Struggling through several years of higher math in engineering school in the 1960s didn't engender a love of mathematics in me. It wasn't until years later that I began to value the beauty and elegance of mathematics. A big part of my appreciation came from mathematicians like Steven Strogatz who wrote about math for readers who appreciated the concepts but had no desire to wade into a morass of complex equations.
In The Joy of x, Strogatz has done a masterful job as our tour guide through the elements of mathematics, and he's done it without "dumbing it down" or making it just another refresher course for the subject. He presented the various mathematical elements and concepts in fresh new ways, but he clearly expected the reader to exercise their mind to understand. The reward was a new appreciation of the beauty of mathematics and for how our knowledge of the subject advanced in fits and starts over several thousand years.
The book has six parts, each presenting certain elements of mathematics: Numbers, Relationships, Shapes, Change, Data, and Frontiers. These sections represent a grand tour through the history and development of mathematics, including the practical - and some whimsical - applications. Never again will I fall into the trap of bungling the answer to the classic "If three men paint three fences in three hours, how long will it take for one man to paint one fence?" (answer: 3 hours). Now I understand why a piece of paper can't be folded in half more than 7-8 times, and how a high school junior was able to beat the record using a monstrously long roll of... toilet paper! I know how Luke could guarantee himself a win over Darth Vader in a game of laser tag (hint: it involves a conic section). For young lovers, mathematics could help in finding the perfect mate (if you make a few simplistic assumptions, that is). And if the prosecution in the O.J. Simpson murder trial had understood probability and statistics, could they have gotten a conviction?
As enjoyable as the first five sections of the book were, my favorite section was the last, "Frontiers," where the author covered topics including prime numbers, where I learned that no one has ever found an exact formula to find primes; group theory, which bridges the arts and sciences; topology; spherical geometry; and infinite series. This section presented some fascinating ideas. For example, group theory suggests how to get the most even wear from a mattress and confirms the old mnemonic "spin in the spring, flip in the fall." For topology, the famous Möbius strip is examined. I thought I understood the properties of a Möbius strip, but they're actually more remarkable than I would have guessed. And the most mind-blowing concept was that some infinities are larger than others. This finding, which was bitterly contested at the time, is brilliantly demonstrated with a parable named the Hilbert Hotel.
I don't always read all of the footnotes or endnotes in a book, but the endnotes in The Joy of x are not to be missed. There are dozens of links to websites and online videos that demonstrate or expound on the concepts presented in the book. Some of these were so intriguing that I spent a couple of hours being spellbound by them.
For anyone who's been disappointed by other math books written for laypersons, The Joy of x may be the book they've been hoping for. With keen insight, a light touch, and a bit of humor, author Steven Strogatz has written a splendid book for anyone who wants a broader understanding of mathematics.
Note: I read an advance reader copy of this book provided by the publisher through NetGalley.
This math-challenged reviewer would not ordinarily consider "joy" in connection with mathematics, so this little book sounded interesting. It is not a textbook of mathematics, not even an introductory one, but rather a quick tour through a range of mathematical ideas and concepts, aimed at the curious, but baffled layman. It covers everything--from numbers and counting, to negative numbers, imaginary numbers, algebra, the elements of calculus, probability, sine waves, geometry, trigonometry, solid geometry, topology, and the challenging problems of infinity. Will you understand all these things after reading "Joy"? No, but the terms and concepts will sound a little more familiar, less intimidating.
Author Steven Strogatz is no dull professor. He writes in a light-hearted entertaining way, with constant reference to the practical applications of mathematics. Along the way he presents some counter-intuitive problems for the reader to play with, amusing illustrations, and personal anecdotes.
No, you won't learn much mathematics from this delightful little book, but you'll learn some interesting things ABOUT mathematics that would never have occurred to you. I enjoyed this book and I may go back and read some chapters again. Forget about those painful experiences with long division when you were in school. This can actually be fun. I recommend it. Reviewed by Louis N. Gruber.
