In today’s last race, a horse named Frenchy was listed at twenty to one. Such pessimistic odds were embarrassing. Why had Frenchy been entered at all?
As usual, Nachman looked at the Racing Form and tip sheets, and then looked at the magnificent horses, particularly Frenchy. His color was mahogany with a strong reddish tint. He was big, with a deep chest and long legs. There was exceptional snap and vibrancy in the muscles of his flanks and shoulders. If you laid your ear against him, thought Nachman, you’d hear a humming. What a pity that such a grand horse was a loser. Even as he thought this, Nachman’s system pressed into mind with strange information. Frenchy would win. Nachman hadn’t wanted to know, but willy-nilly, his system said Frenchy would win, though it was statistically impossible. Nachman knew about the horse. Frenchy was clocked at record-breaking speed during workouts, but after a few early wins he’d come in fourth and fifth, out of the money. He’d lost heart for winning. This happens to a horse, Nachman believed, just as it happens to a person. There were gifted mathematicians who never achieved what was expected of them. High expectations, not mathematical problems, led to mental impotence. Frenchy was like them. He knew he was expected to win, so he couldn’t win. Frenchy was worse than a loser.
But maybe something had changed. Maybe it was the new jockey, a Mexican named Carlos Aroyo whom the owners had brought up to the States to ride Frenchy. Aroyo was reputed to understand problem horses. Knew how to talk to them. Won a lot of races. A great jockey. You could bet on him, if not the horse, but not at twenty to one. Nachman’s system couldn’t handle psychological mysteries. Problems, yes. Mysteries, not likely.
Nachman must have made a mistake in the calculations, or there were subtle factors, implicit in his system, that he’d failed to notice. An honest mistake. But maybe there was something else at work. Nachman wanted Frenchy to win because the horse was beautiful. Frenchy’s beauty and Nachman’s yearning had entered the calculations, and come up with a sentimental assertion. Dishonest but not deplorable. Merely human.
Some of the greatest mathematicians had thought, because their proofs were beautiful, they revealed the secrets of God. Nachman was moved by their visionary enthusiasm, but he wasn’t mystical. Frenchy’s numbers were simply wrong. His beauty was irrelevant. Nachman’s yearning was irrelevant. His system had exceeded itself. He wanted to figure out why, but he couldn’t do it now. The race was minutes away.
Nachman joined the line to the betting window, a twenty-dollar bill in his hand, prepared to bet on a horse named Night Flower, not Frenchy of course. In front of Nachman stood Horace and a little girl, about nine years old. She had the same skin tone as Horace, the same eyes and mouth. Obviously Horace’s daughter. She noticed Nachman smiling at her and said, “My mom is in the hospital. That’s why I’m not in school.”
Horace turned and said, “How are you doing, Nachman?”
“All right. I’m sorry about your wife, Horace.”
“Everything is fine. Don’t listen to her.”
The girl said, “He won’t let me go to school because he’s scared to be alone.”
Horace said, “Be quiet, Camille. And tie your shoelaces.” Then he looked Nachman in the eye and said, “If I stay home I’ll go crazy.”
“You don’t have to explain. It’s none of my business.”
“We went to the hospital this morning.”
The line moved. Horace turned away to the betting window and said, “Fifty bucks on Ladies’ Man to win.”
Impulsively, Nachman said, “No. Fifty bucks on Frenchy.”
Horace pulled his money back, as if he’d burned his hand.
The betting agent said, “Which is it?”
Horace said, “Give me a second, please,” and then to Nachman, “Frenchy is twenty to one. You know something I don’t?”
Nachman said, “Frenchy.”
Nachman’s voice was strong with authority, as if he knew what he was talking about. In fact, he’d never been less certain of himself, but he wanted to give something to Horace. Frenchy was all he had.
Horace turned back and slid the money across the counter. Nachman placed his own bet, then joined Horace and his daughter. They walked down the steps and worked their way through the crowd to the rail. Horace didn’t look at Nachman.
