Editing Martin Gardner (section)

== Gardner's mathematical grapevine ==
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| quote = He had carried on incredibly interesting exchanges with hundreds of mathematicians, as well as with artists and polymaths such as Maurits Escher and Piet Hein.<ref name=allyn_jackson/>
| source = – [[AMS Notices]]
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}}Gardner maintained an extensive network of experts and amateurs with whom he regularly exchanged information and ideas.<ref name=Peterson_2014>Peterson (2014)</ref>  [[Doris Schattschneider]] would later term this circle of collaborators "Gardner's mathematical grapevine" or "MG<sup>2"</sup>.<ref name=Case_2014>Case (2014)</ref><ref>[[David A. Klarner]], editor (1981),  "In Praise of Amateurs" in ''The Mathematical Gardner'', Weber & Schmidt, 1981.</ref>

Gardner's role as a hub of this network helped facilitate several introductions that led to further fruitful collaborations.{{efn|Before there were search engines, the intellectual world relied on human hubs to serve as repositories of knowledge and connectors of people with common interests who otherwise would not have known one another. Martin Gardner was such a connector. His column was the best mathematical watering hole of its day, and behind the scenes he served as a tireless mathematical match-maker. Gardner was a hub par excellence.}}<ref>Propp (2015)</ref> Mathematicians Conway, Berlekamp, and Guy, who met as a result of Gardner's influence, would go on to write ''Winning Ways for your Mathematical Plays'', a foundational book in [[combinatorial game theory]] that Gardner subsequently championed.<ref>Berlekamp (2014):  Partly because of what I had read about them in Martin Gardner’s columns, I was appropriately awestruck in the 1960s when I first met Sol Golomb and then Richard Guy, each of whom had a large influence on my subsequent work. In 1969 Richard introduced me to John Horton Conway, and the three of us immediately began collaborating on a book that eventually became ''Winning Ways for Your Mathematical Plays''. In the 1970s, I joined Conway in some of his many visits to Gardner’s home on Euclid Avenue, in Hastings-on-Hudson, New York. Gardner soon became an enthusiastic advocate of our book project, and he previewed various snippets of it in his ''Scientific American'' columns.</ref><ref>[https://www.cut-the-knot.org/books/WW1/back.shtml Reviews of the first edition of Winning Ways for Your Mathematical Plays] cut-the-knot.org</ref> Gardner also introduced Conway to Benoit Mandelbrot because he knew of their mutual interest in [[Penrose tiling|Penrose tiles]].<ref name=Mulcahy_2014/><ref>Gardner (2013) page 144: Conway had been making new discoveries about Penrose tiling, and Mandelbrot was interested because Penrose tiling patterns are fractals.</ref> Gardner's network was also responsible for introducing Doris Schattschneider and [[Marjorie Rice]], who worked together to document the newly discovered pentagon tilings.<ref name=Peterson_2014/><ref>{{citation|last=Cole|first=K. C.|title=Beating the Pros to the Punch|date=March 11, 1998|url=https://www.latimes.com/archives/la-xpm-1998-mar-11-mn-27706-story.html|journal=[[Los Angeles Times]]}}.</ref>

As he was launching his monthly column in 1956 and 1957, Gardner began corresponding with mathematicians such as [[Claude Shannon]], [[John Forbes Nash Jr. | John Nash]], [[John Milnor]], and [[David Gale]].<ref>AMS Notices (2011)</ref>He credited his network with generating further material for his columns: "When I first started the column, I was not in touch with any mathematicians, and gradually mathematicians who were creative in the field found out about the column and began corresponding with me.  So my most interesting columns were columns based on the material I got from them, so I owe them a big debt of gratitude."<ref name=Case_2014/>

