Beautiful Equations

In 2015, an online community of scientists and mathematicians got together to share a love of equations, and, every day that year, a beautiful equation appeared on Facebook. The page has since attracted almost 6000 "likes", showing that lots of other people love equations as much as we do. What do we mean by "beautiful" in the context of equations? Well, as John Keats put it almost exactly 200 years ago: "Beauty is truth, truth beauty – that is all Ye know on earth, and all ye need to know" The equations in this book each encapsulate a truth. That truth may be drawn from physics, mathematics, biology, engineering, computing - or from economics, psychology, gaming, etc. - any topic can potentially generate an equation. Many of us can appreciate the beauty in a painting or even a sports car, but equations capture the beauty of simplicity. A beautiful equation is one where the bare essentials of a particular relationship between one aspect of reality and another have been captured in a mathematical statement. The beauty is not in the symbols on the paper (although this can be beautiful to some people), but in the almost magical capability of the equation to capture so much about reality. Equations have a profundity that can be breath-taking; stirring up almost every aspect of human emotion. “Truth” is the key here, but there's more to mathematical beauty than truth. Unlike a line of poetry, we can recognise when an equation is as clear and concise as it can possibly be. If the equation is unnecessarily long or unwieldy, or limited in its scope, then it may lack the beauty for which it was destined. There are no such equations here! In setting up the Facebook page, and in publishing this book, we had other aims than simply to revel in the beauty of mathematics. There are more popularisations of science and other technical topics on the market than ever before, for children and adults alike, enthusiastically covering all aspects of their chosen topics. All except one: publishers of popular science books, convinced of the terrors, inextricable complexities and deep unpopularity of mathematics, do their best to eradicate mathematical formulae from their publications. To do this is not only to present an unbalanced view of science, which necessarily focuses on its superficialities at the expense of its heart and soul, but also to deny access to a source of wonder and knowledge. It is like publishing an image-free book about the world's greatest paintings. We hope that, in a small way, this book will help to redress that imbalance. Colour versions of many of the figures can be found on the original Facebook page: https://www.facebook.com/Beautifulequations2015/