternoon had been warm, but now the lake was dark and a wind was stirring the trees.

We were a good way through the meal when I realized that Dad had stopped eating. Cle had come in from the kitchen and was standing behind him, pouring wine with one hand and rubbing his shoulder with the other. Dad set down his fork on the table and looked up. Then he looked back at his plate. Beside him, Cle’s eyes slowly rose. After a moment, I turned around.

Peering through the porch windows were Paulie and my mother.

A Unifying Conjecture

T
HE COMBINATORICS MEETING
had been held at a plush hotel in the West End of London, which was a fifteen-minute walk from my plusher one in Mayfair. A chilly October day, not long after my first trip out to see Dad. The Thames that morning was alive with barges and seabirds. Out front of the hotel, the souvlaki vendors were hawking hot plates, the oily blue sheen of handprints streaking the lobby doors. It wasn’t difficult to spot the mathematicians as they milled among the carts, comparing prices.

The meeting itself was more lavish than I had expected. A chandeliered ballroom with nineteenth-century oil paintings on the walls. On the side tables, carefully fanned advertisements for jet-shares. In the alcoves, the murmur of fountains. I wondered why mathematicians chose these kinds of places if they really wanted to stay in their math departments.

On the Internet I’d been able to find only a meager history of Benedek Fodor. His Wikipedia page was a grainy picture and one sentence about his interests, which were wildly divergent—matroid theory, tensor theory, Riemannian geometry. There was nothing at all about his life. I’d picked up bits on my own: he was an autodidact, the son of a cheese maker from a village in the Mátra. At nineteen, the Abel Prize; at twenty-nine, the Fields. There were only a handful of articles about either one, though, and all of them had been written from the same information. He’d not even bothered to appear at the ceremony for the Fields. No wife and no children. Still shared a house with his parents. In every article, I read the same quotes, from a local precinct official and a tavern owner and a policeman, apparently the only residents of his prefecture who would speak to a reporter. They were all aware that Benedek Fodor had accomplished something significant, but none of them knew what it was.

I’d left my Wall Street clothes back at the hotel.

When I found him, he was standing outside the door of the auditorium, poking his narrow head into a dismal-looking presentation on Dirichlet series. Inside were half-a-dozen mathematicians in a room that could have held a hundred. “Dr. Fodor?” I said, extending my hand. “May I introduce myself? My name is Hans Andret.”

He kept his arms at his side. “Say his name?”

“Hans Andret.”

“
His
name.”

“Do you mean
Milo
Andret?”

“Ah,” he said. Carefully, he raised his hand. The rough palm. The dirty shirt cuff. “Perhaps,” he said, in a precisely edged accent. “Perhaps I know who you are.”

I offered to take him to lunch. He glanced down at the carpet, then nodded. We stepped away from whatever new thing was being revealed about Dirichlet series and walked down the block to a noodle shop off the square, a place I’d noted on the way in. Not for the food but because it looked quiet enough.

He ordered two bowls of soup. When the first arrived, he ate it to the bottom, then lifted the bowl to his lips and sucked down the last bit of broth. All this before we’d spoken anything beyond pleasantries.

“You understand?” he finally said, setting down the dish. “You understand what is it?”

“Understand what what is?”

“The problem.”

The waiter brought him his second soup, and he started in.

“Yes, I do.”

He grimaced.

“So here you come.”

“Yes.”

“You are the first.” He plucked a wedge of meat from the spoon and set it on the tablecloth. “You first to come ask about it.”

“I suppose I’m happy to hear that.”

“You are topologist like him?”

“No, I’m not. I work in a very different field.”

He set another piece of meat on the tablecloth. “A dirty field?”

“A what?”

“A dirty field?”

“It’s not mathematics. Is that what you mean, Dr. Fodor?”

“
Brother
Fodor.” Into the new bowl he lunged. The waiter skirted past and refilled our water glasses. “Like my countryman, Erd
ő
s—every man’s brother.”

“Okay. Good.”

“Financials?” he said over the steaming spoon.

“Is that what I do? Yes, it is.”

