The international best-seller that makes mathematics a thrilling exploration.
In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without . As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone-from those who fumble over fractions to those who solve complex equations in their heads-winds up marveling at what numbers can do.
Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach it to them. Hans Magnus Enzensberger is the author of many highly lauded books, including Civil Wars: From L.A. to Bosnia. He lives in Munich.
Rotraut Susanne Berner is an illustrator who lives in Heidelberg.
Michael Henry Heim is a prize-winning translator who teaches at UCLA.
In twelve dreams, Robert, a boy who hates math, meets a sly, clever number devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without end. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until once-unfamiliar or difficult mathematical theories and principles become crystal clear. Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach them. "Charming and seductive . . . We might all learn more if we each had an Enzensbergian devil to beguile us into a dream [and] to give us a glimpse of the beauty and power of mathematics."John Allen Paulos, The New York Review of Books
"Rare and glorious."Michael Pakenham, The Baltimore Sun
"Adults who know a little about math will find this book as enlightening as younger readers will."Martin Gardner, Los Angeles Times
"This is one devilishly good book for math fans and math phobes alike. It is exactly the book folks are always looking for, wringing their hands and saying, 'Why aren't there more books that show the fun and imaginative parts of math?' Well, here is that bookfull of the dreamlike beauty and power of math in a form that most anyone can understand. Guaranteed to send you to Number Heaven/Number Hell (which, as every kid has always known, is one and the same)."Jon Scieszka, author of The Math Curse
"Children and their parents will find this to be a devilishly clever and instructional romp through mathematical history and theory. Hans Magnus Enzensberger delights and informs in equal measure."Peggy Kaye, author of Games for Math and Games for Learning
"Self-described math-phobe Robert begins having surreal dreams in which he encounters a number devil, who teaches him, just for starters, the crucial importance of zero and how to make all numbers out of ones. More difficult concepts are deliberately repeated in several dreams; occasional additional problems are provided for greater challenges. Infinitely more fun than the usual word problem assignment."Horn Book Excerpt from The Number Devil
by Hans Magnus Enzensberger
In time Robert grew accustomed to dreaming of the number devil. He even came to look forward to it. True, he could have done without his know-it-all attitude and his temper tantrumsyou could never tell when he'd blow up and yell at youbut it was better, so much better, than being swallowed by a slimy fish or sliding down and down into a black hole.
Besides, Robert had made up his mind to show the number devil that he was no fool. You have to put people like him in their place, Robert thought as he got ready for bed one night. The big ideas he has about himselfand all because of a zero. He wasn't much more than a zero when you got down to it. All you had to do was wake up and he was gone.
But to put him in his place Robert had to dream of him, and to dream of him he had to fall asleep. And Robert suddenly noticed he was having trouble doing so. For the first time in his life he lay awake in bed, tossing and turning.
"What are you tossing and turning for?"
All at once, Robert realized his bed was in a cave. There were weird paintings of animals on the stone walls, but he had no time to study them because the number devil was standing over him, twirling his walking stick.
"Rise and shine, Robert!" he said. "Today's our division day."
"Must I?" Robert asked. "You might have at least waited until I was asleep. Besides, I hate division.
"Why?"
"When you add or subtract or even multiply, things come out even. What bugs me about division is that you get this remainder."
"The question is when."
"'When what?"
"When you get a remainder and when you don't. That's what counts. You can tell just by looking at them that some numbers can be divided evenly."
"Right. Like even numbers, which can all be divided by two. No problem. I'm pretty good at threes as well:
9 / 3
0 15 / 3
and so on. It's like multiplying in reverse:
3 x 5 = 15
becomes
15 / 3 = 5
I don't need a number devil for that. I can do it on my own."
Robert shouldn't have said that. The number devil, his mustache quivering, his nose reddening, his head growing bigger and bigger, jerked Robert out of bed.
"What do you know?" the number devil shouted. "Just because you've learned the multiplication table you think you know all there is to know. Well, you know nothing! Nothing whatsoever!"
There he goes again, thought Robert. First he drags me out of bed, then he hits the ceiling when I tell him I can do division.
"Here I come to a rank beginner out of the goodness of my heart, and no sooner do I open my mouth than he starts making wisecracks!"
"The goodness of your heart!" Robert cried. All things being equal, he would have upped and left, but how do you up and leave a dream? He looked all over the cave, but could find no way to leave.
"What are you looking for?"
"A way out."
"If you go now, you'll never see me again! I'll leave you to choke on Mr. Bockel's pretzel problems, or die of boredom in his class."
Robert knew when he was licked.
"I apologize," he said. "I didn't mean to offend you."
"Good," said the number devil, his anger subsiding as quickly as it had come. "Now, nineteen. Try nineteen. See if you can divide it without a remainder."
Robert thought and thought.
"The only way I can come up with," he said at last, "is to divide it by nineteen. Or into nineteen equal parts."
"Doesn't count," the number devil replied. "It's too easy."
"Or divide it by zero."
"Out of the question."
"Out of the question? Why?"
"Because it's forbidden. Dividing by zero is strictly forbidden."
"What if I did it anyway?"
"Then all mathematics would come apart at the seams!"
He was about to lose his temper again, but he managed to pull himself together.
"Tell me," said the number devil, what would you get if you divided nineteen by zero?"
"I don't know. A hundred, maybe. Or zero. Or anything in between."
"But didn't you say when you were talking about the threes that division was like multiplying in reverse? If that's the case, then
3 x 5 = 15
means that
15 / 3 = 5
Well, now try that with nineteen and zero."
"Nineteen divided by zero is, say, 19."
And in reverse?"
"19 times zero ... 19 times zero ... is zero."
"You see? And no matter what number you take, you always get zero. Which means you must never divide a number by zero."
"Okay," said Robert, "I give up. But what do we do with the nineteen? No matter what number I divide it bytwo, three, four, five, six, seven, eight, or nine--I get stuck with a remainder."
"Come a little closer," said the number devil to Robert, "and I'll tell you a secret." Robert leaned so close to the number devil that his mustache tickled his ear.
"There are two types of numbers," he whispered. "The garden variety, which can be divided evenly, and the rest, which cannot. I much prefer the latter. You know why? Because they're such prima donnas. From the very first they've caused mathematicians no end of trouble. Wonderful numbers those! Like eleven, thirteen, or seventeen."
Robert couldn't get over how blissful the number devil looked. He might have had a piece of chocolate melting in his mouth.
Excerpted from The Number Devil: A Mathematical Adventure
by Hans Magnus Enzensberger, Rotraut Susanne Berner, Michael Henry Heim.
Copyright © 1998. Reprinted by permission. All rights reserved
In 12 dreams, Robert, a boy who hates math, encounters a sly, clever number devil who introduces him to the wonders of numbers: infinite numbers, prime numbers, Fibonacci numbers, and numbers that expand without end.
Finally available in paperback, the international best-seller that makes math a thrilling adventure for adults and children alike.
In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without end. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone-from those who fumble over fractions to those who solve complex equations in their heads-winds up marveling at what numbers can do.