The third volume in The New Martin Gardner Mathematical Library collects articles first published in Scientific American in 1959, 1960, and 1961. As in the previous volumes, each article is followed by an “Addendum” (usually but not always from the time of the first book publication, 1966), “Answers” (presumably from the issue following that in which the article first appeared), a “Postscript” bringing the story up to today, and an updated bibliography. The ancillary material and the uniform (and complete) edition are the “new” part in this series.
The articles in Sphere Packing, Lewis Carroll, and Reversi are the usual mixture, some on standard Gardneresque themes (dissections, geometric puzzles, games), others ranging a little further (groups and braids, sphere packing, π, the calculus of finite differences). One of the chapters is really a book review, of H. S. M. Coxeter’s Introduction to Geometry, a book that amply justifies this attention.
Gardner’s humor is also in evidence. The “mathemagician” Victor Eigen (presumably the guy who invented eigenvalues?) has a big role in one article. Another tells of a visit to America by P. Bertrand Apollinax, “the brilliant protégé of the celebrated French mathematician Nicholas Bourbaki.” Apollinax, in particular, seems to have fooled many of Gardner’s readers.
One of the pleasures in re-reading these volumes is recognizing some of Gardner’s correspondents who later went on to other things. Vern Poythress, who got a Ph.D. in mathematics then went on to become a professor of theology, appears in one of the articles. The Stephen Barr who is mentioned five times may well be the one who became a particle physicist, now at the University of Delaware.
Gardner’s writing has something magical to it. He often manages to hold my interest even while talking about subjects that I do not really find compelling, such as dominos and all their progeny. I wonder if Scientific American ever did research on how many of its subscribers bought the magazine mainly to read Gardner’s column. I know I did. I’m glad to have another volume to add to my set.
Fernando Q. Gouvêa, who is Carter Professor of Mathematics at Colby College in Waterville, ME, was never smart enough to be mentioned in Gardner’s columns.
1. The binary system; 2. Group theory and braids; 3. Eight problems; 4. The games and puzzles of Lewis Carroll; 5. Paper cutting; 6. Board games; 7. Sphere packing; 8. The transcendental number Pi; 9. Victor Eigen, mathemagician; 10. The four-color map theorem; 11. Mr. Apollinax visits New York; 12. Nine problems; 13. Polyominoes and fault-free rectangles; 14. Euler's spoilers: the discovery of an Order-10 Graeco-Latin square; 15. The ellipse; 16. The 24 color squares and the 30 color cubes; 17. H. S. M. Coxeter; 18. Bridg-it and other games; 19. Nine more problems; 20. The calculus of finite differences.