Customer Reviews

The Language of Mathematics: Making the Invisible Visible

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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.

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.

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.

The other reviewers have done a fine job reporting that this is a fun, engaging book. I want to say that my level of math includes two semesters of calculus, and that was more than enough to understand and enjoy the contents of this book.

I'd known that knot-theory and set-theory various other kinds of math existed out there, but I didn't know much else. I'd never heard of projective geometry, although after reading this book I've found some nice examples online. I was introduced to these and other forms of math very gently and provocatively by Devlin's book, so if you are in a position similar to me, this is the book you want to read.

I read dozens of books a year; and every year for Christmas I give my father the five best books I've read in that year, with the provision that they must be diverse and comprehensible to him: an intelligent man, though largely self-educated, with no papers to show, but a "working-man's PhD," as Aaron Tippin sang. As a testament to the comprehensibility of this book, it will be waiting for him this December.

As for myself, someday I hope to continue studying math at a universtity; for now my curiosity is sated with books like this, and it pleased me very much.

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!

This book is an incredible account into the ideas of mathematics. Devlin presents simple and extremely abstract ideas into a language that just about anyone can understand. Although some previous knowledge of the fields investigated does help, this book serves as a great introduction into such things as perspective geometry, non-Euclidean geometry, network theory, topology and quantum mechanincs. It also provides some great insights into the history and uses of number theory, algebra, geometry and calculus. I've have never read a mathematical/scientific work that was written with such passion and was a complete page turner (I read it straight over the course of 3 days). I am still amazed on how such a work can be under $50 because it is worth much more than that.

I loved this book. If you want want to know what exactly mathematics is then it's just the ticket. Mr. Devlin doesn't have the whacky humour of Paulos or the literary flourishes of Stuart but I didn't want to be entertained, I wanted to understand and this book has a refreshingly clear style. My only criticism is that all too often the author said "I won't show that here" when you felt if he'd only tried you would have got it. A couple of things like Bayes' theorem felt incomplete but maybe they'll be a sequel.

By the time you get to exactly page 107 and see the logic of differential calculus hanging as beautifully as "Water Lilies", you might want to thank and slap those teachers who did in fact teach you mathematics, but who did not give you even a little of the reason behind the math -- the fundamental problems or quests that give rise to mathematics.

All of this adds context that makes learning a big rush. It's possible that mathematics would not be so patently daunting if it were approached with deeper context instead of the abstraction beginning in chapter 1 of many school texts. This seems to be Mr. Devlin's approach in the book -- helping the reader appreciate and embrace the abstraction that is a prerequisite for opening the mind's eye.

Both the author's and his reviewer's constant usage of terms such as power, elegance and simplicity is clearly in order. It's not just a left-brain affair and Mr. Devlin's book is a powerful exposition on that, especially as he details the creative cognitive leaps by many great minds over the course of thousands of years.

For the record, I don't mean to go slapping anybody - I just got happy; that's all.

Devlin: "The particular topics I have chosen are all central themes within mathematics... But the fact is, I could have chosen any collection of seven or eight general areas and told the same story; That mathematics is the science of patterns, and those patterns can be found anywhere you care to look for them, in the physical universe, in the living world, or even in our own minds. And that mathematics serves us by making the invisible visible."
At this writing it has been more than a few years since my last class in mathematics. But I liked math as a student and still do, even at the point that notation and degree of abstraction begins to hurt my head, so to speak, I still like it. There is a solidity and a beauty in mathematics that eclipses the empirical sciences. It is not only the practical applicability, logical purity, and beauty of mathematics that interest me, it is also its very immateriality. As Devlin states, "music exists not on the printed page, but in our minds. The same is true for mathematics; the symbols on a page are just a representation of the mathematics."
This is a wonderful book. Before 1900, mathematics could be wholly categorized within about a dozen subjects. While advances are still being made in some of these older disciplines -- Devlin discusses how developments in number theory are being applied to encryption for such purposes as banking security -- there are now at least 60-70 somewhat distinct disciplines of mathematics. The author reveals the logical foundations, history, and current applications of number theory, mathematical logic, the calculus, relativistic geometry, topology, and probability. Applications of mathematics to such seemingly far-flung fields as linguistics, electrodynamics, and astrophysics are briefly but aptly considered. He introduces us to the patterns and progressions of perceptive minds, from the Pythagoreans, Platonists, and Peripatetics, to Pascal and Penrose, with glances at Galileo, Gauss and Godel. [Okay, enough alliteration ... just having a little fun with patterns; and patterns, as Devlin instructs, is precisely what mathematics is all about.]

For trying to be a popular exposition on mathematics Devlin's book is too difficult for the lay reader. Unless you have university level mathematics in your luggage you won't understand much. The explanations of basic conepts are missing, the proofs are not there and the history is condensed into a few pages. Thus if your mathematical imagination cannot fill in these gaps you will not extract much pleasure from this book. You will rather be frustrated. I myself have read mathematics at the university and still couldn't follow him everywhere. The problem is that the labeling of the book is misleading. This is not a book of popularized mathematics. This is leizure time reading for mathematics professors and math-freaks. If you want to read something that is easy to understand but still interesting try some of the American Mathematical Society's wonderful publications (you can find them all on amazon).