In the mid-1970s, Martin Gardner and Robert Tappay came up with the idea of producing filmstrips for use in high school classrooms, one about mathematical paradoxes and one about mathematical problems that can be solved easily provided one has just the right insight. The strips featured illustrations by Jim Glen; they were marketed as "The Paradox Box" and "The Aha! Box".
Of course, what Gardner and Tappay didn't realize (hardly anyone did, at the time) was the filmstrip was already dead, about to be replaced by fancier technologies such as video. (Some readers of this review may not even know what filmstrips were…) So the two "boxes" were transformed into books, called Aha! Gotcha and Aha! Insight, originally published in 1982 and 1978, respectively, which are reprinted here in one volume. Both books follow basically the same format: the illustrations from the strip are reproduced together with the text that was supposed to go with them, and then commentary is added, either on the side of the page or on a facing page. The images, unfortunately, are a little small, but the effect is still quite interesting.
I remember Aha! Gotcha from way back when, particularly for two limericks. The first went
There was a young lady of Crewe
Whose limericks stopped at line two.
and the second was
There was a young man of Verdun.
I always found that last one delightful. (How many lines does it actually have?)
Gotcha starts with paradoxes from logic and set theory, then goes on to cover numbers, geometry, probability, statistics, and time. Insight classifies its puzzles along similar lines: combinatorial, geometric, numerical, logical, algorithmic, and lexical.
Most mathematicians and mathematics fans are familiar with most of the paradoxes in Gotcha, and many of the problems in Insight are also well known, particularly to readers of Gardner's other books. On the other hand, since this way of presenting them was originally intended for class use, and in high school to boot, the book contains a lot of nice elementary ways to introduce some interesting mathematical ideas. Some of these pages could be made into really neat little PowerPoint presentations. (Of course, if you plan to reproduce the images, you need to get permission from MAA!) If you ever use puzzles or paradoxes in elementary classes, you can find some help here.
Martin Gardner is a national treasure, someone whose contribution to mathematics has been immense. The books collected here, while not his best, are accessible, intelligent, and fun. If you didn't happen to buy them in 1978 and 1982, here's your chance.
Fernando Q. Gouvêa remembers these books from the 1980s, but he lost them along the way, so he's glad to have them back.