The Year's Best Science Fiction 10

PROBLEM CHILD Arthur Porges

If relief from pain can be found in absorbing mental work, then the mathematician is among the most fortunate of men. In every direction, beyond the well-cultivated plains of basic analysis, lie the unsealed peaks of the great problems, attacked, some of them for generations, and always without success. And surrounding them, or lying over the horizon, out of sight, whole new empires awaiting their inevitable conquerors.

Professor Kadar was like a man within sight of Paradise, but unable to find a path through the impassable terrain that blocked his way. He had patiently tried hundreds, all promising, only to be confronted, at the last moment, by the same yawning chasm that indicated No Highway.

Now it had checked him again. He dropped the pen, sighed, and put his head in his hands. There was a small, sucking sound, and the professor looked up. Briefly, he had forgot; that was one virtue of the thorny analysis that sprawled over a ream of yellow second sheets.

How long had the child been there? He came and went so silently these days. Perched on the tall chrome bar stool, so incongruous a seat for a three-year-old, he slumped like a Buddha across from his father. And always with that same inward look. The wizened face, still wearing that aged-in-the-womb expression of the newborn infant, seemed vaguely Oriental to Kadar today. Not a Mongolian idiot, definitely, the clinical psychologist had assured him. Just retarded.

The professor’s eyes, deep-socketed and melancholy, met Paul’s, which had, he felt, an unmistakable slant. He was conscious, more strongly than ever, of his son’s sweetness and placidity. Odd that they should be so characteristic of the mentally retarded child. As if nature desired to compensate the cheated parents. Not that it was ever compensation enough. And in this case, when he remembered—could he really forget, even for a moment, even when that path to Paradise seemed open?—that Eleanor had died to birth this little vegetable, it was no comfort at all.

The slanting eyes, small and dark, turned inward again. Oriental or gypsy? Many Hungarians had Romany blood. Or was the doctor—all those experts he had consulted—wrong, and Paul Mongoloid?

Names, Kadar reflected bitterly. What did they mean? In mathematics, you called something a ring, a cycle, an ideal. What you named it was unimportant; all that mattered was its place in the structure—never things, but the relations among them; those were what counted. What was Paul’s relation to the world, now and in the future?

For the present, he was only a baby; in many ways, less than a baby. Mrs. Merrit was a kind, motherly woman; not intelligent; not educated; but warm. Paul obviously liked her, if he responded to anybody, which was doubtful. His normal expression, in an adult, often suggested profound boredom.

The professor thought about the tests—the endless, expensive tests. Colored doodads, blocks, strings, geometric forms to be matched—and the brisk, young men and women who presided over the rituals. Paul had confounded all of them; Kadar felt a perverse glow of satisfaction at the thought. The boy didn’t make mistakes; instead, he simply refused to cooperate. Of course, it was nothing to rejoice over. Apathy meant even more severe brain damage, the doctors seemed to think. And Paul’s electroencephalographs certainly were abnormal, suggesting those of an advanced epileptic.

The child nibbled at his lips again, making that tiny murmur in his throat. The eyes turned outward briefly, met Kadar’s somber gaze, then Paul slipped clumsily from the high stool and padded from the room, moving with the rather unbalanced gait of a sedentary elder.

Off for some lunch, Kadar thought. Why didn’t Mrs. Merrit call the boy, instead of letting him set his own schedule? My fault, he told himself immediately. I’m letting her raise him, while I try to forget Eleanor—yes, and him, too—in my work. On the other hand, why impose disciplines on a child who never rebels? The sweet placidity of Paul was reflected in his childish routines. He ate whatever was given him—but only if hungry. He never cried; always lay quietly in bed when put there; and seldom got out until Mrs. Merrit came for him in the morning, although she mentioned occasionally, with some wonder, that he often was awake, stretched out under smooth bedclothes, with his eyes wide open.

Aside from that, his only quirk was the tall stool. At the age of two, he had already shown his preference for the flashy thing, climbing it to overlook Mrs. Merrit at her chores in kitchen and dining room.

Then, after the professor, acting on impulse, put the stool in his study, across from the big desk where he worked, Paul had come to prefer that location. Every day, for at least three hours, while Kadar scribbled away, the child sat there, sometimes apparently fascinated by the motion and hiss of the pen on paper, but more commonly with his eyes blank and unfocused.

Mrs. Merrit, naturally, thought this scandalous and unhealthy. For many weeks she tried to interest the child in a variety of toys, but without success. What the trained psychologists had been unable to accomplish, Kadar thought wryly, was not for a woman like his housekeeper to bring about between cooking and floor-mopping.

Even retarded children may be good artists. But when given crayons and big sheets of paper, Paul had made a few tentative dabs, very awkwardly, and lost interest.

