Martin Gardner's Correspondence
There's an apocryphal story that Martin's hexaflexagons article for Scientific American in Dec 1956 generated more correspondence than the sum of that from the entire prior history of the magazine, going back to 1845. In any case, there was a lot of it, and a great deal more was to follow thanks to the subsequent "Mathematical Games" column which he wrote monthly for Scientific American into the 1980s.
Martin often wrote back to the readers who sent him suggestions—or solutions to puzzles he had posed—and hence developed strong relationships with numerous academics and researchers, as well as with keen youngsters. He certainly directly and indirectly inspired many teenagers to pursue careers in mathematics and science, both in the Sputnik era and the decades that followed.
His friend Donald Knuth wrote in "Memories of Martin Gardner" Notices of the AMS (Mar 2011), "Already when he began his monthly series in 1956 and 1957, he was corresponding with the likes of Claude Shannon, John Nash, John Milnor, and David Gale. Later he would receive mail from budding mathematicians John Conway, Persi Diaconis, Jeffrey Shallit, Ron Rivest, et al. These files of correspondence now have a permanent home at Stanford University Archives."
The Stanford Martin Gardner Papers amounts to 160 boxes of material, and the collection's description reads:
"These papers pertain to his interest in mathematics and consist of files relating to his Scientific American mathematical games column (1957-1986) and subject files on recreational mathematics. Papers include correspondence, notes, clippings, and articles, with some examples of puzzle toys. Correspondents include Dmitri A. Borgmann, John H. Conway, H. S. M Coxeter, Persi Diaconis, Solomon W. Golomb, Richard K. Guy, David A. Klarner, Donald Ervin Knuth, Harry Lindgren, Doris Schattschneider, Jerry Slocum, Charles W. Trigg, Stanislaw M. Ulam, and Samuel Yates."A great deal more information is available at the Guide to the Martin Gardner Papers .
Martin's early 1960s correspondence with Dutch artist Escher is also well documented, M.C. Escher’s Legacy–A Centennial Celebration, edited by Michele Emmer and Doris Schattschneider (Springer, 2003).
Martin corresponded with a great many people on a vast array of topics, much of it totally unrelated to his Scientific American writing. For a peek at a different passion of his, see the Erdnase-related correspondence.
One of the most extraordinary examples of Martin's correspondence with a non-professional fan of mathematics, which led to a signficant advance in research on pentagon tilings, was the mid-1970s case of Marjorie Rice and her new tilings of the pentagon. Her work followed earlier improvements on what Martin had written about by another reader, computer scientist Richard James III.