Who This Book Is For
¶ 1 Leave a comment on paragraph 1 0 This book isn’t meant to be a textbook. Instead, it is meant to be a starter kit for applying mathematics and mathematical thinking to the real world we live in: the one made out of physics and biology and artists and activists and shopkeepers and stockbrokers. It is meant to introduce what is sometimes called “higher mathematics”—a phrase that sounds suspiciously like “High Elvish” or “High Magicks”—to readers who may have given up on mathematics the first time they saw letters getting mixed up in their numbers. It is my strong belief that many concepts of advanced mathematics can be made into concrete stories and examples, mostly without computation and mostly without proofs, in such a way that ordinary humans can imagine and play with the possible implications of these ideas.
¶ 2 Leave a comment on paragraph 2 0 I don’t think it’s right that only those particular nerds with a knack for thinking syntactically (i.e., in step-by-step groupings of crazy symbols) get to play with advanced mathematical notions.1 If you are reading this, you are using your brain to transform symbols on a page or screen into an abstract voice, transmitted across time and space from my mind directly into yours. You are already able to think on a staggering level of abstraction, and you deserve access to the power of abstraction to expand the mind’s conception of what is possible, not only in your neighborhood or town or nation or culture, but what might be possible in worlds that are too impossible to fit into this universe. I’m going to show you some examples of using abstractions, find stories that might explain a bit about why the world is the way it is, and introduce you to how a mathematician thinks about some of the invisible abstract forces that control our lives.
¶ 3 Leave a comment on paragraph 3 0 If you find yourself inspired and motivated to learn more about mathematics, whether to satisfy your curiosity or to use mathematics in your own art or activism, this book will acquaint you with further resources to continue your study. Don’t get me wrong: learning mathematics for real means means spending a lot of time being frustrated, being confused, being stuck, and forcing yourself to learn a very terse and often unfriendly language that the mathematicians who have come before developed in order to think very precisely about very abstract notions. But the rewards are great. If you take the time to follow up on the signposts to “proper mathematics” that are scattered through this text, you will find entire vistas of theory to apply to whatever you practice, and you’ll be just straight up smarter and more frustration-tolerant to boot. Welcome to Wonderland!
¶ 4 Leave a comment on paragraph 4 0 If you already are an initiate into mathematics, I’m hoping you get something a little bit different out of this book. I’m hoping that this book helps you develop your vocabulary for talking about these ideas with people who seem to get all sweaty and nervous when all you’re doing is waxing rhapsodic about polynomials and linear operators. Additionally, I’ve tried to keep current on the cuttingest of the cutting edge on advanced topics like gauge theoretic economics and applied category theory, so that even if you devour group symmetries for breakfast, you’ll see math applied in ways that are genuinely new to our discipline. With swears.