★★★★★ Twenty-five years of recreational mathematics

Hexaflexagons and Other Mathematical Diversions

Martin Gardner

In 1967 my Aunt Althea, the very best of all possible aunts, gave me a subscription to Scientific American for my twelfth birthday. I remined a subscriber until the 1990s. Among the best features of SA were the monthly columns "The Amateur Scientist", where you could learn how to build a laser in your garage -- you think I'm joking, but I'm serious -- and Martin Gardner's Recreational Mathematics column "Mathematical Games". Yes, I know that to many of you the phrase "recreational mathematics" makes about as much sense as "recreational colonoscopy", but there are enough people who were willing to entertain the idea that math could be fun to sustain Gardner's column for 26 years. I was one, and Gardner was brilliant.

These columns were collected and published in fifteen books by SA. The best way to get them now is in electronic form. There is a searchable CD-ROM version, and also the American Mathematical Society will sell you PDFs of all 15 as a package deal. The fifteen books, as numbered by AMS, are

1. Hexaflexagons and Other Mathematical Diversions
2. The Second Scientific American Book of Mathematical Puzzles and Diversions
3. New Mathematical Diversions
4. The Unexpected Hanging and Other Mathematical Diversions
5. Sixth Book of Mathematical Games from Scientific American
6. Mathematical Carnival
7. Mathematical Magic Show
8. Mathematical Circus
9. The Magic Numbers of Dr. Matrix
10. Wheels, Life, and Other Mathematical Amusements
11. Knotted Doughnuts and Other Mathematical Entertainments
12. Time Travel and Other Mathematical Bewilderments
13. Penrose Tiles to Trapdoor Ciphers and the Return of Dr. Matrix
14. Fractal Music, Hypercards & More Mathematical Recreations from Scientific American Magazine
15. The Last Recreations

(Most of The Magic Numbers of Dr. Matrix was originally published as number four in the series, which was later reprinted and expanded, explaining why Sixth Book of Mathematical Games from Scientific American is number five in the AMS numbering.)

There's a lot here. A "Greatest Hits" compilation would be nice. The closest thing to that that I have found is this SA blog post, listing ten of Gardner's best articles. Unfortunately, the links take you to paywalled SA pages. Still, if you have bought the books, it's useful.

Gardner sometimes made the silly claim that he was not a professional mathematician. There is no sensible understanding of the term "professional mathematician" under which this claim is true. I was tempted to write "uncharacteristically silly" in the above sentence, but then I remembered that Gardner was often very silly, for instance in his annual April Fools column. This was a man who was always up for a little fun and knew how to find it.

Gardner's work was revered by professional mathematicians, and Mathematical Games was great in part because they talked to him and told him about their latest work. Some important new math was thus first published in Mathematical Games.

A regular feature of the column was puzzles. I remember this one in particular:

EVE/DID = .TALKTALK...

The puzzle is to assign a distinct digit to each letter (E, V, ..., K) such that the equation is true. The fraction is in lowest terms. The unique solution is

242/303 = .79867986...

As a high-school student I had fun solving that. Gardner published a collection of his best puzzles My Best Mathematical and Logic Puzzles (Dover Recreational Math).

The AMS collection is a great deal for anyone who likes math.

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