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In Pursuit of the Unknown: 17 Equations That Changed the World [Hardcover]

Ian Stewart
5.0 out of 5 stars  See all reviews (2 customer reviews)
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Book Description

March 13 2012
In In Pursuit of the Unknown, celebrated mathematician Ian Stewart uses a handful of mathematical equations to explore the vitally important connections between math and human progress. We often overlook the historical link between mathematics and technological advances, says Stewart-but this connection is integral to any complete understanding of human history.Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents-from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity-within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today.An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

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Review

Publishers Weekly

“Stewart shares his enthusiasm as well as his knowledge in this tour of ground-breaking equations and the research they supported…. An entertaining and illuminating collection of curious facts and histories suitable for random dipping-in or reading straight through.”


Kirkus Reviews

“Stewart provides clear, cogent explanations of how the equations work without burdening the reader with cumbersome derivations…. He gives a fascinating explanation of how Newton’s laws, when extended to three-body problems, are still used by NASA to calculate the best route from Earth to Mars and have laid the basis for chaos theory. Throughout, Stewart’s style is felicitous.”
 
Discover

“Seemingly basic equations have enabled us to predict eclipses, engineer earthquake-proof buildings, and invent the refrigerator. In this lively volume, mathematician Ian Stewart delves into 17 equations that shape our daily existence, including those dreamed up by the likes of Einstein, Newton, and Erwin Schrödinger.”
 
Maclean’s
“Stewart is the finest living math popularizer – a writer who can tackle eye-spraining mathematical topics approachably, and yet dazzle hard-core nerds with new and surprising information. It is hard not to get your money’s worth from him, and in a book like this he is at his best because of the very wide ground covered.”
 
Library Journal
“Stewart’s expertise and his well-developed style (enhanced by a nice sense of humor) make for enjoyable reading…. [A] worthwhile and entertaining book, accessible to all readers. Recommended for anyone interested in the influence of mathematics on the development of science and on the emergence of our current technology-driven society.”

Washington Independent Review of Books

“Stewart has managed to produce a remarkably readable, informative and entertaining volume on a subject about which few are as well informed as they would like to be.”



New York Journal of Books

“Stewart is a genius in the way he conveys his excitement and sense of wonder…. He has that valuable grasp of not only what it takes to make equations interesting, but also to make science cool.”

 


Steve Mirsky, Scientific American

“[Stewart] takes the reader on an engaging tour of vital math for a modern world…. I highly recommend Stewart’s wonderfully accessible book.”

Physics Today
In Pursuit of the Unknown is an interesting and highly entertaining book. It would make a great gift for a bright high school grandchild who has expressed interest in a technical life, or for a physicist’s own secret reading.”

About the Author

Ian Stewart is Emeritus Professor of Mathematics and active researcher at the University of Warwick. He is also a regular research visitor at the University of Houston, the Institute of Mathematics and Its Applications in Minneapolis, and the Santa Fe institute. His writing has appeared in New Scientist, Discover, Scientific American, and many newspapers in the U.K. and U.S. He lives in Coventry, England.

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3 of 4 people found the following review helpful
5.0 out of 5 stars Important Equations: Their History and Meaning April 7 2012
By G. Poirier TOP 50 REVIEWER
Format:Hardcover
As a quick glance through this book will indicate, some of the equations presented are well-known and simple whereas others can look awfully intimidating. A given reader may be intimately familiar with several of these equations while at the same time be totally unaware of some of the others or their significance. The author does not provide mathematical derivations of these equations. Instead, he describes how they came about, explains their meanings and applications and then discusses their legacy. Several fields are covered in this fascinating book: physics, engineering, mathematics, statistics, information theory, chaos and economics.

The author writes very clearly and in a friendly, lively and engaging style. In some sections the author seems to assume very little or no pertinent knowledge on the part of the reader and as a result is very careful and detailed in his explanations, e.g., logarithms, calculus. In other cases, the discussions are much more challenging, and although new terms are briefly defined, the discussions may still result in some head scratching, e.g., quantum mechanics, Black-Scholes equation. Consequently, it is difficult to determine at what population this book is aimed. Science buffs may be bored by some of the more elementary discussions but find themselves more challenged by the topics on which they know very little. On the other hand, a younger (or less-informed) reader may learn quite a bit from the elementary discussions but get lost in some of the other sections.

Overall, I think that it is safe to say that this book has something for everyone. Although I did find some sections rather challenging, I must admit that I thoroughly enjoyed it.
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5.0 out of 5 stars 17 reasons to read this book Dec 8 2013
Format:Hardcover|Verified Purchase
I wouldn't pretend to understand all the math in this book, but I thoroughly enjoyed the overall discussion. It's absolutely amazing to realize that so much of our reality can be represented in mathematical equations. It makes me wish I had paid more attention in math class!
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.2 out of 5 stars  51 reviews
68 of 71 people found the following review helpful
5.0 out of 5 stars Fantastic book for the inquisitive. March 25 2012
By Charles Chen - Published on Amazon.com
Format:Hardcover
What could be more boring than mathematical equations? The majority of folks would be hard pressed to find something to answer that hypothetical query. Myself included :) I'll be honest, I'm a math minor and I picked up this book on a whim in a bookstore thinking to myself "Now why would anyone want to write or _buy_ a book on 17 equations?" I flipped through it and immediately knew that I had to consume the rest of this book.

