The Number Devil
Encyclopedia
The Number Devil: A Mathematical Adventure is a book for children and young adults which explores mathematics
. It was originally written in German
by Hans Magnus Enzensberger
and illustrated by Rotraut Susanne Berner
. The book follows a young boy named Robert, who is taught mathematics
by a sly "number devil
" called Teplotaxl through the course of twelve dreams. The book was a best-seller, and was translated into 26 languages. It was later translated into English by Michael Henry Heim
.
due to his boredom in school. He also experiences recurring dream
s—including falling down an endless slide
or being eaten by a giant fish
—but is interrupted from this sleep habit one night by a small devil
esque creature who introduces himself as the Number Devil. Although there are many Number Devils (from Number Heaven
), Robert only knows him as the Number Devil before learning of his actual name, Teplotaxl, later in the story.
Over the course of twelve dreams, the Number Devil teaches Robert mathematical principles. On the first night, the Number Devil appears to Robert in a oversized
world and introduces the number one. The next night, the Number Devil emerges in a forest
of tree
s shaped like "ones" and explains the necessity of the number zero
, negative numbers, and introduces hopping, a fictional term to describe exponentiation
. On the third night, the Number Devil brings Robert to a cave
and reveals how prima-donna numbers (prime number
s) can only be divided
by itself and one without a remainder
. Later, on the fourth night, the Number Devil teaches Robert about rutabaga
s, another fictional term to depict square root
s, at a beach
.
For a time after the fourth night, Robert could not find the Number Devil in his dreams; later, however, on the fifth night, Robert finds himself at a desert
where the Number Devil teaches him about triangular numbers through the use of coconut
s. On the sixth night, the Number Devil teaches Robert about the natural occurrence of Fibonacci numbers, which the Number Devil shortens to Bonacci numbers, by counting brown and white rabbit
s as they reproduce multiple times. By this dream, Robert's mother has noticed a visible change in Robert's mathematical interest, and Robert begins going to sleep earlier to encounter the Number Devil. The seventh night brings Robert to a bare, white room, where the Number Devil presents Pascal's triangle
and the patterns that the triangular array
displays. On the eighth night, Robert is brought to his classroom
at school. The Number Devil arranges Robert's classmates in multiple ways, teaches him about permutation
s, and what the Number Devil calls vroom numbers (factorial
s).
On the ninth night, Robert dreams he is in bed, suffering from the flu, when the Number Devil appears next to him. The Number Devil teaches Robert about natural numbers, which the Number Devil calls ordinary numbers, the unusual characteristics of infinite, and infinite series
. Robert finds himself at the North Pole
, where the Number Devil introduces irrational number
s (unreasonable numbers), as well as aspects of Euclidian geometry, such as vertices
(dots) and edges
(lines). By the eleventh night, Robert has shown considerable increased interest in mathematics, but questions its validity, to which the Number Devil introduces the concept of mathematical proof
s, ending with the Number Devil showing Robert a complicated proof of basic arithmetic
. On the twelfth night, Robert and the Number Devil receive an invitation (which names the Number Devil as Teplotaxl) to Number Heaven, as Robert's time with the Number Devil has finished. At Number Heaven, Robert learns of imaginary number
s, which Teplotaxl describes as imaginative numbers, as well as the Klein bottle
, and they both meet various famous mathematician
s.
Professor of Slavic Languages Michael Henry Heim
translated the book from German to English. The translation was particularly difficult in that it required special attention to the numerical aspect of the book. He was also challenged by the necessity to use simple English words appropriate for the target audience of The Number Devil—that is, children aged eleven to fourteen. Because of its alleviating approach to mathematics, The Number Devil is often used in the curricula of youth mathematics education
.
published an educational
computer game, similarly titled The Number Devil: A Mathematical Adventure, based on the book.
of Temple University
wrote an article for The New York Review of Books
, praising The Number Devil as a "charming numerical fairy tale for children." Likewise, mathematics writer Martin Gardner
of the Los Angeles Times
applauded Enzensberger's introduction of mathematics "in such an entertaining way." In a book review for The Baltimore Sun
, Michael Pakenham approved of the book's simplicity, writing, "it's not incomprehensible. Not for a minute."
