April is Math Awareness Month, and this year’s theme of “Mathematics, Magic, and Mystery” has been wonderfully illustrated by videos and activities at mathaware.org. Some of these topics were previewed in the March “Pun and Taylor” magic show. On April 16, two more magical topics were covered by Dr. Karin Saoub and Dr. Hannah Robbins. Dr. Saoub’s talk centered on the seemingly ridiculous idea that 1+2+3+4+5+… is equal to -1/12: not only a finite sum, but negative and fractional! There is a “proof” of this result that certainly appears valid (well, it looks complicated, and sometimes we shut our brains down at that point) and the result is used in string theory. Dr. Saoub guided us through the flaws in the “proof” and used this oddity as a launching point for a discussion of the importance of definitions in mathematics. The importance of definitions was further emphasized in Dr. Robbins’ demonstration (this one valid) that a certain braid could not be done. This followed a remarkable video demonstration of how to braid a three-slot ribbon. By counting crossings in a braid, we can show that a four-slot ribbon cannot be braided. As Dr. Robbins discussed, proving that something cannot be done is a challenge; how do you go beyond “I don’t know how to do it” to a “Nobody can ever do it” conclusion? Mysterious and magical problems that lead directly to the heart of mathematics: there are 30 of them to explore at mathaware.org!
