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Magic, Puzzles Delight Math Fans at G4G


From March 20-23, Atlanta attracted hundreds of people with diverse backgrounds who communicated in the lingua franca of Martin Gardner. Perhaps the last true polymath, Gardner has inspired so many people over the last five decades that they are almost compelled to seek each other out and share their latest discoveries.

The focus of the meeting, the 11th Gathering for Gardner (G4G), is mostly on his contributions to mathematics and its relation to art, music, architecture, puzzles and… fun. Math for this crowd was never boring because participants all somehow evaded the dreary, cut-and-dried experience that math education is for so many. So it is not surprising that the principal undercurrent of the nearly 100 presentations was how to make math come alive for everyone else.

Gardner, who wrote the monthly “Mathematical Games” column for Scientific American for a quarter century and passed away in 2010, had the ability to tie a single mathematical concept to literature, art, magic and paradox. And his readers would take his observations and run with them, improving and generalizing to Gardner's delight. Take the following example. It is an old magic-trick-slash-bar-bet to arrange six cigarettes so that each touches the other:

Gardner gave the above solution (left), well known to magicians. But his readers found that seven cigarettes can also be so arranged (right)! There is typically a deeper mathematical question underlying such challenges, however. Notice the solution requires the cigarettes to be cut at one end. Consider cylinders of fixed diameter that extend without bound in each direction – call these infinite cigarettes. The mathematician J.E. Littlewood asked if seven infinite cigarettes could be arranged so that each touches all the others. This question was answered at G4G. Sándor Bozóki, Tsung-Lin Lee and Lajos Rónyai set up a system of 20 polynomials in 20 variables, and after five weeks using 16 computer processors they found two solutions (such that two of the cylinders were at right angles; see image below). It might even be possible to achieve the same feat with eight infinite cigarettes

This is the life cycle in recreational math: playfulness, "aha" solutions and mathematical exploration, all leading back to new playful observations. The G4G crowd talked about at least 50 problems at all stages of the cycle.

A crowd favorite was Tadashi Tokieda. For years, he has demonstrated the delights of what he calls "toys." A toy is simply an object that delights the observer, but you do not play with it so much as you marvel at it and wonder how it works. A current YouTube sensation is the sight of a chain that rises up in the air as it slips out of a cup. He demonstrated how various cylinders roll down a ramp in very counterintuitive ways. Tokieda wants you to try and figure it out – but he also will help you. It's all about the interplay of wonder and education.

A feature of all the G4G has been magic. Gardner was an inventor of magic effects for eight decades, but shied away from performance. However, well-known magicians owe a debt to those like Gardner for creating the principles they use. There were three magic shows at the most recent conference where an array of magicians delighted the crowd. A special treat was the mentalist team of Ginny and Simon Aronson. They have honed their techniques for so many years that anyone would be forgiven if they thought they were witnessing true mind reading. The whole G4G experience is due to the active involvement year after year of magicians such as Mark Setteducati, Lennart Green and John Railing, to mention just a few.

Another theme that dominates the G4Gs is the interplay of mathematical principles and the fabrication of real objects. Sometimes these are puzzles, such as take-apart puzzles, twisty-puzzles, and a block of wood that rolls downhill and then rolls uphill! But this year most speakers were concerned with art.

Mathematical art starts with the desire to have math come alive for students and the public, but the speakers would impress the crowd with the aesthetics of their creations. Among others thing, we learned of the beauty of stochastic geometry used by John Shier. Craig Newswanger told of holographic visualization. Karen Mortillaro is embarked on a project of sculpting anamorphic Alice in Wonderland scenes that are viewed in wavy mirrors. Susan Goldstine created a seven-colored torus using beadwork. And the G4G tradition of building a sculpture garden continued with erection of four new mathematical artworks of metal, wood, string and plastic. The participants were allowed to help build them.

Music was unusually popular this time. Hilarie Orman explained the relationship of music to the Platonic solids and John Miller showed us how sound can be used to understand caroming billiard balls within polygons. Philip Shepard discoursed on string theory – the theory of stringed instruments that is. And he entranced everyone with virtuoso demonstrations on the cello.

This year is the centennial of Gardner's birth, and much of the discussion was how to keep his vitality in front of the next generation. April is Math Awareness Month, and this year it will focus on the legacy of Gardner; it is entitled Mathematics, Magic and Mystery. Eoin Gill and Sheila Donegan, of the Centre for the Advancement of Learning of Maths, Science and Technology (Calmast), spoke of promoting math to a wider audience. But the entire G4G effort is about sharing ways to do just that.

Finally there were more introspective speakers who addressed the mental side of this whole enterprise. Kristine Hjulstad, creator of Norway’s Magisk Teater, provided new insights into how magicians fool our brain. Anany Levitin, a professor at Villanova University, discussed how to solve puzzles. Gary Antonick—who blogs about math and logic for the New York Times—argued that curiosity is the central component of all the dimensions that make us human.

For me "wonder" is the key word. Magician Lisa Menna explicitly explored how a sense of wonder is the precursor to creativity and discovery. Gardner wrote many essays about how a sense of wonder (or awe or surprise) is the antidote to the hubris of the human condition. He always felt honored by the efforts of G4G to surround us with wonderful things.

The views expressed are those of the author and are not necessarily those of Scientific American.

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