“You don’t win, I’ll give you fifty dollars,” said Nachman, regretful and anxious. It became worse when Horace said, “I made the bet. I lose, I lose. Any other day but today, Nachman. Any other day.”
“What?”
“I wouldn’t have done it.”
“You did the right thing,” said Nachman, bluffing, unable to shut up. “When Frenchy wins, you’ll make a thousand dollars.”
“I don’t need a thousand dollars.”
“What do you need?”
Horace didn’t answer, which made things still worse. Apparently, the race now meant a great deal to him. The race was on. Nachman had to force himself to look.
The pack bunched up coming out of the gate and stayed tight until Night Flower took the lead. Nachman couldn’t see Frenchy, but he heard the announcer say Frenchy was running fifth. Nachman stared strictly at the horses. He thought he could feel Horace glance at him. Then the announcer said Frenchy was coming up through the pack, running fourth, running third. Camille began screaming, “Frenchy, Frenchy,” as the horses came into the stretch. Horace placed his fists on the rail and hammered it slowly, methodically. Nachman looked at him, hoping for a connection, anticipating Horace’s disappointment and maybe anger. Frenchy couldn’t win. At least he looked better than usual, thought Nachman. Horace’s face showed nothing, but Nachman saw terrible intensity in his fists. In the stretch, Frenchy pulled ahead fast and won by three lengths.
Nachman said, “Thank God.”
Horace was grinning and shaking his head. “I don’t believe it.”
“Believe it. Frenchy could have won by more,” said Nachman with a knowing tone.
“He won good enough.”
Horace took Camille’s hand, then headed off to collect his winnings. He glanced back and nodded, and his eyes said thanks to Nachman.
Nachman went toward the exit. He’d bet intuitively on Night Flower. The horse came in last. As he entered the vast parking lot, he stopped to light a cigarette and collect himself. People streamed by on either side. Then Nachman heard his name called and saw Horace coming toward him through the crowd with Camille.
Horace said, “I don’t believe I said thanks.”
“Please don’t mention it. I’m glad I could help.”
“How’d you know he’d win?”
“A feeling.”
“Don’t give me that jive, Nachman. You knew something, didn’t you?”
“I had a strong feeling.”
“You had a strong feeling.”
“Yes.”
“Maybe you had a strong feeling, but I think it wasn’t about a horse. It was about me. I needed a sign and you gave it to me. Maybe the Lord sent you and you don’t even know that, but I appreciate what you did, and I thank you.”
“Everything is going to be all right,” said Nachman, overwhelmed by affection and sympathy. He wanted to hug Horace, but he hardly knew the man. Besides, the affection he felt was mainly for himself. Nachman said again, “Everything is going to be all right.”
“I know it is.”
They shook hands, said goodbye. Nachman walked away purposively, like a soldier. You could even say he marched, exhilarated, down a long aisle of cars, feeling too much to think clearly. He’d mistrusted his system, but it had been right, which was wonderful, if somewhat unnerving. Maybe he was a better mathematician than he knew. When he got home he would take pencil and paper to the numbers, try to figure out what happened. No. Best to leave well enough alone. Nachman suddenly realized he was marching aimlessly, not purposively. He didn’t remember at all where he’d parked. There were thousands of cars. He was confused, helpless as a lost child, and yet no less happy. Sooner or later his car would t
urn up. The feeling wasn’t so bad, the feeling of being lost.
The Penultimate Conjecture
FROM THE BEACH IN SANTA MONICA, Nachman could look across the water toward LAX and watch airplanes take off and land. The sight reminded him that he hated to travel. Nevertheless, he’d decided to make the short flight to San Francisco, where he would attend this year’s meeting of the Pythagoras Society, an international organization dedicated to pure mathematics. Nachman wanted to hear the featured talk on the Penultimate Conjecture. It would be given by the Swedish mathematician Bjorn Lindquist.
Nachman packed a clean shirt, a razor, a toothbrush, and a change of underwear and socks, though he planned to return the same day. He didn’t expect to become involved in a discussion and could think of no friends he might meet in San Francisco who would cause him to prolong his stay, but any trip held unpredictable elements. Every time you walk out of your house, thought Nachman — and then let it go. He was aware of a compulsive strain in his thinking.
