Language of Mathematics

Keith Devlin is one of the best popular mathematics writers around, and this is one of his best works. The eight chapters cover number theory, set theory, calculus, group theory, topology, probability and the application of mathematics to the physical world. The discussion in each chapter, couched generally in English, not mathematics, is so clear that a math-phobic can understand it. By the end of each chapter a great deal of fascinating mathematics has been described, and in some cases the formal basis is sketched--but the emphasis is always on narration, and a lay reader who doesn't even want to understand mathematics can still read this and get a sense of the dramatic history of mathematics.Devlin states at the end that he decided to exclude many areas of mathematics in order to focus more effectively on what he did cover. As a result there is little or no coverage of chaos theory, game theory, catastrophe theory, or a long list of other topics. The fact is there will always be holes in a book this size--mathematics has expanded so much in the last hundred years that even a book ten times this size could barely survey it. The decision to focus was a good one, and the subjects chosen are good: the truly exciting stories are here: Archimedes, Fermat, Gauss, Galois, Riemann, Wiles, and many more.Potential purchasers should note, by the way, that this book was reworked from Devlin's "Mathematics: The Science Of Patterns". In Devlin's words (not from either book): "The Language of Mathematics is a restructuring of Science of Patterns that omits most of the color illustrations (a minus) but has two new chapters covering topics not in Science of Patterns (a plus). If you want lots of color, go for patterns; Language of Mathematics covers more ground." I've read both, and I have to say they're both worth getting. The two new chapters in this book are the ones on probability and the applications of mathematics in science; they're well done and interesting. However, the pictures in Science of Patterns are very high quality.They're both fine books, and I can strongly recommend each of them. If you have to get one, I'd say get Science of Patterns. Even though Language of Mathematics does have some colour plates, Science of Patterns is really a gorgeous book to read with many good illustrations. I ended up buying both, and you may end up doing that too.

Most people either misunderstand what math is all about, or see it as a collection of rather disjointed areas collected together under a single name. Devlin does an admirable job of re-educating us all, and showing how the different areas of mathematics are linked together, often in rather surprising ways.This book is simply brilliant. The amount of information Devlin has managed to cram between two covers is amazing. Having spent years studying this stuff, it's rather depressing to see that most of the important things I've learned can fit into a 350 page book, but then this is surely a testament to Devlin's skill.Although this book makes no formal educational expectations of the reader, I feel that a true beginner would have trouble following a lot of parts, although they would still get the general idea. This would be better then nothing, but I think that this book would be best appreciated by those with some formal math background. I would be curious to see what a high school student would make of this, since I really wish I'd had this book back then. When you see the beautiful ways that mathematics connects the most seemingly disparate ideas, you can't help but want to learn more!

I've always had a like-hate relationship with math; I didn't do well in it in college, but I've long been fascinated by physics. There are many books for the lay person about the cutting edge in physics; books like that are harder to find in the world of mathematics.But Keith Devlin has done it. He surely captured me near the beginning when he described mathematics as the study of patterns; a wonderful description that starts to get at why mathematics seems to be the language underlying the physical universe.This was not an easy book for a slightly math-averse person, but Devlin's explanations were always clear, and more importantly, always gave a sense of context of what he was discussing.

I never thought I would read, nevertheless enjoy, a book on math. This book is unquestionably one of the best works I have ever read on the sciences. Devlin writes in an uncannily concise and proficient style that actually makes the topic of math interesting and understandable to a lay person. Devlin intricately weaves history, mathematical concepts, and complex theories into a very readable text. (I did not think it could be done.)The text is divided into eight sections ranging from numbers to astrophysics. While the book does build on the information offered in each chapter, it is not necessary to read the book in a linear fashion. Devlin makes it very easy to choose chapters of interest.The first chapter deals with numbers. Ironically, we assume a lot about numbers when considering math. Devlin does an excellent job of defining what numbers are apart from the symbols we ascribe to them.The second chapter provides a concise explanation of mathematical proofs, reason, and logic. Using his unique style, Devlin is able to cover this chapter with examples from classic math (algebra) to modern linguistic analysis. The latter is an excellent example of how Devlin applies math theories presented to natural real world examples.Chapter 3 deals with the calculus. If you have ever asked: what is calculus used for, there is finally a concise, understandable presentation available in this chapter.Chapter 4 refers to geometries. Devlin traces the evolution of geometries and provides a good introduction to dimensions beyond the third dimension. (These ideas are continued in Chapters 6 and 8.)Chapter 5 is rather odd but seems to build on analyzing patterns in geometries. It treats topics like packing objects and snowflake patterns.Chapter 6 is the most difficult chapter, in my opinion, but also the most rewarding. This chapter alone is well worth the book. If you ever wanted to understand donuts, coffee cups, manifolds, strings, and knots, this is an excellent chapter. Chapter 7 is my favorite chapter. For once, someone has the insight to simply state that gambling and insurance are derived from the same origins. The chapter is an excellent treatment of regressions, means, and other "statistical" math.Chapter 8 reminds me of Michiu Kaku. It takes many of the mathematical theories and information presented and applies it to modern scientific pursuits like gravity, relativity, and space time.