The Number Devil – A Mathematical Adventure, written by Hans Magnus Enzensberger, tells the story of Robert, a young boy plagued by recurring nightmares. These nightmares, such as being swallowed by a giant fish, slipping into a never-ending slide into a black hole, or being swept away by a raging river, always have a negative impact on Robert. They fill him with fear, anger, and disappointment. Robert longs for a dreamless sleep, but instead of his nightmares ceasing, his dreams become increasingly strange and peculiar.
In his dreams, instead of experiencing unfortunate events like falling down holes, Robert encounters the Number Devil. The Number Devil utilizes various tools such as giant furry calculators, stacks of coconuts, electronic glass boxes, and an unlimited supply of scrolling paper to introduce Robert to diverse numeric concepts. Through a series of twelve dreams, Robert delves deeper into mathematical theories and becomes fascinated by the potential of numbers. The initial encounter with the Number Devil on the first night leaves Robert feeling unhappy.
Robert was relieved to finally escape his usual nightmares, but he was not pleased when he encountered a little red man who was solely interested in discussing numbers. When Robert and the Number Devil first met, the Number Devil taught him that numbers don’t have to be complex. From my understanding, the Number Devil explained that if someone is intimidated by large numbers, all they need to do is begin with the number one and continue counting. The Number Devil stated, “If you’re scared of [five million], all you have to do is start with 1+1… until you reach five million.”
In addition to discovering the meaning of the word ‘indefinite’ and its relation to the number one, I also had another dream that involved Robert being transported to a land filled with trees in the shape of the number one, while flies buzzed around in the shapes of numbers two through nine. The Number Devil pointed out the absence of zero in this mix. From him, I learned that the Romans did not include zero when they created their number system, which contributes to its complexity. Furthermore, The Number Devil taught me about the connection between zero and subtraction, as well as how zero is utilized in powers and in the concept of place value.
After explaining it all, the Number Devil enthusiastically informed Robert, “Rejoice my boy, for you are much better off than the Romans… with the help of your friend zero” (p. 41).
Over time, Robert developed a preference for the Number Devil over his other dreams and eagerly anticipated their encounters.
In the third dream, the Number Devil educated Robert about division and remainders. He provided evidence for why dividing by zero is considered “forbidden” (p. 54).
He also taught Robert about prime numbers, which he whimsically referred to as “prima donnas,” stating that they have historically caused mathematicians a great deal of trouble (p. 5).
In the fourth dream, the concept of “taking the square root” was introduced by the Number Devil. However, he insisted on referring to it as “taking the rutabaga,” likening it to pulling a root vegetable out of the ground (p. 76). He also taught about “unreasonable numbers” (i.e., irrational numbers), remarking that they are not rare but rather abundant, akin to sand on a beach (p. 83).
The fifth dream focused on “triangle numbers” and their various applications and connections (p. 93).
The Number Devil used coconuts and ice cubes as examples to teach quadrangle numbers. In the sixth dream, he introduced Robert to ‘Number Heaven,’ where his favorite boss, Fibonacci, reigns and teaches the Fibonacci pattern with the rabbit’s reproductive cycle as an example. In the seventh dream, the Number Devil guided Robert in constructing a pyramid (triangle) using electronic glass boxes. Each cube had the sum of the cubes directly above it written on it. From this, I learned that no matter how far down we go, the numbers on the sides of the pyramid will always be ones.
And I can complete the numbers in the next diagonal rows on both sides with regular numbers like 1, 2, 3, 4… (p. 131). Using the pyramid, I discovered techniques for adding triangle numbers, calculations involving powers of 2, as well as patterns related to Fibonacci numbers. In the eighth dream, I learned about the various possibilities for a given quantity of items. The Number Devil provided an example using the different ways a specific number of students can be seated at a certain number of desks. In the ninth dream, Robert realizes that there is an infinite number of normal numbers together with an infinite number of odd numbers.
He proceeded to teach Robert about fractions, explaining that they too are infinite. In the tenth dream, the Number Devil revealed the significance of the number 6, including its relationship to Fibonacci numbers, the pentagon shape, and the star shape. He also explained that the formula for flat figure shapes is Dots + Spaces + # of Lines = 1, while for 3D shapes it is Dots + Spaces + # of Lines = 2. The eleventh dream conveyed the idea that every extraordinary number, whether large or small, can be followed by one and only one number, which is the original number plus one. It also mentioned that a point cannot be divided because it has no area, and that two points on a flat plane can only be connected by one line that extends infinitely in both directions (p. 219). The book concludes with Robert’s visit to Number Heaven/Hell with the Number Devil. They encounter various mathematicians and review everything they have learned before Robert becomes an “apprentice” in “The Order of Pythagorus” and develops a love for numbers (p. 248). This book influenced my future teaching by emphasizing the enjoyment and excitement that can be found in mathematics.
It is comforting to know that if math is not a student’s strong point, but reading is, there is a way to engage them. I would incorporate The Number Devil – A Mathematical Adventure into my classroom by reading a chapter to the students alongside the math lesson. This book provided me with a unique and fantastical perspective on math. As the Number Devil proclaimed, “[Numbers] really are fantastic creatures. In fact, there’s no such thing as an ordinary number” (p. 75) (Enzensberger and Berner, 2000).
