Performing Mathematical Magic

The performance of mathematics on stage is not very common although many mathematicians are amateur magicians. In this paper we discuss mathematical magic as a performing art, given some tips on presentation as well as the description of mathematical tricks that work fine in a mathematical magic show. Everything is contrasted by personal experience performed in different contexts. Mathematics and Magic The relation between mathematics and magic lasts for more than 500 years. From Luca Pacioli's manuscript De Viribus Quantitatis, where it is described the first card magic trick in the literature, to the last column of Colm Mulcahy in his Card Colm section in the MAA webpage (December 2010, at the time of writing this paper), there has been a lot of work showing how mathematical ideas can be applied to different types of magic tricks, involving quick number magic for children, geometrical and topological ideas for stage magic and, of course, card tricks. Among magic writers there are two names that should be especially highlighted for being also well known in the mathematical world. One of them is Girolamo Cardano, who wrote, in The Subtilitate rerum, the first description in a printed book of a card trick (is it by mere chance that the first appearences of card tricks in the literature in both manuscript and printed were written by mathematicians?) and the other one is Martin Gardner, recently deceased, who left us lots of material to study. Most people fond of recreational mathematics know Martin Gardner because of his Mathematical Games column in Scientific American. In almost each one of his books on recreational mathematics there is something related to mathematical magic. The surprising fact is the influence he had in both communities: the mathematical and the magical. In the latter, he is regarded as a magical creator, not only a mathematical magic creator. Although his role as inventor of magic tricks, Gardner tells he was not a performer and that he performed a magic show just once, when he was a student, and in his own words “that was the first time I realized that you’re really not doing a magic trick well until you’ve done it in front of an audience about a hundred times” [2]. To introduce mathematics in culture and to reach the general public it is necessary to use a format similar to the cultural scheme people are used to. In this sense, mathematical sculptures or mathematical photographs are regarded as sculptures or pictures, removing the adjective “mathematical” that frightens some citizens (and we don't know why!). Consequently a mathematical magic show should be similar to a magic show: an amusing performance, enjoyed by the public, with participation of the audience and where the trick is not revealed. It is very difficult to do it since we mathematicians always intend to explain why things happen. In any case, there are always methods for educate without breaking the magic. One of the alternatives is just making a Bridges 2011: Mathematics, Music, Art, Architecture, Culture