Before you buy this book, take a second to examine yourself. If you always hated math, don't bother with this book. You will just use it to reinforce your dislikes. But if you have ever looked at numbers, triangles, or even google page rankings and wondered how anyone ever figured any of that stuff out, this might be your book.
=== The Good Stuff ===
* This is not a math book. You won't learn how to calculate the area of a triangle, the odds of a no-hitter or the present value of a 40 year annuity. But if you are willing to read carefully and think about the concepts presented, you will have a better understanding of how math is used to model and predict the way the world works.
* I am an Electrical Engineer, a field that uses moderate level math on a daily basis. Even though none of this material was new to me, there was some interesting ways of explaining things which I had never considered before. This always comes in handy, even among fellow techies. And there were numerous facts and observations which, while I probably could derive them myself, were interesting enough to spend some time examining.
* All the material presented in the book is certainly at the level that any high-school graduate could understand. You might not be able to grasp the nuances of the material, or be able to use the concepts to solve real world problems, but you will have an understanding of how the math works. Depending on the amount of math your have been exposed to, some topics might require the reader to think a bit to understand the concepts.
Think about a two page article that describes how an internal combustion engine works. After reading it, you might understand the basic concept operation-gas/air mixture igniting and driving pistons, which rotate a shaft, which drives the wheels. You certainly couldn't design one, or fix one, and you would not know how to drive a car. But you certainly would have a better appreciation for what goes on under the hood, and it might spark your interest to learn more.
* All of the sections are short, and err on the side of over simplification and minimal explanation. This is not a math textbook, or a history of math. It is more an overview of various topics.
=== The Not So Good Stuff ===
* Strogatz tries to do too much. As an example, the equations of James Clerk Maxwell are some of the most profound mathematical models ever conceived by the human race. They predict and allow analysis of just about anything in the world that uses electricity or magnetism. But they are not at all simple, either in conception or mathematical constructs. A three page summary of them borders on the absurd. I doubt whether any person without a decent physics and math background would ever see the beauty or elegance of them.
* The chapters all seem to need to be the same length, likely a result of the newspaper articles this material was originally developed for. As a result, some simple topics seem stretched out to fill space, while some of the more complex topics are condensed beyond usefulness.
* "Advanced" math users, such as those who have studied differential and integral calculus, analytic geometry and differential equations will find some limited tidbits, but will mostly be bored by the book.
=== Summary ===
Strogatz sets himself a fairly difficult task. He tries to write a single book, which gives introductory explanations of topics ranging from integers and rational numbers all the way to linear algebra and differential equations. He tries to do this is a "mass market" book, targeted at readers with a wide gamut of math experience.
I am not sure that is a reasonable goal. In fact, I think it borders on the impossible.
Still, Strogatz makes as valiant an attempt as possible. I believe the book is "readable" by users of advanced math, and there are enough tidbits and interesting ways of explaining things to hold their interest. The book is also simple enough that most anyone can work their way through the examples and appreciate the concepts.
I enjoyed it, but not sure I would recommend it.
on October 14, 2012
I loved, loved, loved this book! It doesn't teach you how to do math, but it really helps you understand how the various equations, formulas, and types of math are used and why. The author's voice throughout is entertaining and friendly. He gives wonderful examples, analogies, and metaphors for the math concepts. I finally understand what logarithms are and what they're used for! I learned how to calculate log equations recently, but I couldn't fathom why you'd need or want to do that. Steve explained it in ways that made sense and using examples I'll remember. The chapters are organized nicely, all terms are explained, and it ends with a lot of resources.
But I have to say, I'm disappointed to have reached the end of the book! I want more. This was a fun read, and I learned a lot. It made so much sense of the math I'm learning. I also want to remark I am 50 years old and decided to finally learn math because of my interest in science. I have plenty of math text books and watch online videos to learn *how* to do math. But this was the best book ever to *understand* math and the ways it's used.