Gardner prepared each of his columns in a painstaking and scholarly fashion and conducted copious correspondence to be sure that everything was fact-checked for mathematical accuracy.<ref>AMS Notices (2011)</ref> Communication was often by postcard or telephone and Gardner kept meticulous notes of everything, typically on index cards.<ref>BBC News (2014):  His secret was a fantastic card index system of his own, going back to the 1930s, stored in shoe boxes.</ref> Archives of some of his correspondence stored at [[Stanford University]] occupy some 63 linear feet of shelf space.<ref>[https://oac.cdlib.org/findaid/ark:/13030/kt6s20356s/ Stanford University Archives: Gardner (Martin) Papers] Online Archive of California</ref> This correspondence led to columns about the [[rep-tile]]s and [[pentominos]] of Solomon W. Golomb; the [[Gosper curve|space filling curves]] of Bill Gosper;<ref>''[https://books.google.com/books?id=twp0-yA-GVAC&dq=gosper+martin+gardner&pg=PA1 Discrete Geometry, Combinatorics and Graph Theory]'' : Revised selected papers; Jin Akiyama, William Y.C. Chen, Mikio Kano</ref> the [[aperiodic set of prototiles|aperiodic]] tiles of Roger Penrose; the [[Conway's Game of Life|Game of Life]] invented by John H. Conway; the [[superellipse]] and the [[Soma cube]] of Piet Hein; the [[trapdoor function]]s of [[Whitfield Diffie|Diffie]], [[Martin Hellman|Hellman]], and [[Ralph Merkle|Merkle]]; the [[flexagon]]s of [[Arthur H. Stone|Stone]], [[Bryant Tuckerman|Tuckerman]], [[Richard Feynman|Feynman]], and Tukey; the geometrical delights in a book by H. S. M. Coxeter; the [[game of Hex]] invented by Piet Hein and John Nash; Tutte's account of [[squaring the square]]; and many other topics.

The wide array of mathematicians, physicists, computer scientists, philosophers, magicians, artists, writers, and other influential thinkers who can be counted as part of Gardner's mathematical grapevine includes:<ref name=Case_2014/><ref name=BBC_News>BBC News (2014)</ref><ref name=hofstadter/><ref name=gardner_1998>Gardner (1998)</ref><ref name=teller/><ref name=Mulcahy_2013/><ref>[http://mathfactor.uark.edu/2010/06/ha-conway-on-gardner/ The Math Factor Podcast Website] John H. Conway reminisces on his long friendship and collaboration with Martin Gardner.</ref><ref name=Antonick_2014/><ref name=Peterson_2014>Peterson (2014)</ref>

{{div col|colwidth=12em}}
* [[Robert Ammann]]
* [[Mitsumasa Anno]]
* [[Elwyn R. Berlekamp]]
* [[Dmitri A. Borgmann]]
* [[Gregory Chaitin]]
* [[Fan Chung]]
* [[John Horton Conway]]
* [[H.S.M. Coxeter]]
* [[Erik Demaine]]
* [[Persi Diaconis]]
* [[M. C. Escher]]
* [[Solomon W. Golomb]]
* [[Bill Gosper]]
* [[Ronald Graham]]
* [[Richard K. Guy]]
* [[Frank Harary]]
* [[Piet Hein (scientist)|Piet Hein]]
* [[Douglas Hofstadter]]
* [[Ray Hyman]]
* [[Scott Kim]]
* [[David A. Klarner]]
* [[Donald Knuth]]
* [[Harry Lindgren]]
* [[Benoit Mandelbrot]]
* [[Robert Nozick]]
* [[Penn & Teller]]
* [[Roger Penrose]]
* [[James Randi]]
* [[Marjorie Rice]]
* [[Ron Rivest]]
* [[Tom Malin Rodgers|Tom Rodgers]]
* [[Rudy Rucker]]
* [[Lee Sallows]]
* [[Doris Schattschneider]]
* [[Jeffrey Shallit]]
* [[David Singmaster]]
* [[Jerry Slocum]]
* [[Raymond Smullyan]]
* [[Ian Stewart (mathematician)|Ian Stewart]]
* [[W. T. Tutte]]
* [[Stanislaw Ulam]]
* [[Samuel Yates]]
* [[Nob Yoshigahara]]
{{div col end}}