For a moment he appeared jubilant. Then angry. Then puzzled. He poured his water into his soup bowl, twisting off the glass like a sommelier. “Clearly you are three times more intelligent than your father.”

“Clearly not.” I signaled to the waiter for more water, then for tea. “Look,” I said. “I read your proof. I read it thoroughly. It’s very good.”

“Is logic.”

“Yes, of course. It’s logic. I understand how it pertains. I understand what it means.” I composed my features. “About the Malosz theorem, Dr. Fodor. Brother Fodor.” I cleared my throat. “It could disprove what my father proved. What he won the Fields for.”

He smiled gaily. “The Fields is a plate of shit.”

“Perhaps so.”

“Yes,” he said into the bowl. “Perhaps so. I love this. Perhaps so!”

I tried to smile.

He said, “I did for the curse.”

Another piece of meat onto the tablecloth.

“The curse of knowledge.” Steam drifted from his mouth like exhaust from a dryer. He was still smiling. “I did for the curse of humanity.”

I looked closely at him. The oily lips, the damp glasses, the starved eyes. “Ah, yes,” I said. “Of course. All for the
cause
of knowledge. The
cause
of humanity.”

“Yes, excuse!” He laughed. “
Átok. Curse
is
átok
. I meant
cause
.”

His own mistake seemed to win him over.

“Would you like another soup?”

“Yes, please!”

The waiter was quick with the third one. Fodor poured another glass of water into it, then attacked. By now a half circle of meat dampened the linens. When he’d finished, he said, “Of course I do not wish to hurt anyone reputation.” He set his spoon upright into the glass and folded his hands. “He is great man, your father. And he is the father, so you have come for defending.”

“Yes, perhaps. Though perhaps we don’t think of it exactly the same way. I’m obliged to defend him, but in other ways I don’t feel that I am. I’m obliged more to the truth. That’s what it is. I believe my father would agree with that statement.”

He looked curiously at me.

“I meant no offense, Dr. Fodor.”

“Tell me, he is well?”

“No, he’s not well. Actually, he’s rather ill.”

“I do not mean to cause harm. Particularly.”

“I can see that you don’t.”

“You are his friendly son.”

“Perhaps.”

“Why perhaps?”

“Yes, I am.”

“Do you understand however?”

“Do I understand what? The proof?”

“Yes.”

I sipped my tea. “Yours or his?”

“His. Mine is not proof. Mine is question. The maths are of your father.”

“Yes, I do understand. A reasonable part of the proof, anyway. I think I do. But I’m no topologist.”

Another silence. He looked at me suspiciously.

“Would you like another bowl of soup?”

“No. Is good.”

He turned his head suddenly, looking out the door.

Finally, I said, “Brother Fodor, may I ask you something?”

Without turning around, he said, “Yes. Please ask it.”

“Do you think my father knew?”

At that very moment the tea arrived. It was poured. Fodor turned and gazed into his cup. Held his hands in the steam. Their backs were lashed with pen marks. Finally he raised his head. “Does he knew
what
?”

“That there was an error. That the logic, at a certain point—that the logic of his proof falters.”

He leaned across the table and stared at me. With his hand he moved a piece of meat on the tablecloth: slightly left, slightly left again, slightly right. His eyes were wide, looking through to the back of my skull.

Then, just like that, he composed himself. “Is complicated proof,” he said, looking up again. “Mr. Andret. Do you know how complicated?”

“Yes, I think so. I work in probability. As I said, I’m no topologist, but I believe I do understand. What he did and what you did. Both of you.”

“Is a very, very complicated proof. You saw this?” He was smiling broadly now. Dark gums shading his molars. “Very. Very. Very. Very. Very. How many would you say?”

“How many what?”

“How many
very
.”

“Five is good.”

“Yes, agreed! Very. Very. Very. Very. Very complicated.” He grinned like a boy now. “Few understand. Few topologist even.” Then he bowed from the neck. “I no topologist, either. I think myself as nothing. Not even nothing. Only shadows of nothing.” He nodded at me, still amused. “I believe however that you are one really?”

“One what? A topologist? No.”

