The Number Devil: "The Seventh Night"–"The Eleventh Night"

But Robert knew exactly what he had in mind and had no intention of telling his mother about it.

“Child’s play,” he said.
“Don’t be so cocky, my boy. You’ve only just begun.”

“The last line is 216,” said the number devil, “and that’s quite a hefty number: 65,536 in case you’re interested.”

“Well, I’m worried about you.”
“Don’t be, Mother. You know the saying: The Devil is never so grim as he is painted.”

“What do you think would have happened if you hadn’t sent Enrique, Felice, Gary, Hugh, Iris, Jamil, and Karen home?”
“Utter confusion. Pandemonium,” replied the number devil.

The schoolyard was strewn with soda cans, newspapers, and sandwich wrappings.

“I thought I could use a little holiday,” said the number devil. “You can always talk numbers with Mr. Bockel.” It wasn’t the greatest prospect in the world, but he had no choice.

At that moment the door flew open and in walked the inevitable Mr. Bockel with a briefcase chock-full of pretzels.

Fire-spewing mountains had flung him into the air, and he was about to descend slowly—slowly, how curious—into the maw of the volcano.

Fire-spewing mountains had flung him into the air, and he was about to descend slowly—slowly, how curious—into the maw of the volcano.

“Second row, fall in!” he shouted, and immediately a new contingent of numbers stormed in and found their places with a great clatter and shuffle: 1 3 5 7 9 11 13 15 17 19 21 23 25…

They stood directly in front of the others, making the room look even more like an interminable tunnel. They were all decked out in identical red T-shirts.

The number devil laughed, but it wasn’t a nice laugh. Robert thought it sounded sarcastic.

“You don’t need to scream at them, do you?” Robert said angrily. “This isn’t an army barracks. Try being a little more polite.”

“Rows one through seven, dismissed!” the number devil roared. In a flurry of scraping, pushing, puffing, and trampling, the numbers left the room. They were replaced by an exquisite stillness.

“Rows one through seven, dismissed!” the number devil roared. In a flurry of scraping, pushing, puffing, and trampling, the numbers left the room. They were replaced by an exquisite stillness.

Then the snowflakes swirling around the face of the freezing Robert started growing in size, and the other, warm, Robert, lolling comfortably in his armchair, noticed that no snowflake was like any other.

“Now try dividing them by their neighbors,” the number devil suggested. “The larger by the smaller.”
“Okay,” said Robert, and he went at it with great gusto, curious about what would come up on the screen…

“A fraction!” Robert cried. “A fraction that never ever ends, a fraction so grotesque it hurts my eyes to look at it! I hate fractions! Mr. Bockel loves them. He loves to torture us with them. Get that monster out of my sight. Please!”

“Don’t panic now. It’s just a continued fraction. Though it is amazing that we can entice our ‘crazy number’ 1.618 • • • out of a set of ones that keep shrinking and shrinking, don’t you think?”

“Now I’m going to draw an orange star inside the pentagon: The star consists of five orange lines. Ask me how long any one of those lines is and I’ll tell you: precisely 1.618 • • • quang and not one iota more or less.”

“All week long I’ve been brooding over what you showed me last time and how it hangs together. I’m glad you showed me all those tricks. They’re fun...."

“To make a long story short, you’re dissatisfied. Well, that’s good. Do you think we number devils are always satisfied with what we come up with? Not on your life! No, we’re constantly contemplating new ways of proving things. Thinking, pondering, meditating—it’s a way of life with us. But when a light finally does go on—and it can take ages, because in mathematics the centuries fly by—then we’re pleased as punch. Only then are we satisfied.”

“To make a long story short, you’re dissatisfied. Well, that’s good. Do you think we number devils are always satisfied with what we come up with? Not on your life! No, we’re constantly contemplating new ways of proving things. Thinking, pondering, meditating—it’s a way of life with us. But when a light finally does go on—and it can take ages, because in mathematics the centuries fly by—then we’re pleased as punch. Only then are we satisfied.”

“To make a long story short, you’re dissatisfied. Well, that’s good. Do you think we number devils are always satisfied with what we come up with? Not on your life! No, we’re constantly contemplating new ways of proving things. Thinking, pondering, meditating—it’s a way of life with us. But when a light finally does go on—and it can take ages, because in mathematics the centuries fly by—then we’re pleased as punch. Only then are we satisfied.”

“But since mathematicians have spent a few thousand years finding ways to cross the stream, you don’t need to start from scratch. You’ve got all kinds of rocks to rely on. They’ve been tested millions of times and are guaranteed slip-resistant. When you have a new idea, a conjecture, you look for the nearest safe rock, and from there you keep leaping—with the greatest of caution, of course—until you reach the other side, the shore.”

The number devil looked at Robert. “That the Man in the Moon was wrong. His wonderful formula worked almost always, but not always. And almost isn’t enough. The poor devil! He was working on prima-donna numbers. A ticklish business, let me tell you, and fiendishly difficult to prove.”

“Ugh!” said Robert with a shiver. “That’s horrendous. And all to show that 1 + 1 = 2? Something he knew anyway?”

“Sounds easy, doesn’t it? Well, let me tell you, a good many people have lost a good deal of sleep over it. Even some of the most crafty number devils. And not one of them has cracked it, not to this day.”

"...So good-bye for now, my boy. First thing in the morning I’ll be looking into the simplex algorithm for polytopic surfaces.”