The American Mathematical Society
's Deborah Loewenberg Ball
and Hyman Bass
reviewed the book from a mathematical perspective. Although they praised its "attractive and imaginative fantasy
," the two mathematicians found several issues. Ball and Bass were concerned with the The Number Devil' s negative characterization of math teacher
s, its apparent presentation of mathematics as magical
rather than factual
, as well as a number of other contentions.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. It was originally written in German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
by Hans Magnus Enzensberger
Hans Magnus Enzensberger
Hans Magnus Enzensberger , is a German author, poet, translator, and editor. He has also written under the pseudonym Andreas Thalmayr. He lives in Munich.- Life :...
and illustrated by Rotraut Susanne Berner
Rotraut Susanne Berner
Rotraut Susanne Berner is a German graphic designer and illustrator. She illustrated The Number Devil....
. The book follows a young boy named Robert, who is taught mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
by a sly "number devil
Devil
The Devil is believed in many religions and cultures to be a powerful, supernatural entity that is the personification of evil and the enemy of God and humankind. The nature of the role varies greatly...
" called Teplotaxl through the course of twelve dreams. The book was a best-seller, and was translated into 26 languages. It was later translated into English by Michael Henry Heim
Michael Henry Heim
Michael Henry Heim is a Professor of Slavic Languages, at the University California at Los Angeles . He received his doctorate at Harvard in 1971...
.
Plot
Robert is a young boy who suffers from mathematical anxietyMathematical anxiety
Mathematical anxiety is anxiety about one's ability to do mathematics independent of skill.-Math anxiety:Math anxiety is a phenomenon that is often considered when examining students’ problems in mathematics. Mark H. Ashcraft, Ph.D. defines math anxiety as “a feeling of tension, apprehension, or...
due to his boredom in school. He also experiences recurring dream
Recurring dream
A recurring dream is a dream which is experienced repeatedly over a long period.A person who experiences post-traumatic stress disorder may have recurring dreams about the traumatic event....
s—including falling down an endless slide
Playground slide
Playground slides are found in parks, schools, playgrounds and backyards. The slide may be flat, or half cylindrical or tubular to prevent falls. Slides are usually constructed of plastic or metal and they have a smooth surface that is either straight or wavy...
or being eaten by a giant fish
Fish
Fish are a paraphyletic group of organisms that consist of all gill-bearing aquatic vertebrate animals that lack limbs with digits. Included in this definition are the living hagfish, lampreys, and cartilaginous and bony fish, as well as various extinct related groups...
—but is interrupted from this sleep habit one night by a small devil
Devil
The Devil is believed in many religions and cultures to be a powerful, supernatural entity that is the personification of evil and the enemy of God and humankind. The nature of the role varies greatly...
esque creature who introduces himself as the Number Devil. Although there are many Number Devils (from Number Heaven
Heaven
Heaven, the Heavens or Seven Heavens, is a common religious cosmological or metaphysical term for the physical or transcendent place from which heavenly beings originate, are enthroned or inhabit...
), Robert only knows him as the Number Devil before learning of his actual name, Teplotaxl, later in the story.
Over the course of twelve dreams, the Number Devil teaches Robert mathematical principles. On the first night, the Number Devil appears to Robert in a oversized
Resizing (fiction)
Resizing , is a theme in fiction, in particular in fairy tales, fantasy, and science fiction.- Early instances in fiction :...
world and introduces the number one. The next night, the Number Devil emerges in a forest
Forest
A forest, also referred to as a wood or the woods, is an area with a high density of trees. As with cities, depending where you are in the world, what is considered a forest may vary significantly in size and have various classification according to how and what of the forest is composed...
of tree
Tree
A tree is a perennial woody plant. It is most often defined as a woody plant that has many secondary branches supported clear of the ground on a single main stem or trunk with clear apical dominance. A minimum height specification at maturity is cited by some authors, varying from 3 m to...
s shaped like "ones" and explains the necessity of the number zero
0 (number)
0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...
, negative numbers, and introduces hopping, a fictional term to describe exponentiation
Exponentiation
Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...
