Creativity

It may be surprising for some to read that creativity is fundamental in mathematics . Often thought of as the subject “ where there is always and only one right answer ,” there is a common perception that math is a straight-down-the-middle , solve-it-or-you-don ’ t endeavor . With the possible exception of a claimed ability to bend spoons with your mind , nothing could be further from the truth . Mathematicians are problem solvers , and while some of the problems have standard solution methods , others require a great deal of creativity and outside-of-the-box thinking . ( Here you can picture the scene in the classic film Apollo 13 where the mathematicians and engineers are challenged to create a survival plan using only items that were in the stranded capsule .) In my classes , I love to try and find opportunities for students to practice this sort of creativity . Not only does it help them in my class , but it also helps them to become better thinkers and problem solvers in general .

I often use Magic Monday opportunities to do this . After I demonstrate an effect , I give students time to brainstorm a bit to come up with as many ways as they can as to how the trick worked . The goal is not for them to find the way I did it , but rather to identify ways that I might have done it . A great example of this is Fitch Cheney ’ s Five Card Trick . This is the effect in which the magician , seeing four of five randomly selected cards is able to identify the fifth . The effect requires an assistant who is in-the-know , and it uses a mathematical system to use four cards to encode the identity of the fifth . I enjoy hearing the possible methods that the students suggest .

Another way to tap into the students ’ creativity is to ask them to modify my effects to create new ones . For the five-card trick , they ask themselves if they could do the same trick with fewer ( or more ) cards . They like the idea of encoding the identity of things using other things , and they think of lots of different ways to use these codes .

Communication

As students progress through math courses and math majors , they begin to understand the importance of precise communication . In mathematical writing , symbols and terms have precise meanings , and any sort of sloppiness in their use can turn a true statement into a false ( or nonsensical ) one . I use Magic Mondays to give students a chance to practice this precision , and I do this by having them write clear , detailed instructions regarding how an effect looks in performance and how the working is accomplished .

One example that I use a lot in this setting is the classic 21 card trick . The effect is fairly simple to do , but it can be a challenging exercise to write the instructions for someone who has never seen or heard of it . As students prepare drafts , we have other students try to read and follow the instructions as literally as possible . Errors and lack of precision get revealed very quickly this way , and this is both instructive and fun .

Magic , math , and teaching are three of my favorite things . I feel very fortunate to be able to combine all of these things with my Magic Mondays . From hesitant to eager students and from introductory to advanced levels , magic can enrich perceptions , foster creativity , and deepen understanding of the beautiful subject of mathematics . ■

Magic and Mathematics in the Classroom at Princeton and Harvard

“ The Mathematics of Magic Tricks and Games ,” a class taught at Princeton and Harvard , explores the mathematical principles behind games and magic tricks . Students then use those principles to create and master their own tricks and games .

JOHN HARRIS John Harris is a Professor of Mathematics at Furman University . His research spans sports analytics , recreational mathematics , and graph theory . Recent projects include analyses of board games and card games , work on baseball and soccer analytics , and studies of mathematical magic tricks .