# A Gardner's Dozen—Martin's *Scientific American* Cover Stories

Martin wrote about
300 articles for *Scientific American*between 1952 and 1998, most famously in his legendary "Mathematical Games" column starting in Jan 1957. Many of those articles are now viewed as classics, from his seminal piece on hexaflexagons in Dec 1956—which led to the offer to write a regular column for the magazine—to his breakthrough essays on pentomnoes, rep-tiles, the Soma cube, the art of Escher, the fourth dimension, sphere packing, Conway's game of Life, Newcomb's paradox, Mandelbrot's fractals, Penrose tiles, and RSA cryptography, not forgetting the recurring numerological exploits of his alter ego Dr. Matrix, and the tongue-in-cheek April Fool column from 1975.

Many of those gems just listed were associated with beautiful graphics and
artwork, so it's no surprise that Martin scored some *Scientific American*
covers over the years, though as we'll see below, there's surprisingly little
overlap between his "greatest hits" and his "cover stories."

It's worth noting that, just as the magazine editors selected the titles under
which his original articles appeared—he generally ditched those in favor
of his own when he republished them in the spin-off books—artwork submitted
was often altered by *Scientific American* staff artists.

The number of his cover stories is a tidy dozen, and here they are.

**
Vol 199, No 5, Nov 1958 | "How rectangles, including squares, can be divided
into squares of unequal size" **

**
**
Included (in revised form) as "Squaring the Square" in *More Mathematical Puzzles and
Diversions* (1962). See the recent blog
"Squaring the Square"
at the Celebration of Mind site for
a survey of the background to this story, along with an account of exciting later
developments.

**
Vol 201, No 5, Nov 1959 | "How three modern mathematicians disproved a celebrated
conjecture of Leonhard Euler" **

**
**
Graeco-Latin squares,
i.e., orthogonal Latin squares, had been studied by Euler, who showed in the
1780s that they existed if the square side was odd or a multiple of 4. He
conjectured that none existed for other even values, although it wasn't until
1901 that the case of 6 was definitively ruled out. In the late 1950s, an
example of size 22 was found by R. C. Bose and S. S. Shrikhande, much to
everyone's surprise. With computer help, E. T. Parker found a size 10 example,
and in Apr 1959, the three mathematicians announced the existence of examples
for *all* sizes except unlucky 6. Euler had made an uncharacteristically
poor guess.

Included (in revised form) as "Euler's Spoilers: The Discovery of an Order-10
Graeco-Latin Square" in *New Mathematical Diversions from
Scientific American * (1966).

**
Vol 204, No 4, Apr 1961 | "Diversions in a new book on geometry (Coxeter's
Introduction to Geometry)" **

**
**
Included (in revised form) as "H.S.M. Coxeter" in *New Mathematical Diversions from
Scientific American)* (1966). This cover feature a staff-colorized
version of a now-iconic M. C. Escher image, which the Dutch artist had offered
Martin the use of after writing to him to express his admiration for
*The Annotated Alice* from 1960.

**
Vol 210, No 3, Mar 1964 | "The remarkable lore of prime numbers" **

**
**
This hot-off-the-press item concerned Stan Ulam's discovery of a new pattern in
the distribution of prime numbers when the counting numbers are displayed in a
square spiral,
and was strikingly illustrated by an early example of a computer generated
binary image. The cover image—effectively a colorized re-creation of the
doodle which lead Ulam to his discovery in 1963—spoke volumes.
Included (in revised form) as "Patterns and Primes" in *Martin Gardner's Sixth Book of
Mathematical Diversions from "Scientific American" * (1971).

**
Vol 213, No 1, Jul 1965 | "Four bug problem" **

**
**
Included (in revised form) as "Op Art" in *Martin Gardner's Sixth Book of
Mathematical Diversions from Scientific American* (1971).

**
Vol 221, No 5, Nov 1969 | "Patterns"(1969) **

**
**
Featured the game Patterns from Sid Sackson's Book *A Gamut of Games*.
Included (in revised form) as "Patterns of Induction" in *Mathematical Circus* (1978).

**
Vol 224, No 2, Feb 1971 | "Cellular automata" **

**
**
Martin's Oct 1970 account of John H. Conway's cellular automata game of Life was
perhaps his biggest journalistic success ever, spurring immediate and sustained
interest among both mathematicians and computer scientists, but it didn't make
the cover. This follow-up did. It's included (in revised form) as "The Game of
Life, Part II" in *Wheels,
Life and Other Mathematical Amusements* (1983). See Alvy Ray Smith's
story of how the cover image came about.

**
Vol 230, No 1, Jan 1974 | "I Ching" **

**
**
Included (in revised form) as "The I Ching" in *Knotted Doughnuts and Other
Mathematical Entertainments* (1986).

**
Vol 232, No 1, Jan 1975 | "The curious magic of anamorphic art" **

**
**
Included (in revised form) as "Anamorphic Art" in *Time Travel and Other Mathematical
Bewilderments* (1988).

**
Vol 233, No 5, Nov 1975 | "On map projections (with special reference to some
inspired ones" **

**
**
Included (in revised form) as "Curious Maps" in *Time Travel and Other Mathematical
Bewilderments* (1988).

**
Vol 236, No 1, Jan 1977 | "Extraordinary nonperiodic tiling that enriches the theory of tiles" **

**
**
Here, Martin explains the developments leading to the discovery and recent
refinement of sets of tiles that can only tile the plane aperiodically; those
now called Penrose tiles (or, darts and kites, in Conway's notation).
Included (in revised form) as "Penrose Tiling I" in *Penrose Tiles to Trapdoor
Ciphers...and the Return of Dr. Matrix* (1989). The original sketch for
this cover was made by Conway.

**
Vol 238, No 4, Apr 1978 | "White and brown music, fractal curves and 1/f fluctuations" **

**
**
Included (in revised form) as "White, Brown and Fractal Music" in *Fractal Music, Hypercards and
More* (1992).

Thanks to the MAA, seven of Martin's classic *Scientific American*
articles are available online, as they appeared in later
books (expanded and updated). This includes some of the above cover story articles.

#### Martin Gardner's "Mathematical Games" columns (page 1)

#### The Canon: The fifteen "Mathematical Games" books (page 2)

#### The other "Mathematical Games" spin-offs (page 3)

#### What made "Mathematical Games" special (page 4)

#### Index to "Mathematical Games" (page 5)

#### "The Top 10 Martin Gardner *Scientific American* Articles" (page 7)

*Scripta Mathematica*/

*Mathematics, Magic and Mystery*/

*Scientific American*/

Puzzle Books / Logic /

*Calculus Made Easy*/

*Articles*/

*Reviews*/ Pleasure / Math Legacy