. On the third night, the Number Devil brings Robert to a cave
Cave
A cave or cavern is a natural underground space large enough for a human to enter. The term applies to natural cavities some part of which is in total darkness. The word cave also includes smaller spaces like rock shelters, sea caves, and grottos.Speleology is the science of exploration and study...
and reveals how prima-donna numbers (prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s) can only be divided
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
by itself and one without a remainder
Remainder
In arithmetic, the remainder is the amount "left over" after the division of two integers which cannot be expressed with an integer quotient....
. Later, on the fourth night, the Number Devil teaches Robert about rutabaga
Rutabaga
The rutabaga, swede , turnip or yellow turnip is a root vegetable that originated as a cross between the cabbage and the turnip; see Triangle of U...
s, another fictional term to depict square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
s, at a beach
Beach
A beach is a geological landform along the shoreline of an ocean, sea, lake or river. It usually consists of loose particles which are often composed of rock, such as sand, gravel, shingle, pebbles or cobblestones...
.
For a time after the fourth night, Robert could not find the Number Devil in his dreams; later, however, on the fifth night, Robert finds himself at a desert
Desert
A desert is a landscape or region that receives an extremely low amount of precipitation, less than enough to support growth of most plants. Most deserts have an average annual precipitation of less than...
where the Number Devil teaches him about triangular numbers through the use of coconut
Coconut
The coconut palm, Cocos nucifera, is a member of the family Arecaceae . It is the only accepted species in the genus Cocos. The term coconut can refer to the entire coconut palm, the seed, or the fruit, which is not a botanical nut. The spelling cocoanut is an old-fashioned form of the word...
s. On the sixth night, the Number Devil teaches Robert about the natural occurrence of Fibonacci numbers, which the Number Devil shortens to Bonacci numbers, by counting brown and white rabbit
Rabbit
Rabbits are small mammals in the family Leporidae of the order Lagomorpha, found in several parts of the world...
s as they reproduce multiple times. By this dream, Robert's mother has noticed a visible change in Robert's mathematical interest, and Robert begins going to sleep earlier to encounter the Number Devil. The seventh night brings Robert to a bare, white room, where the Number Devil presents Pascal's triangle
Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...
and the patterns that the triangular array
Triangular array
In mathematics and computing, a triangular array of numbers, polynomials, or the like, is a doubly indexed sequence in which each row is only as long as the row's own index.Notable particular examples include these:...
displays. On the eighth night, Robert is brought to his classroom
Classroom
A classroom is a room in which teaching or learning activities can take place. Classrooms are found in educational institutions of all kinds, including public and private schools, corporations, and religious and humanitarian organizations...
at school. The Number Devil arranges Robert's classmates in multiple ways, teaches him about permutation
Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
s, and what the Number Devil calls vroom numbers (factorial
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
s).
On the ninth night, Robert dreams he is in bed, suffering from the flu, when the Number Devil appears next to him. The Number Devil teaches Robert about natural numbers, which the Number Devil calls ordinary numbers, the unusual characteristics of infinite, and infinite series
Series (mathematics)
A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....
. Robert finds himself at the North Pole
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets its surface...
, where the Number Devil introduces irrational number
Irrational number
In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number....
s (unreasonable numbers), as well as aspects of Euclidian geometry, such as vertices
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...
(dots) and edges
Edge (geometry)
In geometry, an edge is a one-dimensional line segment joining two adjacent zero-dimensional vertices in a polygon. Thus applied, an edge is a connector for a one-dimensional line segment and two zero-dimensional objects....
(lines). By the eleventh night, Robert has shown considerable increased interest in mathematics, but questions its validity, to which the Number Devil introduces the concept of mathematical proof
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
s, ending with the Number Devil showing Robert a complicated proof of basic arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
. On the twelfth night, Robert and the Number Devil receive an invitation (which names the Number Devil as Teplotaxl) to Number Heaven, as Robert's time with the Number Devil has finished. At Number Heaven, Robert learns of imaginary number
Imaginary number
An imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...
s, which Teplotaxl describes as imaginative numbers, as well as the Klein bottle
Klein bottle
In mathematics, the Klein bottle is a non-orientable surface, informally, a surface in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a...