“Yes.”

“My question is, Mr. Fodor—may I ask you? I believe you may be one of the few, I believe you may be the only—perhaps in the world—the only one who might be able to answer this.” I leaned down and tried to capture his eyes, but they darted away. “Your paper isn’t exactly a refutation of my father’s proof. I understand that. But nonetheless it alludes to a mistake. A central mistake.”

“A problem in the maths.”

“Yes, exactly. My question, Mr. Fodor. My question is, do you think my father knew of this problem?”

“Ah.” The smile switched off like a lamp. He looked away. “You mean, at
then
moment?”

“Yes, did he know of it at the time it occurred?”

“You will not speak this, please.”

“Of course not.”

Then he thought. The way another man might have signaled for the bill, or turned his back to place a phone call, or stood to fetch the car, Benedek Fodor sat across the table from me and thought. He closed his eyes, brought his bearing straight, and sat. A pulse showed in his jaw.

After fifteen minutes—I was checking the clock—he made a little nod with his chin. “I will pose question,” he said.

“What is it?”

“Do
you
think he knew?”

I closed my own eyes. I pictured him. The boxed-up bottles. The useless drawings.

I opened them again. “Yes,” I said. “I believe he probably did.”

“Then, yes, Mr. Andret. I say that I agree. Great mathematician always knows.”

Contra Deum

D
R.
G
ANDAPUR LEANED
to the window, half crossing himself. “Does the Lord not work in unexpected ways?”

“He’s been like this since they arrived.”

With his women around him now, Dad had mustered himself. In the garden, Cle was trickling water from a bucket, and my mother was drawing a rusted hoe through the clods. Dad made the rear, bending forward as he moved up the line, wrapping long weeds in his fist and trying to pull them up. Now and then he succeeded. Sitting alongside the plot was a wheelbarrow, where he’d toss them. When my mother bent to move it a few feet, he lifted his head to watch her.

“And your mother?” said Dr. Gandapur. “She doesn’t mind the arrangement?”

“My mother is a saint.”

“Ah.” He closed his bag and turned to the window. Dad was struggling with a stalk; when it came free, he staggered, then recovered and set it on top of the pile in the wheelbarrow. He pushed himself up the line, his eyes fixed on the back of Mom’s legs. After a moment, he turned and looked at Cle’s.

“I am afraid I cannot agree,” said Dr. Gandapur.

“With what?”

He reddened. “My apologies to the good fathers of Lahore,” he said, crossing himself, “but if there is one thing I have learned in this life, it is that there is no such thing as a saint.”

—

“B
UT SHE
IS
,
”
said Paulie. “If she can still care about
him
”—she pointed out at the dock, where he was sitting between Mom and Cle—“anybody who could still care about him—oh, God, look at that—she’s more than a saint. She could be
deified
.”

We were in our old bedroom upstairs, watching from the window.

“You look good, by the way,” I said. Her outfit was divided by two sets of matched creases, as though the skirt and blouse had been pulled a few minutes ago from the same packet of dry cleaning. She was wearing heels, too, which was new for my sister, and her hair had been pinned back in a bun. “You look like the lord mayor of Zanzibar, Paulie.”

“Well, Hansie, you look like one of my savages.”

We hugged.

“I’m glad you decided to come.”

“Well,” she said, “we’ll see about that.” Her gaze dropped to my hand.

“Grapefruit juice.” I raised the glass. “Scurvy, you know.”

She laughed. Then she moved to the wall, where her bed was still made under the old yellow blanket. Next to it, under the old green one, was my own. She picked up the goldfish bowl from the table between them. “I used to keep my crayfish in here,” she said.

“I remember. Mom used to have to throw the water out whenever we got the call from the department of public health.”

She looked over at me. “What?”

“You knew that, Paulie. They stunk so bad, we had to hold our noses with clothespins when she brought them down to the lake.”

She set down the bowl. “I guess I had a dream once that they just climbed out. Maybe that’s why I forgot. I used to be afraid of stepping on them when I had to go to the bathroom.”

She leaned down and peeked under the bed.