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The Language of Mathematics: Making the Invisible Visible [Hardcover]

Keith J. Devlin
4.4 out of 5 stars  See all reviews (43 customer reviews)

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Book Description

January 1998 071673379X 978-0716733799 1
"The great book of nature", said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics".In The Language of Mathematics, Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life -- patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within.Taking the reader on a wondrous journey through the invisible universe that surrounds us -- a universe made visible by mathematics -- Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to forecast the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers -- all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture.An award-winning author, Keith Devlin is a key participant in the new six-part PBS television series "Life by the Numbers", airing in the Spring of 1998. In his books, he conveys both the historical development and the current breadth of mathematics without assuming any technical knowledge or ability on the part of the reader. A brilliant exploration of an often woefully misunderstood subject, The Language of Mathematics celebrates the simplicity, the precision, the punty, and the elegance of mathematics.

Editorial Reviews 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

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.

Product Details

  • Hardcover: 300 pages
  • Publisher: W.H. Freeman & Company; 1 edition (January 1998)
  • Language: English
  • ISBN-10: 071673379X
  • ISBN-13: 978-0716733799
  • Product Dimensions: 9.3 x 6.2 x 1.1 inches
  • Shipping Weight: 1.4 pounds
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (43 customer reviews)
  • Amazon Best Sellers Rank: #886,725 in Books (See Top 100 in Books)

More About the Author

Dr. Keith Devlin is a mathematician at Stanford University in California. He is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He has written 31 books and over 80 published research articles. His books have been awarded the Pythagoras Prize and the Peano Prize, and his writing has earned him the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio. (Archived at

He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition.

He writes a monthly column for the Mathematical Association of America, "Devlin's Angle":

Customer Reviews

Most Helpful Customer Reviews
149 of 150 people found the following review helpful
5.0 out of 5 stars Clear and engaging February 1, 2001
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.
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40 of 41 people found the following review helpful
5.0 out of 5 stars Step into the shoes of a mathematician April 18, 1999
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.
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33 of 34 people found the following review helpful
5.0 out of 5 stars we all agree October 20, 2005
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.
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26 of 27 people found the following review helpful
5.0 out of 5 stars Bring it on, baby! September 19, 2000
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!
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18 of 18 people found the following review helpful
5.0 out of 5 stars Right Brain Joins Party June 27, 2000
By A Customer
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.
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Most Recent Customer Reviews
5.0 out of 5 stars What a great framework to build on
I am only a few chapters in and already this book has answered a lot of questions I have had about mathematics. Read more
Published 1 month ago by Alonzo Archer
3.0 out of 5 stars Still somewhat advance for me.
Would've been a good book for me when I was sophomore in high school.
Maybe I don't like math anymore. I find it a bit dry but still better than a textbook. Read more
Published 3 months ago by Ekorre
5.0 out of 5 stars A very good overview of math
I was looking around for a text to assign for the class I'll be teaching in the Fall, and this turned out to be just about right.
Published 4 months ago by Jac
3.0 out of 5 stars I'm not sure what I took away...
I finished the Language of Mathematics yesterday, and I'm not sure I'll take away a whole lot from it. Read more
Published 6 months ago by Ryan
5.0 out of 5 stars Math demystified
The book is an amazing journey through the history of mathematics that touches upon and connects discoveries and inventions in number theory, reasoning (logic), calculus, shape... Read more
Published 8 months ago by Venkatesh Prasad Ranganath
5.0 out of 5 stars Book Review
This book deserves a place on anyones shelf who wants to be viewed as a liberally educated well informed person. Read more
Published 10 months ago by Mike Ziemianski
5.0 out of 5 stars Great book for a Maths Tragic
I struggled with maths at university. I wish this book had been around back then. Keith Devlin (aka The Math Guy) reveals the foundations of mathematics in a most effective... Read more
Published 12 months ago by CyberFonic
5.0 out of 5 stars Understanding origin
This is a great read for understand where mathematics originated from and how it progressed and how it still is progressing! I love it!! Read more
Published 14 months ago by Willow
4.0 out of 5 stars Informative yet difficult
I really enjoyed this book. However, I have a bachelor's degree in mathematics and I struggled to understand parts of it. Do not expect it to be an easy read. Read more
Published 15 months ago by Cory
3.0 out of 5 stars I have just stated the book
I have just begun reading the book and so far it has met my expectations. I bought the book to use as a supplement for my highschool math classes when I begin teaching.
Published 15 months ago by Michael Allen
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