Puzzles and tricks from Martin Gardner inspire math and science
Martin Gardner was a great man of many talents. He was an amateur mathematician, a puzzler, a professional magician, a debunker of pseudoscience, and a popular writer about all of these topics. He wrote more than 65 books and published a column, “Mathematical Games,” in Scientific American for 25 years, from 1957 to 1982. Because of his influence on countless readers, Gardner became known as the father of “recreational mathematics”—playful mathematical problems designed and solved purely for fun. Gardner’s accessible, inviting prose and his ability to correspond with impressive numbers of readers gave the general public the opportunity to enjoy mathematics and to participate in mathematical research. Many of today’s mathematicians, including myself, entered the field at least in part due to Gardner’s influence.
Sadly, Gardner died on May 22, 2010, at the age of 95. His death has been sorely felt by mathematicians around the world. But rather than dwell on our loss, I feel compelled to celebrate the tradition that Gardner started. Roughly every two years since 1993, Tom Rodgers has organized a conference in Atlanta called the Gathering for Gardner. It brings together mathematicians, puzzlers, magicians and debunkers who love the work of Martin Gardner and the spirit he embodied—playful intellectual curiosity. Gardner’s own absence from the Gathering since 1996 has not stopped it from continually growing in participation and intensity. The ninth Gathering, held last March, was the most prodigious yet, with 300 participants, a half-day sculpture-building party and two evening magic shows.
I am a theoretical computer scientist, which puts me at the boundary of computer science and mathematics. The goal of the field is to use mathematics to understand computation—what it is and what it can do. Readers of this column already know that computation is extremely powerful, offering new perspectives, approaches and solutions in perhaps every discipline. Computer science is highly unusual in this universality of influence—the only other example I know of is mathematics—and it’s what excites me about the field. The interdisciplinary field of “computational x” is central to most fields where it has been considered (the “x” could be biology, chemistry, neuroscience, geometry, linguistics, finance, and so on)—and for other fields, I believe it is simply yet to be discovered.
What I’d like to show here is that computation is a useful way to think about more recreational pursuits, too—specifically puzzles and magic. Martin Gardner is my inspiration: He did not consider puzzles, magic and mathematics as separate pursuits, but blurred the traditional boundaries between them. He routinely illustrated mathematics using puzzles and magic, and he studied puzzles and magic using mathematics. I like to apply the same spirit to theoretical computer science, where the computational perspective offers new ways to think about puzzles and magic—specifically, how to design challenges and tricks automatically. Voilà, recreational computer science!
Gardner’s work continues to influence researchers such as myself. The three examples I’ll describe are solutions to problems that Gardner posed—ones he stated explicitly or ones that have been inferred from his work. Throughout Gardner’s writings are countless mathematical questions, puzzles and magic tricks that deserve further research and extension. I encourage everyone to read through his collected works, for the fun this always brings, as well as to help find these seeds for future research. I will collect your suggestions, which you can send to martingardner at csail dot mit dot edu dot Long live the spirit of Martin Gardner!
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