Knots and Borromean Rings, Rep-Tiles, and Eight Queens

This is the fourth entry in the first complete collection of Martin Gardner's Mathematical Library, covering the entire twenty-five-year run of his Scientific American columns. Oddly, the cover and spine have no indication of this ordinal or the count of volumes. It is not immediately obvious this is part of a set.

The back cover does cite Don Knuth as saying that this material is “…always worth reading and rereading.” I agree. This edition contains extensively updated material from Gardner, so that the detailed afterwords and extensive bibliographies are often longer than the original columns. Gardner’s contributions are from as late as 2005, meaning we can read Gardner citing Web sites and considering 3D printing applications. This gives this compendium a different voice from any other Gardner collection I have perused.

Strict completists should be made aware that some material has been redacted. “Thirty-Seven Catch Questions” is now “Thirty-Six Catch Questions”. Since this collection was published in 1968 (and 1991) as The Unexpected Hanging and other Mathematical Diversions, readers are no longer to be confronted with a quandary beginning “The third woman, who weighs 300 pounds, is sitting on a hippopotamus skin…”

“The Unexpected Hanging” is a favorite riddle of mine and while pushed off the cover by topological flash, the hangman’s paradox is still here with enigmas around the cat’s cradle, the fourth dimension, gambling, peg solitaire, the transcendental and popular e, and more. Gardner’s engaging explorations telegraph an awe of the beauty of mathematics making this collection a treat and a challenge for any mathematics enthusiast.

Tom Schulte enthusiastically teaches mathematics at Oakland Community College and first fell in love with Martin Gardner’s writings through the Aha volumes.