I’ve been focusing a fair amount of energy lately on sharpening the math skills, so I was intrigued when I stumbled upon this book, Letters To A Young Mathematician by Ian Stewart. The format of this book is awesome — each chapter is a letter to an up-and-coming mathematician, starting from high school all the way through tenure.  The book provides a very accessible overview of what real mathematics is all about and why it is useful and even beautiful. Dr. Stewart does a great job explaining some of the most famous math problems and personalities in history, provides a wonderful overview of what a proof is and why it’s important.  One of my favorite things about this book is the way that he applies math to the real world, making it abundantly clear how much modern society relies on mathematics to solve some of the biggest problems of the day.  He laments that society doesn’t really give math a fair shake, often treating it as a nuisance and highlighting that most people don’t think about math much beyond basic arithmetic.  Then he offers several examples of critical infrastructure that rely on mathematics to work, from shipping to economics.  He paints a fine picture by saying that he almost wishes that everything that relied on math came with a bright red sticker that says “Math Inside” — and that the globe would literally be covered in such stickers. The touching part of the text though is of course the illustration of mathematics operating in nature.  My favorite example is how Ian explains the math behind rainbows — that each individual droplet in the rainbow reflects light differently off of its spherical structure and thus each person observing the rainbow actually sees a completely different and unique rainbow from other observers, stating that in this sense every rainbow is a personal experience.  The author definitely put his heart into crafting this text and it is most deserving of a read.