The boy must at least get some exercise, Mrs. Merrit insisted, so the professor bought a jungle gym, and, to his surprise, Paul condescended to scramble about in the thing for half an hour now and then. But Kadar suspected it was that same urge to attain purely physical elevation—did the child seek a height equivalent to that of the adults around him? Was that the only break in his apathy?

Paul came back to the study, and approached the stool.

“Come here, son,” the professor said, moved to try establishing a relationship that always eluded him.

Meekly, in silence, Paul padded over. Kadar looked into the slanted eyes, searching for some kind of warmth. There were undoubtedly little lights inside, but they conveyed nothing to his understanding. He put one hand on the boy’s silky hair, ruffling it, and Paul stepped back—not alarmed, but somehow rejecting the act. The professor felt a sudden urge to hug him, but quelled it, he couldn’t have said just why. Paul went back to the stool, scrambled up in his queerly uncoordinated way, and sat there, lumpishly, his eyes again turned inward.

It came to Kadar, then, that Eleanor had sometimes worn such a look: an expression of deep self-communion. And yet—and yet—Uncle Janos had also looked that way often—Crazy Janos, who bungled everything he tried. Come to think of it, didn’t Janos have an Oriental cast of features, too? It was all so far back, and in Hungary; Kadar couldn’t remember. Besides, Janos died while his nephew was still a child.

The professor reached for a fresh sheet of paper, and began again, searching for the high road to Paradise. Fifty pages of the most advanced research—a new field of mathematics; a place beside Gauss, Abel, and Galois— hung on his finding that path. If a certain sequence converged to an irrational number, the key theorem and all that it implied was valid. And still the proof eluded him. Enough; enough; no more today; his head was on fire. Return with a fresh mind, like Poincare and the Fuchsian Functions; that was the only hope, now. But he knew it wouldn’t solve anything. Only a fresh approach, something revolutionary, could smash through the iron wall.

Swaying a little, almost like Paul in his gait, Kadar left the room. He mixed a stiff Martini, drank it slowly, and felt some of the tension go out of his muscles. Mrs. Merrit hastily made him a hot snack; she was resigned to his behavior, and knew better than to try changing it.

“Tell me,” he asked her, “has Paul ever tried to say anything yet? Anything at all?”

“No,” she said, her eyes full of sympathy. “Just little noises in his throat. But he understands; I’m sure he understands. You know how good he is about doing what we tell him.”

“I know,” Kadar said darkly. “That’s hardly normal, either. No mischief; no rebellion; nothing. A vegetable— sweet, insipid; like a spoiled melon.”

And he thought of Eleanor—vital, alert, bubbling: beauty without slickness or affectation; warmth without sentimentality. This was the child not of Eleanor and himself, but Crazy Janos: that was a typical joke of heredity—genes and DNA and Janos ending in Paul Kadar, whose father had five paragraphs in “American Men of Science.”

He left most of the lunch untouched, and went back to the study. I won’t work, he told himself; but maybe just glance over the equations again. Let my mind refresh itself; no use to keep prodding it. Deep inside his brain a tiny alarm bell was ringing. What if the theorem is false? What then? Fifty pages of meaningless squiggles: a magnificent structure with no foundation.

He entered the study, and walked to the desk. The top sheet lay there, mocking him—but what was this? The last equation was crossed out, and above it there was a long line of pencil marks. Almost like mathematical symbols, but not—by God, upside down!

Bewildered, he reversed the sheet. For a moment the writing still seemed without content, then Kadar felt his heart contract like a clenched fist. A new integral transform—powerful, elegant, and startlingly original. It would crack the tough kernel of the problem as lightning shatters an oak.

He looked up, wild-eyed. Paul met his gaze squarely. The slender throat was working; the lips moved.

“Like that ... it has to be like that. Other way ... the pattern is ugly,” the boy mumbled, his voice a queer, high-pitched stammer, as if he had to claw the words out of a diaphragm never before used.

Kadar, still uncomprehending, stared at the writing again. Upside down—because that’s the way Paul, on his high perch, always saw the symbols. Their validity didn’t depend on how they were written, of course.

An illiterate might conceivably, while listing words, write a simple declarative sentence. With luck, he might even hit upon a compound one, perfectly grammatical. But what were the odds against his writing immortal poetry, like: “Rough winds do shake the darling buds of May”?

Kadar looked at Paul again. The boy didn’t need blocks or crayons because his mind saw every concept with perfect and immediate clarity. Just sitting on the high stool, he had absorbed a complete mathematical education from Kadar’s work. Before that, he had overlooked Mrs. Merrit, but found nothing to stir his intellect. As for speaking, no doubt that, like his gait, was a matter of physique, and relatively unimportant to such a mind.

The professor felt a great surge of joy; yet, in a moment, it was tempered with sorrow. Paul was a monster, but a superior one. He was probably above—or beyond—love in the human sense. But their minds could commune, and maybe that was the best communion of all.