Abstract / Synopsis

Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity, enlightenment, etc. One key theme that underlies many of these qualities is surprise or the unexpected. In this article, I discuss the integral role surprise plays in mathematical beauty. Through examples, I argue that simplicity alone is oftentimes not enough for a piece of mathematics to be considered beautiful, but rather it is unexpected simplicity that we seek. I propose, moreover, that surprise is necessary for enlightenment. The paper also reports results from an activity designed to elicit an appreciation of mathematical beauty from elementary preservice teachers; the majority reaction was a feeling of surprise. Understanding the relevance of surprise to mathematical beauty may offer us a feasible way to create opportunities for students to experience mathematical beauty.



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