Since the days of Pythagoras, numbers have appealed to our sense of the mystical and spooky as well as to our rational and analytic faculties. Whether they are constructs or inventions, facets of an idealized reality, or just rule-governed symbols and squiggles are issues that have resounded all through the history of philosophy. Whatever one’s philosophy of mathematics, however, there is something ethereal about numbers. They do seem, at least in uncritical moments, to reside in some sort of Platonic heaven. Numbers are up there somewhere.
Some recent manifestations of this apotheosis of numbers are the movie Pi and its depiction of a mathematician obsessed with finding secret messages in the number’s decimal expansion; the best-selling The Bible Code, with its silly claim of so-called equidistant letter sequences in the Torah foretelling future events; the recent biographies of the monastic number theorist Paul Erdos; the excitement over the proof by Andrew Wiles of Fermat’s 350-year-old last theorem; millennial anxiety with its associated Y2K problem; and, perhaps, even the new cologne named Pi.
To many, however, numbers have a less ambrosial scent. In contrast to their heavenly aspects, numbers and computation are also seen as grubby and oppressive. “Ambition, Distraction, Uglification, and Derision” is how Lewis Carroll referred to the basic arithmetic operations, and this is how many people still view school computation (except for “ambition,” which never seemed to belong on the list, “admonition” seeming more appropriate, perhaps). The reason for this repugnance is that computation is so often boring and tiresome. Worse than this, it can forever color (or should I say discolor) people’s views of real mathematics.
Tasks such as adding fractions, calculating with percentages, or solving artificial “story problems” about trains and rates have failed to delight billions of young students through the ages. Stripped of even a minimal narrative pretense, the stultifying four hundred long divisions that students have to perform in elementary school evolve into the equally mind-numbing four hundred polynomials to factor in high school algebra and then the four hundred functions to differentiate in freshman calculus. Later, as adults, we’re inundated with polls, studies, and torrents of demographic statistics, stock prices, and sales figures—certainly important, but nonetheless frequently drudgery.
In his recent book, The Number Devil: A Mathematical Adventure, the distinguished German journalist, critic, and poet Hans Magnus Enzensberger plays off both these ubiquitous attitudes toward numbers and mathematics to fashion a charming numerical fairy tale for children. Most parents, I suspect, will also learn from the book, which was a best seller in Germany and Spain and has now been translated from the German by Michael Henry Heim.
Robert, a friendless young boy who detests school mathematics, has disturbing dreams of fish, bicycle locks, and falling. Then one night he begins dreaming of an irascible little imp, the number devil, who gradually introduces him to some of the wonders of elementary number theory. In a sequence of twelve dreams the twelve-year-old boy (and, presumably, the young …