Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"A Quarter Century of Recreational Mathematics,"by Martin Gardner. Scientific American, August 1998.

The line between recreational math and serious math is a blurry one.Math is considered recreational if it has a playful aspect that can beunderstood and appreciated by nonmathematicians. At times, these typesof problems generate simple and elegant solutions, but they can alsolead to mind-bending paradoxes, bewildering magic tricks, and topologicalcuriousities such as Mobius bands and Klein bottles.

It is in this world that Martin Gardner lives. From 1956 to 1981, he wroteScientific American's column "Mathematical Games." He took no math courses in college, but as a journalist who loves math, he has been ableto coax interesting problems out of professional mathematicians. Earlyon he worked with Solomon Golomb, who studied polyominoes, shapes formedby joining identical squares along their edges (the domino being a simpleexample). In 1977, MIT's Ronald Rivest allowed Gardner to be the firstto reveal the "public-key" cipher system that Rivest invented.

At times, seemingly purely recreational problems have turned serious. Magicsquares, arrangements of numbers that add up to the same number in everyrow, column, or diagonal, have always been a popular part of recreationalmath. Extending this idea, retired railroad clerk Clifford Adams deviseda magic hexagon. After receiving it in the mail, Gardner passed it onto mathematician Charles Trigg, who proved that Adams' elegant patternwas the only possible magic hexagon of any size.

Gardner sees recreational math as potentially educational. For example,he regards ticktacktoe, a game so simple and well-known, to be a superbway to introduce students to combinatorial mathematics, game theory, andprobability. With the latest teaching trend emphasizing problem solvingand cooperative learning, Gardner believes that recreational math problemswould be extremely valuable and should be integrated with the standardcurriculum.

---Ben Stein

American Mathematical Society