Steve, please, please, please write another Joy of X. Maybe call it, The Joy of X^. You know you only touched on a few mathematics in this book. I'd love to read another by you, written in the same style, digging into more algebra, geometry, trigonometry, calculus, linear algebra, etc.
This was a great book. I highly recommend it. This book is a fun, interesting read even if you don't do math, even if you're not interested in learning more math, and especially if you are doing math.
on November 3, 2012
This book is indeed a joy to read. There were many "aha" moments, some of which are :
1) Google's Page rank explained using a simple Markov chain example. Demonstrates the power of linear algebra.
2) Thinking about conditional probability in terms of frequencies is more intuitive and less confusing than the usual Bayes formula.
3) Power Law is the new Normal Distribution of the world.They are everywhere.
4) Log scale verbalized brilliantly :Markings on the axis differ by the same factor than same absolute number.
5) Div, Grad and Curl in Maxwell's equations.
6) Differential equation to understand a love affair. In the same context, Newton's three body problem has no closed form solution. May be that's the reason why love triangle movies always seem to work, for there is always some novelty that audience can expect.
7) To explain Euler's constant, an example with some equation is usually the standard choice. But the author does it in style when he says "e arises when something changes through the cumulative effects of tiny events."
8) Usage of Goldilocks Principle in many places in the book.
9) Stair case analogy to explain Fundamental theorem of Calculus.
10 Zero antiderivative property of slopes and peaks verbalized as : Things always change slow at the top or bottom.
11) "Sine qua non" - word used to cutely explain the ubiquitous sine curve, the nature's building block .
12) Cone's hidden role in the manifestation of parabola, ellipse and hyperbola .
13) Solving a quadratic equation visually.
14) Exploring Connections between "Using Newton Raphson to solve an equation with multiple roots" , Chaos theory and fractals. Truly amazing!
15) Why Hindu Arabic system of numbering flourished while others fell astray? The unsung background hero of the story is the "Zero".
16) Gibbs Phenomenon and the way it unpleasantly crops up in digital photographs and MRI scans.
17) Connection between "How to effectively use Mattress" and group theory.
18) Mention of Mobius Strip and its strange characteristics
The book begins with natural numbers that made counting and tallying easy. It ends with with the subject of infinity where everything is on a slippery ground. In this journey from natural numbers to infinity, the book explores various subfields of mathematics.
This book is a pleasure to read as the author connects some basic math stuff with everyday life.
Upon reading this book, you will never look at numbers, word problems, math equations or math symbols in the same way again. Mr. Strogatz's passion for numbers is so contagious, I couldn't stop reading this book. He explains mathematical concepts in such easy to understand language, and with plenty of humor and wit. You might think it would take a doctoral dissertation to do this, but Mr. Strogatz does it with just enough context and information that even the most math-phobic person would be able to read this and get it, but more importantly, really, really enjoy it.
Written for the lay person and lover of all things numerical, this book was sheer fun. Mr. Strogatz weaves science, literature, history, philosophy, physics, technology and more throughout the book. I gave this to my reluctant 10-year reader and while many of the concepts (like calculus) are somewhat foreign to him, he got it (this doesn't mean he could solve a calculus problem, but he does understand the logic behind it). He couldn't help but be wowed by everything he read. If was as if the mysteries of the universe were revealed to him (which in a way, they were!). He's sees math as something really exciting and wants to learn a whole lot more (thank you, thank you, thank you, Mr. Strogatz and Kahn Academy!).
The idea behind the book is not to make you into a mathematician, but draw back the curtain so all can see how truly magical numbers are and how they help us in our daily lives. If you have someone in your life who has even the slightest affection - or aversion - to numbers, this book would make an excellent gift!! I learned so much more about the many math concepts than I thought possible, and have a whole new appreciation for the real beauty of numbers. I hope Mr. Strogatz plans on writing more!
on October 2, 2012
This book is a wonderful addition to the growing library of mathematical works aimed at the math-phobic. The topics covered are quite varied but always include practical examples that are very valuable in explaining the subject in focus. My favourite chapter was the one entitled "Chances Are" (Chapter 23). Here, the discussion on medical statistics is extremely valuable and is something that, I believe, everyone should be intimately familiar with - especially medical doctors.
