Martin Gardner has had no formal education in mathematics, but he has had an enormous influence on the subject. His writings exhibit an extraordinary ability to convey the essence of many mathematically sophisticated topics to a very wide audience. In the words first uttered by mathematician John Conway, Gardner has brought “more mathematics, to more millions, than anyone else." In January 1957, Martin Gardner began writing a monthly column called “Mathematical Game” in Scientific American. He soon became the influential center of a large network of research mathematicians withwhom he corresponded frequently. On browsing through Gardner’s old columns, one is struck by the large number of now-prominent names that appear therein. Some of these people wrote Gardner to suggest topics for future articles; others wrote to suggest novel twists on his previous articles. Gardner personally answered all of their correspondence. Gardner’s interests extend well beyond the traditional realm of mathematics. His writings have featured mechanical puzzles as well as mathematical ones, Lewis Carroll, and Sherlock Holmes. He has had a life-long interest in magic, including tricks based on mathematics, on sleight of hand, and on ingenious props. He has played an important role in exposing charlatans who have tried to use their skills not for entertainment but to assert supernatural claims. Although he nominally retired as a regular columnist at Scientific American in 1982, Gardner’s prolific output has continued. Martin Gardner’s influence has been so broad that a large percentage of his fans have only infrequent contacts with each other. Tom Rodgers conceived the idea of hosting a weekend gathering in honor of Gardner to bring some of these people together. The first “Gathering for Gardner” (G4G1) was held in January 1993. Elwyn Berlekamp helped publicize the idea to mathematicians. Mark Setteducati took the lead in reaching the magicians. TomRodgers contacted the puzzle community. The site chosen was Atlanta, partly because it is within driving distance of Gardner’s home. The unprecedented gathering of the world’s foremost magicians, puzzlists, and mathematicians produced a collection of papers assembled by Scott Kim, distributed to the conference participants, and presented to Gardner at the meeting. G4G1 was so successful that a second gathering was held in January 1995 and a third in January 1998. As the gatherings have expanded, so many people have expressed interest in the papers presented at prior gatherings that A K Peters, Ltd., has agreed to publish this archival record. Included here are the papers from G4G1 and a few that didn’t make it into the initial collection. The success of these gatherings has depended on the generous donations of time and talents of many people. Tyler Barrett has played a key role in scheduling the talks. We would also like to acknowledge the tireless effort of Carolyn Artin and Will Klump in editing and formatting the final version of the manuscript. All of us felt honored by this opportunity to join together in this tribute to the man in whose name we gathered and to his wife, Charlotte, who has made his extraordinary career possible. Elwyn Berlekamp Tom Rodgers Berkeley, California Atlanta, Georgia

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