A New Round-up of Tantalizers and
Puzzles from Scientific American
With 115 Pictures and Diagrams

Introduction

A TEACHER of mathematics, no matter how much he loves his subject and how strong his desire to communicate, is perpetually faced with one overwhelming difficulty: How can he keep his students awake?

The writer of a book on mathematics for laymen, no matter how hard he tries to avoid technical jargon and to relate his subject-matter to reader interests, faces a similar problem: How can he keep his readers turning the pages?

The "new math" proved to be of no help. The idea was to minimize rote learning and stress "why" arithmetic procedures work. Unfortunately, students found the commutative, distributive, and associative laws, and the language of elementary set theory to be even duller than the multiplication table. Mediocre teachers who struggled with the new math became even more mediocre, and poor students learned almost nothing except a terminology that nobody used except the educators who bad invented it. A few books were written to explain the new math to adults, but they were duller than books about the old math. Eventually, even the teachers got tired of reminding a child that he was writing a numeral instead of a number. Morris Kline's book, Why Johnny Can't Add, administered the coup de grace.

The best way, it has always seemed to me, to make mathematics interesting to students and laymen is to approach it in a spirit of play. On upper levels, especially when mathematics is applied to practical problems, it can and should be deadly serious. But on lower levels, no student is motivated to learn advanced group theory, for example, by telling him that he will find it beautiful and stimulating, or even useful, if he becomes a particle physicist. Surely the best way to wake up a student is to present him with an intriguing mathematical game, puzzle, magic trick, joke, paradox, model, limerick, or any of a score of other things that dull teachers tend to avoid because they seem frivolous.

No one is suggesting that a teacher should do nothing but throw entertainments at students. And a book for laymen that offers nothing but puzzles is equally ineffective in teaching significant math. Obviously there must be an interplay of seriousness and frivolity. The frivolity keeps the reader alert. The seriousness makes the play worthwhile.

That is the kind of mix I have tried to give in my Scientific American columns since I started writing them in December, 1956. Six book collections of these columns have previously been published. This is the seventh. As in earlier volumes, the columns have been revised and enlarged to bring them up to date and to include valuable feedback from readers.

The topics covered are as varied as the shows, rides, and concessions of a traveling carnival. It is hoped that the reader who strolls down this colorful mathematical midway, whether he is "with it" as a professional mathematician or just a visiting "mark"," will enjoy the noisy fun and games. If he does, he may be surprised, when he finally leaves the lot, by the amount of nontrivial mathematics he has absorbed without even trying.