American Scientist

The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems.
Martin Gardner. xii + 724 pp. W. W. Norton, 2001. $35.

Careers in modern society are largely predictable: lawyer, doctor, businessman, scientist—so it goes. But who could possibly have predicted the career of Martin Gardner? Even Gardner couldn't have, although in time he invented it himself. And what a great invention!

Born and raised in Tulsa, Oklahoma, Gardner went to the University of Chicago (Class of 1936). He liked the place so much he couldn't bear to leave. After a brief tour as a reporter with the Tulsa Tribune, he returned to Chicago as a staff writer in the university's public relations office. From that vantage he could audit courses in mathematics and philosophy that went beyond his undergraduate curriculum in philosophy. After serving in the Navy from 1941 to 1945 (a tour of duty that included two years on a destroyer escort in the North Atlantic), he returned to Chicago once more to take a graduate degree with Rudolf Carnap, an eminent philosopher of science and refugee from Hitler who had joined the faculty. (Gardner greatly admired Carnap and later edited a collection of his writings on the philosophy of physics.)

At this point Gardner became a freelance writer. He sold several short stories to magazines and then decided to pursue a writing career in New York. There he met and married Charlotte Greenwald, who was with him until her death this past year. He got a job on the staff of Humpty Dumpty's magazine for children, and while he was working there he proposed an article to Scientific American, of which I was then editor. The subject was logic machines, and the article included a nifty paper machine that the reader could cut out and use to solve syllogisms.

On meeting Gardner, we asked him if he thought there were enough subjects in recreational mathematics to support a monthly column in the magazine. He allowed that there were, and starting in January 1957, he proceeded to write no fewer than 312 columns under the heading of "Mathematical Games." The columns were a big hit with readers and contributed substantially to the magazine's success. In 1981, Gardner retired, I suspect to clear his desk of the hundred other things he wanted to do. Among them was playing a leading role in the Committee for the Scientific Investigation of Claims of the Paranormal (CSICOP), which has done heroic work in exposing quackery, scientific and otherwise. For CSICOP's magazine, the Skeptical Inquirer, Gardner writes a regular column, "Notes of a Fringe Watcher."

In the nature of things, columns in a periodical, however delightful, tend to be forgotten. It was thus a logical development that Gardner's contributions to "Mathematical Games" should be regularly collected in book form. Fifteen such collections had been published when W. W. Norton asked Gardner to assemble a new one consisting of 50 of his "best" pieces. The result is The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems.

Gardner's owlish title is scarcely an exaggeration; the book contains sections on arithmetic and algebra, plane geometry, solid geometry and higher dimensions, symmetry, topology, probability, infinity, combinatorics, games and decision theory, physics, and logic and philosophy. For good measure there is a concluding "Miscellaneous" section that is so full of fun it is worth the entire price of admission. One chapter in it concerns "Six Sensational Discoveries" of the year 1974. One of them was made by Augusto Macaroni of the Catholic University of Milan; it was a missing page from Leonardo da Vinci's notebooks that showed he had invented the flush toilet. Another was the invention, by Robert Ripoff of Prague, of the Ripoff Rotor, a machine that runs solely on psi (psychic) energy. When Ripoff was visited by Henrietta Birdbrain, an American expert on Kirlian photography, he showed her how to make the rotor, which she then demonstrated to audiences in America. Since Gardner had used such outlandish names, he had no idea that anyone would not recognize that the "discoveries" were an elaborate April Fools' Day joke. Yet he received more than a thousand letters from readers who took them seriously!

The columns and their illustrations are not merely reproduced as they appeared in Scientific American. They are accompanied by answers to questions arising from them, together with addenda commenting on their content. The bibliographies are greatly expanded, and interesting correspondence is included. The book is colossal, all right.

To return to Gardner's having invented himself, his pieces on mathematical recreations would be sufficient unto the day, but the invention goes a lot further. The online catalogue of the Library of Congress lists more than 60 books by Gardner other than his collected columns. Among them are Fads and Fallacies in the Name of Science; Relativity Simply Explained; The New Ambidextrous Universe; Codes, Ciphers, and Secret Writing; Did Adam and Eve Have Navels?; and a novel, The Flight of Peter Fromm. Reflecting his lifelong interest in conjuring, Gardner has even published 12 Tricks with a Borrowed Deck and a 574-page Encyclopedia of Impromptu Magic.

Some of Gardner's best books are, strictly speaking, not his at all, but wonderful annotated editions of such classics as "Casey at the Bat" and Alice's Adventures in Wonderland. A few years ago I was asked to write a jacket blurb for a new edition of Gardner's Alice, with the following result:

'Tis Gardner, and that wily cove
Does gambol, not gimble, on the page.
All exegeezed is Carroll's prose
It's an Alice for our age!

Martin Gardner's invention turns out not only to be a peerless mathematical gamester but a philosophical writer for all seasons.