Customer Reviews

Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe

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Keith Devlin is one of the best popular mathematics writers around, and this is one of his best works. The six chapters cover number theory, set theory, calculus, group theory and topology; but to state it baldly like this is to miss the main value of this seductively illustrated book. Devlin titles his chapters innocuously--"Shape", or "Position"--and the initial discussion, 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. And of the dramatis personae, too; one nice feature is the large number of good pictures of mathematicians, including several more recent figures such as Ribet and Thurston.

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.

The illustrations deserve an extra comment. I've already mentioned the pictures of mathematicians. There are good diagrams, of the quality you'd expect from Scientific American. There are also plenty of pictures of the sort you see in every maths book of this kind--Escher tessellations, Kepler's nested Platonic solids, a Durer perspective drawing. But there are several more that I've never seen (and I've read a lot of these books). Two notable pictures: a cardboard model of an aperiodic tiling of space, by John Conway; and a picture of a set of tiles at a Dutch high school, designed by Escher: I'm an Escher fan and have never seen these before.

Potential purchasers should note, by the way, that this book was reworked into Devlin's "Language of Mathematics". 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."

This is a fine book. Strongly recommended.

This book is a brilliant example of mathematics at it's best. It is from Scientific American, so you know you can trust it. And it is written at an understandable level, quite a feat for many very complex topics. The book features incredible illustrations, every concept is laid out in a colorful image. If you like the works of M.C. Escher, you will like this book. It has a lot of substance to it, and it will keep you busy thinking for a long time, and that's time well spent

This marvelous book to explains to non-mathematicians the joy, beauty and power of mathematics. Each topic is presented in an original manner with alot of colorful illustrations to delight the eye and mind. Devlin shows how mathematical thinking is critical to our exploration of the world around us. This is one my top ten of all time list

When I teach a course entitled "Fundamentals of Arithmetic and Logic" I constantly emphasize the fact that the basics of mathematics is all about the use of more sophisticated and abstract patterns. For example, I use the following argument to demonstrate why the commutative law of addition holds:

1) Positive integers can be considered shorthand representations for piles of sticks.
2) If you have two piles of sticks, which pile you move on top of the other has no affect on the number of sticks you have.

While this is simplistic, the students find it easy to understand and they do remember it when we move on to other sets of numbers such as the rationals and the reals.
In this book, Devlin does an excellent job of taking similar, simple concepts and then abstracting it to an initial general pattern. From this pattern, he then expands it out to more generalized patterns. This is the essence of mathematics and in my experience, one that students find easier to follow when learning. Humans naturally carry out inductive reasoning, taking distinct yet similar experiences and reaching generalized conclusions. In fact, it can be argued that such activities are a signature characteristic of intelligence.
Devlin cites many examples of fundamental mathematical concepts that are the basis of mathematics. I try to include as many of them as possible in my basic math courses, because in my opinion together they form the best way for people to learn mathematics. It is natural and consistent with how humans do a large percentage of their learning.

Keith Devlin is well known for his concise treatments on modern mathematics and of his excellent explanations of the history of mathematics. In Mathematics: The Science of Patterns, Devlin blends these two excellent treatments into one book which is further improved with first rate diagrams and photographs. Only in the chapter on reasoning and communicating did I find myself tempted to skip ahead due to a bit of dryness. I have read this book several times and highly recommend it.

This book by Keith Devlin is an enjoyable survey for the general reader with a serious interest in mathematics. The presentation is conceptual and there's very little formalism, but Devlin still manages to go into meaningful depth on many topics, so some readers may find portions of the book somewhat challenging. The text is acccompanied by abundant and excellent color graphics.

Devlin at least touches on most of the main areas of mathematics, such as number theory, algebra, logic, set theory, series, functions, calculus, differential equations, geometry, group theory, and topology, but of course this also leaves out areas such as probability, statistics, computational complexity, optimization, nonlinear dynamics, and game theory. But choices have to made in a book of this size, and I think Devlin's tradeoff between breadth and depth is good.

The book gives the reader a meaningful sense of the beauty, power, and mystery of mathematics, so I highly recommend it to people looking for this sort of thing. Just keep in mind that this isn't a textbook, so the book is oriented towards showing the big picture rather than teaching details of mathematics.

Suggested further reading:

1089 and All That - A Journey into Mathematics
Mathematics: A Very Short Introduction

This book helps the lay reader understand the meaning of why we study math. I recommend it to all of my students!

I am updating this review, original one is below the dotted line.

Keith Devling takes us through a grandiose tour de force on the question wahts is mathematics, by starting from its originis as the "sceince of numbers .. and space" a concept that is 2.300 years old and was the one I had in my mind, until Mr.Devling noted it was a bit dated.

This book does call for some sort of sophistication form the reader. It is not atextbook, so some of the examples and invitation to solve certain problems (such as to discover Aristotle's logic mistakes by using Boolean algebra) are a bit challenging to the unitiated.

The graphics and examples of mathematical explanations abound, and just for this the book is worth it.

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Its from Scientific American, its written by K. Devlin, its wonderfully ilustrated.. what more can you expect?!

Yes its math explained

The book is fun to read ,very informative and very clear.
It doesnt matter if you know some university mathematics or not ,anyhow you will find this book a pleasure to read ,and if you dont know nothing about mathematics it will change your perspective on the world. I suggest you will get a copy and read it.Excellent book!.

This book has a lot of good information along with some excellent illustrations.

It is undoubtedly a very good book for one who is a great lover of mathematics. It is not, however, a book that is difficult to put down. It did not captivate me and convince me about all I am missing by not being a math junkie.