Razor, toothbrush, underwear, socks, and shirt went into his briefcase, along with a writing pad and some ballpoint pens. He added a bottle of aspirin, too, as if he expected to have a headache. At the airport, he bought a package of chewing gum to help relieve the anticipated pain in his ears on takeoff and landing. He particularly disliked flying, with its discomforts and terrors; also having to breathe unhealthy gases.
The flight was uneventful except for ten minutes of turbulence. However, shortly before landing, an argument erupted a few rows behind Nachman. A passenger and a flight attendant were yelling. It was about something serious. When the plane landed, police rushed into the cabin. Nachman heard shouts amid the commotion of a struggle as he shoved past the passengers in the aisle who were gaping toward the rear.
“What the hell happened?” asked a man at the front of the plane, his eyes wild and prurient, crazed with desire for information.
“How would I know?” said Nachman, pulling his arm free of the man’s grip and pushing by him. He didn’t know because he’d been thinking about the Penultimate Conjecture, and scribbling notes throughout the commotion. He continued thinking about it as he walked through the airport to the taxi stand. Television reporters, lugging a camera, went by, rushing in the direction Nachman had come from.
The problem of the Penultimate Conjecture was formulated during the Second World War by brilliant English cryptographers who broke the German code Enigma. Germans, also brilliant, broke English codes. Obscure men, and some women, who had a knack for solving puzzles, analyzed the coded messages of the enemy so that nameless soldiers, sailors, and airmen could be blown to bits, drowned, burned alive. A proof of the Penultimate Conjecture would have no such practical consequences — at least none yet known — but for mathematicians, it was a glamorous problem indirectly associated with horrendous violence. As a graduate student, Nachman had brooded over it. The problem was exceedingly difficult. He was afraid he might spend years on it and fail to prove anything. A mathematician had only so much time. Nachman then turned to other problems, and built a reputation for solid, indispensable work. Bjorn Lindquist would know the name Nachman.
As for Lindquist’s reputation, it rested on a number of dazzling publications, all co-authored. Mathematicians worked together more than they had in previous years. Lindquist’s name appeared first on the publications he co-authored. He was considered a genius for his ability to see the implications of the work of others, and also for his devastating questions. In San Francisco, Lindquist would be the one who was questioned. The sole author of his lecture on the Penultimate Conjecture, Lindquist had taken the risk Nachman cautiously declined, making a bid for greatness, something beyond mere reputation.
Nachman, who was unusually slow, was never asked to collaborate. It didn’t much matter. He preferred to work alone. He had sometimes wondered about returning to the Penultimate Conjecture, but he assumed that even if many mathematicians engaged it seriously, none would be successful. When he was ready, Nachman imagined, the problem would be waiting for him like Penelope watching for Odysseus. Suddenly it was too late.
According to gossip, Lindquist had an amazing proof. As if the problem had been stolen from him, Nachman was somewhat hurt and suffered a touch of jealousy, but he felt no ill will toward Lindquist. He wanted only to see Lindquist demonstrate his proof. Nachman was extremely curious. He didn’t want to wait for Lindquist to publish his proof on the computer or in a paper, but wanted to see him do it in person, in public. Nothing else would have made Nachman buy his own ticket to go to San Francisco in a terrifying airplane, breathing plague.
The taxi from the airport arrived at the hotel an hour before Lindquist’s scheduled talk. Nachman sat in the lobby, reviewing the notes on the Penultimate Conjecture that he’d made feverishly during the hourlong flight. He’d worked more quickly than ever before, as if fueled by drugs, and it almost seemed, now that it was too late, that Nachman was approaching a solution to the problem. It was rather like racing west, as the sun goes down, to make the day longer. If he only had a little more time — but why should he care? The problem had been solved by Lindquist. In a sense, there was no longer any problem. Immersed in the nonexistent problem, Nachman noticed a crowd of people heading toward the auditorium where Lindquist would talk. Thrusting his notes into his briefcase, he joined the crowd. He felt humble, like a member of a religious congregation. The room was large, and almost every chair was taken. A blackboard had been wheeled to the front. As in a theater before the curtain rises, the crowd was full of spirited chatter.
