Why are the 300-odd "Mathematical Games" columns that Martin wrote for
Scientific American so consistently good? There are some obvious reasons:
He spent a great deal of time researching each of them, often in the public
library on 5th Ave at 42nd St in New York City. He once told Persi Diaconis that
he spent about twenty-five days a month on his column.
He had a seemingly endless supply of top-notch material, which never dried
up. Indeed, as he became better known, he was befriended by mathematicians and
others who fed him more ideas.
He showed excellent taste in selecting what to write about.
He always displayed admirable clarity of thought and economy of words.
He covered a wide diversity of topics; one never knew what he might write
The things Martin wrote about for Scientific American varied enormously. There were topics he'd touched on in earlier writing (e.g., in his book Mathematics, Magic and Mystery), such as,
Magic squares; cards; dice; dominoes; modular arithmetic; Fibonacci and Lucas numbers; geometric vanishes; Pascal's triangle; Möbius strips and Klein bottles; knots; and illusions of various kinds.There were columns that became regarded as classics, covering,
Hexaflexagons; the Soma cube; Eleusis; polyominoes; tangrams; pentominoes; rep-tiles; origami; the art of M. C. Escher; the 3n + 1 problem; Conway's game of Life; Fermat's last theorem; the four-color map problem; RSA cryptography; fractals; Gödel's theorem; and paradoxes from A to Z (all crows are black, grue-and-bleen, infinity, Newcomb's, nontransitive dice, unexpected hanging, Zeno's).Much additional fascinating terrain was explored, including,
mathematical music; spirals and helices; cycloids; conic sections; curves of constant width; superellipses; squaring the square; tesseracts and 4D space; 4D tic-tac-toe; nonconservation of parity; machines that learn or think; fallacies in mathematical reasoning; Nim and its variants; properties of e and pi; random walks; hyperspheres; palindromes; impossible objects; graph theory; pseudo-random numbers; time reversal and time travel.
Peter Renz was Martin's editor at W. H. Freeman and Company in the 1980s, and again (with Don Albers) in the last decade of his life, at the MAA. He worked with Martin on the searchable CD-Rom Martin Gardner’s Mathematical Games: The Entire Collection of His Scientific American Columns (MAA, 2006), and also set up arrangements for the The New Martin Gardner Mathematical Library (a joint project of the MAA and Cambridge University Press). Peter recalls,
"When I was tracking down the artists who illustrated Martin's columns, I went back to the original magazine articles and looked at all of them. I was struck by how interesting they were, by the great impact they have had over the years, by the fact that Martin picked up on what may have seemed obscure at the time and of limited interest, but what subsequently came to be seen as important (or at least quite interesting).
To mention just one thing, the Kakeya problem is mentioned in the column on curves of constant width (Book 4, Chapter 18, The Unexpected Hanging and Scientific American, 148–156, Feb 1963). This problem, in generalized forms, is of burning interest in harmonic analysis and in computer data processing.
What bore in on me was how short these original columns were. Martin had a perhaps unique ability to say just enough and then let the reader carry things further or move on, as the spirit moved."
In the delightful and generously illustrated 32-page booklet that accompanies the MAA CD-rom, Martin gave an interesting response to the challenge "Complete the following: 'I enjoy mathematics so much...'" from interviewer Don Albers. He said,
"Because it has a strange kind of unearthly beauty. There is a strong feeling of pleasure, hard to describe, in thinking through an elegant proof, and even greater pleasure in discovering a proof not previously known."Martin then mentioned some of his own experiences of this pleasure.
Index to "Mathematical Games" (page 5)
Puzzle Books / Logic / Calculus Made Easy / Articles / Reviews / Pleasure / Math Legacy