The Language of Mathematics: Making the Invisible Visible (Paperback)

by Keith Devlin (Author)
Key Phrases: additional hypersphere, null knot, prime number conjecture, Daniel Bernoulli, New York, Jacob Bernoulli (more...)

Editorial Reviews

Amazon.com Review
Keith Devlin is trying to be the Carl Sagan of mathematics, and he is succeeding. He writes: "Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent of a pair of ears. Mathematics can be seen only with the eyes of the mind." All of his books are attempts to get around this problem, to "try to communicate to others some sense of what it is we experience--some sense of the simplicity, the precision, the purity, and the elegance that give the patterns of mathematics their aesthetic value."

Life by the Numbers, Devlin's companion book to the PBS series of the same name, is heavily illustrated and soothingly low on equations. But as he says, wanting mathematics without abstract notation "is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language."

The Language of Mathematics is Devlin's second iteration of the approach he used in Mathematics: The Science of Patterns. It covers all the same ground (and uses many of the same words) as the latter, but with fewer glossy pictures, sidebars, and references. Devlin has also added chapters on statistics and on mathematical patterns in nature. --Mary Ellen Curtin --This text refers to the Hardcover edition.

From Scientific American
...he skillfully gives both a history of the subject and a guide through the terrain.... Keith Devlin is an apt teacher of the language. --This text refers to the Hardcover edition.

See all Editorial Reviews

Product Details

• Paperback: 344 pages
• Publisher: W. H. Freeman; 1 edition (March 13, 2000)
• Language: English
• ISBN-10: 0716739674
• ISBN-13: 978-0716739678
• Product Dimensions: 9.2 x 6.1 x 1 inches
• Shipping Weight: 1.2 pounds
• Average Customer Review: 4.7 out of 5 stars See all reviews (23 customer reviews)
• Amazon.com Sales Rank: #962,282 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

162 of 167 people found the following review helpful:

5.0 out of 5 stars A true five star rating, December 2, 1998

By	S. Brown "s_brown" (Potsdam, NY United States) - See all my reviews (REAL NAME)

This review is from: The Language of Mathematics: Making the Invisible Visible (Hardcover)

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.

96 of 97 people found the following review helpful:

5.0 out of 5 stars Clear and engaging, February 1, 2001

By	Mike Christie (Austin, TX USA) - See all my reviews (REAL NAME)

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.

27 of 27 people found the following review helpful:

5.0 out of 5 stars Step into the shoes of a mathematician, April 18, 1999

By	J. Paul Holbrook "jph-atlanta" (Atlanta, GA USA) - See all my reviews (REAL NAME)

This review is from: The Language of Mathematics: Making the Invisible Visible (Hardcover)

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.