, and they both meet various famous mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s.
History
The Number Devil was ultimately written on suggestion from his eleven-year-old daughter Theresia. Because Enzensberger was displeased with the way mathematics was taught to students at school, he decided to pen a book that teaches mathematics in an innovative way. The UCLAUniversity of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
Professor of Slavic Languages Michael Henry Heim
Michael Henry Heim
Michael Henry Heim is a Professor of Slavic Languages, at the University California at Los Angeles . He received his doctorate at Harvard in 1971...
translated the book from German to English. The translation was particularly difficult in that it required special attention to the numerical aspect of the book. He was also challenged by the necessity to use simple English words appropriate for the target audience of The Number Devil—that is, children aged eleven to fourteen. Because of its alleviating approach to mathematics, The Number Devil is often used in the curricula of youth mathematics education
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
.
Other media
Viva MediaViva Media
Viva Media, LLC is a privately owned New York company dedicated to publishing a wide array of interactive content in family entertainment and educational software....
published an educational
Educational game
Educational games are games that have been designed to teach people about a certain subject, expand concepts, reinforce development, understand an historical event or culture, or assist them in learning a skill as they play...
computer game, similarly titled The Number Devil: A Mathematical Adventure, based on the book.
Reception
The Number Devil received mostly positive reviews from critics. Mathematics professor John Allen PaulosJohn Allen Paulos
John Allen Paulos is a professor of mathematics at Temple University in Philadelphia who has gained fame as a writer and speaker on mathematics and the importance of mathematical literacy...
of Temple University
Temple University
Temple University is a comprehensive public research university in Philadelphia, Pennsylvania, United States. Originally founded in 1884 by Dr. Russell Conwell, Temple University is among the nation's largest providers of professional education and prepares the largest body of professional...
wrote an article for The New York Review of Books
The New York Review of Books
The New York Review of Books is a fortnightly magazine with articles on literature, culture and current affairs. Published in New York City, it takes as its point of departure that the discussion of important books is itself an indispensable literary activity...
, praising The Number Devil as a "charming numerical fairy tale for children." Likewise, mathematics writer Martin Gardner
Martin Gardner
Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
of the Los Angeles Times
Los Angeles Times
The Los Angeles Times is a daily newspaper published in Los Angeles, California, since 1881. It was the second-largest metropolitan newspaper in circulation in the United States in 2008 and the fourth most widely distributed newspaper in the country....
applauded Enzensberger's introduction of mathematics "in such an entertaining way." In a book review for The Baltimore Sun
The Baltimore Sun
The Baltimore Sun is the U.S. state of Maryland’s largest general circulation daily newspaper and provides coverage of local and regional news, events, issues, people, and industries....
, Michael Pakenham approved of the book's simplicity, writing, "it's not incomprehensible. Not for a minute."
The American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
's Deborah Loewenberg Ball
Deborah Loewenberg Ball
Deborah Loewenberg Ball is an educational researcher noted for her work in mathematics instruction and the mathematical preparation of teachers. She currently is dean of the School of Education at the University of Michigan and William H. Payne Collegiate Professor...
and Hyman Bass
Hyman Bass
Hyman Bass is an American mathematician, known for work in algebra and in mathematics education. From 1959-1998 he was Professor in the Mathematics Department at Columbia University, where he is now professor emeritus...
reviewed the book from a mathematical perspective. Although they praised its "attractive and imaginative fantasy
Fantasy literature
Fantasy literature is fantasy in written form. Historically speaking, literature has composed the majority of fantasy works. Since the 1950s however, a growing segment of the fantasy genre has taken the form of films, television programs, graphic novels, video games, music, painting, and other...
," the two mathematicians found several issues. Ball and Bass were concerned with the The Number Devil
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
s, its apparent presentation of mathematics as magical
Magic (paranormal)
Magic is the claimed art of manipulating aspects of reality either by supernatural means or through knowledge of occult laws unknown to science. It is in contrast to science, in that science does not accept anything not subject to either direct or indirect observation, and subject to logical...
rather than factual
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
, as well as a number of other contentions.