Nachman took a chair beside a skinny young man who wore a blue suit of cheap synthetic material. He noticed that the jacket was too big in the shoulders and the lapels seemed asymmetrical, but it was a new suit and the young man obviously felt good in it. He smiled at Nachman, revealing large, vigorously thrusting teeth. His eyes were greenish yellow, a feral hue, and slanted. They had a strange intelligence, and a fine hot savoring look.
The man said, “You’re Nachman.”
Nachman nodded.
“I’m Nikolai Chertoff. How do you do? I heard you lecture in Cracow.”
They shook hands, Nachman muttering for no reason, “I don’t like to travel.” Chertoff’s eyes were unnerving. To turn away or modify their attention, Nachman asked, “Where are you from, Chertoff?”
“Moscow Communication Labs. You know me?”
The eyes and their attention were unchanging.
“I’m sorry.”
“Don’t be so sorry. Nobody knows me. I published one paper in a Russian journal of robotics. Who read it? Nobody.”
“What is the paper about?”
“Of no importance. Who cares? But everybody knows Nachman. It should be Nachman who solved the Penultimate Conjecture.”
“I walked away from it many years ago. Lindquist solved it.”
“If you say so.”
“What do you mean — if I say so?”
“Do you believe Lindquist solved it?”
“Of course.”
“If I were you, I would be inclined to kill, not believe.”
“Kill?”
“Look, here he is. Your worst enemy.”
There was a flurry of applause as Lindquist walked to the front. Nachman was startled, but with a surge of anxious pleasure, he joined the others, including Chertoff, in applause. Nachman whispered, “Why did you say that? My worst enemy.”
“If he’s a mathematician, what are you?”
Chertoff’s face assumed an expression of disdain, pretending to the attitude he expected in Nachman.
“There’s room for more than one mathematician, Chertoff.”
Chertoff grinned. “Sure, sure. You’re in the same field, and you do the same work. But why not? Like Newton and Leibniz. Maybe five other mathematicians also discovered the calculus. Plenty of room.”
The greenish-yellow eyes narrowed with laughter. As Chertoff’s head tipped back, his sharp, prominent teeth pointed at Nachman.
> Nachman laughed, too, though with imperfect delight. Chertoff’s comments had touched a nerve. In truth, Nachman’s feelings toward Lindquist were darkened by thoughts of himself. He should have taken the risk. He should have been more like Lindquist, more manly. “Enough, Nachman,” said Nachman to himself. “You didn’t fly to San Francisco to reproach yourself.” Letting it go and getting free of himself, Nachman got hold of himself.
Lindquist was tall and lean and pale. His blond hair was streaked grayish-white. He had cold, light-blue eyes and a wide tragic mouth, bent at the corners as if it might release a wail. He began abruptly, pacing before the blackboard as he talked, stopping to write equations. Evidently, Lindquist had chosen to suggest the nature of his proof rather than exhibit it in exhaustive detail, but each time he wrote an equation he was taken by a rush of excitement. Unable to contain himself, he proceeded to offer more, then more. His fingers squeezed the chalk hard, and it broke. He continued with the broken piece, and then it, too, broke, and he snatched up a fresh stick. His English was first-rate, Oxford faintly mixed with Stockholm. The audience, submerged in silence, was like a many-eyed crocodile, the body suspended underwater, inert. The chalk squeaked and pulverized as Lindquist dragged it against the board.
Beautiful work, thought Nachman. Tears formed, blurring his vision slightly, but then — actually, within the first two minutes of Lindquist’s demonstration — even as Nachman thought it was beautiful, he’d begun to suffer a dark excitement. He tried to ignore it as Lindquist progressed. He even nodded once or twice, a motion of assent to Lindquist’s voice, and he exerted himself to focus strictly on Lindquist’s demonstration. But the excitement persisted, clutched Nachman like a nameless, primordial apprehension.
The Collected Stories Page 40