As suggested in this review's title, the author's writing style is very friendly, chatty, light-hearted, engaging and clear. The information is presented in an authoritative yet pleasant manner - as though the author is gently guiding the potentially hesitant reader through a world of painless discovery and surprising wonder. In addition, the author has included several anecdotes and side issues that help enliven the text.
I suspect that the math-phobic are the readers who risk being the most enchanted by this book. But there is also something, I believe, for the math/science enthusiasts like me: a manner of presentation that is absolutely charming and topical discussions that can bring some of us back several decades. A truly enjoyable and worthwhile read!
on November 4, 2012
Supposedly publishers ask authors to begin writing by defining the audience for whom they are writing their book. Later, reviewers delight, de rigueur, in saying who the book was "intended for". When this book starts with arithmetic and gets to topics like group theory, we might wonder. But he is NOT trying to teach us any of these things. He is telling us, I think, why these things REALLY are so interesting, why he loves them, and why we should too. And he has done a remarkable job of establishing a relatively uniform level of understanding (or is appreciation the word) despite varying levels of mathematical sophistication that WOULD be necessary, IF one were inclined to take on an extensive study. Perhaps his MO was to put himself in the position of being asked at a party "What is X all about?" knowing that the questioner really wanted to know, was an intelligent person, had limited time, and really would be derailed by any patronizing snags in any descriptions proffered. Everything here is thoughtful and respectful.
So it may have been intended by some involved in the publication as basically an introduction, but it is hard for me to envision anyone who would not find this interesting, if not compelling. Will a professional mathematician of engineer be bored? Not likely. I had never thought of "fish, fish, fish, fish, fish, fish" as being different from 6 fish - he is making a point about numbers, not about arithmetic. Later, seemingly more profound ideas emerges, such as: "Whenever a state of featureless equilibrium loses stability - for whatever reason, and by whatever physical, biological, or chemical process - the pattern that appears first is a sine wave, or combination of them." In some sense, the sine wave and fish comments are equally deep.
So I envision Strogatz as enthusiastically sitting you down to tell you some things that he finds interesting, and imagining that you would too. Perhaps his narratives are accordingly described as infectious. Reading this, you have run into a person who delights in telling you interesting things - the kind of person who is sometimes a pest - if he really did grab you off the street and begin his spiel. But after all, YOU picked up the book. Oh - did I mention that you really should pick up this book?
on July 5, 2015
Steven Strogatz makes me believe math is for everyone. He doesn't just tell you how (the rules of math), but attempts, and usually succeeds, in explaining why something works a certain way. His explanation of completing the square opened my eyes to what is really happening in the math and why the formula works. I have found a whole new respect for e. If I had had a math teacher like him in school, I might have done better in math and enjoyed it more like I do today.
At some point in life I started wondering whether things I wasn't familiar with were things I had never known or merely things I once knew and had since forgotten (or misplaced the key to its location in my brain). I had several conversations with myself during the reading of this book. To be fair to myself, or perhaps to make excuses, it has been more than half a century since I have "studied" some of the things that Strogatz includes.
All in all this book is interesting. It is not going to "teach" anyone math. It isn't going to change those never known or forgotten math subjects into learned or relearned math topics. Like most of the "popular" math/science books, it is fun to expose yourself to the subjects - and that might lead to actually "studying" them. The notes at the end expand the topics without weighing down the main text.
This is not a textbook and in no way does it read like one. In thirty short chapters we go from the basic concept of numbers and a basic look at addition to a look at infinity. In between, the author takes us on a trip of ever increasing complex topics.
If you have an interest in the subject matter, then this is an interesting book to read. If not, and you are still in school, then you might gain from a reading of this. The "stories" were well written and contained enough humor to lighten the complexity. Again, this is not a "teaching math" book, but it is a book that teaches why we should learn math. That's incredibly important.