“No,” Simon replied sweetly. ‘I doubt if I’m qualified, even after studying the problem for years. If you come up with a solution, we’ll submit it to any good mathematical journal, and their referee will decide. And you can’t back out - the problem obviously is soluble: either the theorem is true, or it is false. No nonsense about multivalued logic, mind. Merely determine which, and prove it in twenty-four hours. After all, a man-excuse me-demon, of your intelligence and vast experience surely can pick up a little math in that time.”
“I remember now what a bad time I had with Euclid when I studied at Cambridge,” the devil said sadly. “My proofs were always wrong, and yet it was all obvious anyway. You could see just by the diagrams.” He set his jaw. “But I can do it. I’ve done harder things before.. Once I went to a distant star and brought back a quart of neutronium in just sixteen -“
“I know,”. Simon broke in. “You’re very good at such tricks.”
“Trick, nothing!” was the angry retort. “It’s a technique so difficult-but never mind, I’m off to the library. By this time tomorrow-“
“No,” Simon corrected him. “We signed half an hour ago. Be back in exactly twenty-three point five hours!
Don’t let me rush you,” he added ironically, as the devil gave the clock a startled glance. “Have a drink and meet my wife before you go.”
“I never drink on duty. Nor have I time to make the acquaintance of your wife … now.” He vanished.
The moment he left, Simon’s wife entered.
“Listening at the door again?” Simon chided her, without resentment.
“Naturally,” she said in her throaty voice. “And, darling - I want to know - that question - is it really difficult?
Because if it’s not - Simon, I’m so worried.”
“It’s difficult, all right.” Simon was almost jaunty. “But most people don’t realize that at first. You see,” he went on, falling automatically into his stance for Senior Math II, “anybody can find two whole numbers whose squares add up to a square. For example, 32+42=52; that is, 9+16=25. See?”
“Uh huh.” She adjusted his tie.
“But when you try to find two cubes that add up to a cube, or higher powers that work similarly, there don’t seem to be any. Yet,” he concluded dramatically, “nobody has been able to prove that no such numbers exist. Understand now?”
“Of course.” Simon’s wife always understood mathematical statements, however abstruse. Otherwise, the explanation was repeated until she did, which left little time for other activities.
“I’ll make us some coffee,” she said, and escaped.
Four hours later as they sat together listening to Brahms’ Third, the devil reappeared.
“I’ve already learned the fundamentals of algebra, trigonometry, and plane geometry!” he announced triumphantly.
“Quick work,” Simon complimented him. “I’m sure you’ll have no trouble at all with spherical, analytic, projective, descriptive, and. non-Euclidean geometrics.”
The devil winced. “Are there so many?” he inquired in a small voice.’
“Oh, those are only a few.” Simon had the cheerful air suited to a bearer of welcome tidings. “You’ll like non-Euclidean”,” he said mendaciously. “There you don’t have to worry about diagrams - they don’t tell a thing! And since you hated Euclid anyway -
“With a groan the devil faded out like an old movie. Simon’s wife giggled.
“Darling,” she sang, “I’m beginning to think you’ve got him over a barrel.”
“Shh,” said Simon. “The last movement. Glorious!”
Six hours later, there was a smoky flash, and the devil was back. Simon noted the growing bags under his eyes. He suppressed a grin. “I’ve learned all those geometrics,” the devil said with rim satisfaction. “It’s coming easier now. I’m about ready for your little puzzle.”
Simon shook his head. “You’re trying to go too fast. apparently you’ve overlooked such basic techniques as calculus, differential equations, and finite differences. Then -, here’s -“
“Will I need all those?” the devil moaned. He sat down and knuckled his puffy eyelids, smothering a yawn.
“I couldn’t say,” Simon replied, his voice expressionless. ‘*But people have tried practically every kind of math there is on that ‘little puzzle,’ and it’s still unsolved. Now, I suggest -” But the devil was in no mood for advice from Simon. This time he even made a sloppy disappearance while sitting down.
“I think he’s tired,” Mrs. Flagg said. “Poor devil.” There was no discernible sympathy in her tones.
“So am l,” said Simon. “Let’s get to bed. He won’t be back until tomorrow, I imagine.”
“Maybe not,” she agreed, adding demurely, “but I’ll wear the black lace-just in case.”
It was the following afternoon. Bach seemed appropriate somehow, so they had Landowska on.
“Ten more minutes,” Simon said. “If he’s not back with a solution by then, we’ve won. I’ll give him credit; he could get a Ph.D. out of my school in one day - with honours! However-“
There was a hiss. Rosy clouds mushroomed sulphurously. The devil stood before them, steaming noisomely on the rug. His shoulders sagged; his eyes were bloodshot; and a taloned paw, still clutching a sheaf of papers, shook violently from fatigue or nerves.
Silently, with a kind of seething dignity, he flung the papers to the floor, where he trampled them viciously with his cloven hoofs. Gradually then, his tense figure relaxed, and a wry smile twisted his mouth.
“You win, Simon,” he said, almost in a whisper, eyeing him with ungrudging respect. “Not even I can learn enough mathematics in such a short time for so difficult a problem. The more I got into it, the worse it became. Non-unique factoring, ideals-Baa!! Do you know,” he confided, “not even the best mathematicians on other planets-all far ahead of yours-have solved it? Why, there’s a chap on Saturn-he looks something like a mushroom on stilts-who solves partial differential equations mentally; and even he’s given up.” The devil sighed. “Farewell.” He dislimned with a kind of weary precision.
Simon kissed his wife -- hard. A long while later she stirred in his arms.
“Darling,” she pouted, peering into his abstracted face, “what’s wrong now?”
“Nothing except I’d like to see his work; to know how close he came. I’ve wrestled with that problem for-” He broke off amazed as the devil flashed back. Satan seemed oddly embarrassed.
“I forgot,” he mumbled. “I need to-ah!” He stooped for the scattered papers, gathering and smoothing them tenderly. “It certainly gets you,” he said, avoiding Simon’s gaze.
”Impossible to stop just now. Why, if I could only prove one simple little lemma”
He saw the blazing interest in Simon, and dropped his apologetic air. “Say,” he grunted, “you’ve worked on this, I’m sure. Did you try continued fractions? Fermat must have used them, and-move over a minute, please-” This last to Mrs. Flagg. He sat down beside Simon, tucked his tail under, and pointed to a jungle of symbols.
Mrs. Flagg sighed. Suddenly the devil seemed a familiar figure, little different from old Professor Atkins, her husband’s colleague at the university. Any time two mathematicians got together on a tantalizing problem …
Resignedly she left the room, coffee pot in hand. There was certainly a long session in sight. She knew. After all, she was a professor’s wife.