What Stewart is able to do is to take these 17 equations that manifest in everything we do, everything we observe, every bit of space around us and bring life to them. To be clear, this is more a book about history than pure math, but there is no doubt that these 17 core equations are at the heart of the book. He presents the opening of each chapter with a concise summary of these equations in laymen's terms that helps immensely in revealing the underlying nature of the equations and then goes into the history of the creation (discovery?) of each of these equations and it's been an eye-opening read.

As an example, having majored in computer science, I worked constantly with logarithms and natural logs (there's lumber joke here somewhere) but never once understood the nature of logarithms. How did they come about? Why do they exist? What problem do they address? Just what in the heck _is_ a logarithm? I knew them only in the abstract -- as operations that yielded a result; I knew them as a general pattern but not the nature of the logarithm. The second chapter simply blew me away with the clarity and simplicity with which Stewart was able to pull back the covers on what logarithms actually mean -- there's actually a very good reason why they're called logs. No one in my years of formal education had bothered to explain it in the same way that Stewart does in this book; the existence of logarithms finally makes sense to me.

While I cannot say that this book is for everyone (I'm sure my wife would be asleep after the first chapter :), I will say that I find it is surprisingly approachable for most folks who are scientifically or mathematically inclined. Certainly, there are many equations and plenty of mathematics and it gets especially complex (pun intended :) in the later chapters; you WILL get lost in the math. However, I think this book is still immensely readable and approachable, even for those who have never ventured deep into the vast field of mathematics or have long moved past their days of calculus, linear algebra, and so on. I, for one, will make sure that my daughter reads the chapter on logarithms as it starts to seep into her curriculum one day to make sure she understands the "why" and so that she has an appreciation for all of the history and magic behind that little "log n" button on her calculator.

This book is incredibly well written, well presented such that it is approachable for a large audience, an entertaining read, and highly recommended. If you've read this review to this point, you should probably just go ahead and by this book!
43 of 46 people found the following review helpful
5.0 out of 5 stars Equations We Non-Mathematicians Use Every Day March 12 2012
By R. Hardy - Published on Amazon.com
Format:Hardcover
The mathematician Ian Stewart knows the famous story about equations versus book sales. Stephen Hawking's publisher told him that every equation published in _A Brief History of Time_ would halve the number of books sold. One equation got in: E = mc^2, and maybe it really did cut the sales of the book by half. If this rule is true, Stewart is in real trouble with his newest book, _In Pursuit of the Unknown: 17 Equations That Changed the World_ (Basic Books). Readers who know his work, however, know that they are in good hands. Stewart has undoubtedly written mathematical papers that would be over the heads of us other mortals, but his books for the public on the problems, range, and philosophy of mathematics are clear, funny, entertaining, and educational. His seventeen chapters include some simple equations that everyone knows; that E = mc^2 is here, simple to write and to memorize, but pointing to complexities that most of us cannot easily comprehend, even a hundred or so years after it was developed. Some of the equations, like Schrödinger's Equation, are full of Greek letters and only physics experts will recognize them. Throughout the book, however, Stewart shows that these are equations that run our lives in our technical age. The equations may be used professionally just by the egghead experts, but in a wider sense, we all use them, every day.

The first chapter here is on the old familiar a^2 + b^2 = c^2, the Pythagorean Theorem. This is pure math, straight from Euclid, and not (as are many of the equations here) from applied mathematics or mathematical physics. But that does not mean the Pythagorean Theorem is forever locked within the mathematicians' ivory tower; it led to trigonometry. When he does get to E = mc^2, Stewart reflects about how Pythagoras helps understand relativity, because of light paths understood as sides of triangles. All of the equations here have improved our understanding of how nature works, and have supplied reason to wonder at how consistently mathematics underlies everything. The basic equation for calculus is here, which is responsible for most of mathematical physics. Among the simplest of equations here is Euler's formula that shows how faces, edges, and corners of a solid shape are related. Like each simple formula, it has created complications, including the powerful pure mathematics of topology, which has implications for how DNA works and why planets may move in a chaotic way. Another simple one is i^2 = -1, indicating that minus one, which should have no square root since it is negative, does have one, the imaginary number i. Although i may be called imaginary, it is essential for understanding waves and electricity, not to mention quantum mechanics. Chaos theory is here, with an equation that helps show how the flapping of that butterfly's wing may lead to a tornado later on; that's the most famous effect, but the equation models, for instance, how a population of creatures changes over generations if they have to be curtailed by limited resources or predators. Stewart gives clear explanations, but they are relatively deep for the non-mathematician. Many people who read this book will want to take long breaks between its pithy chapters, each of which has been expanded elsewhere into many volumes. Equations are useful for explaining the world, but like any tool they can be misused. Stewart's final chapter is on the Black-Scholes Equation, invented in 1973 and since then used to analyze the changes of price of a financial derivative. Derivatives could thus be traded before they matured. It was a useful formula as long as it was applied only when market situations fit, but it was abused. Stewart makes clear that the formula didn't cause the 2008 - 2009 financial crisis, but abuse of it, along with financial and political ineptitude and lax regulation, made for a crash that didn't have to happen.

In an epilogue, Stewart reflects that most equations aren't important: "I write them down all the time, and believe me, I know." Here are some important ones, though, equations that run our world, always in ways that the inventors of the equations could never have predicted. It may be, Stewart writes at the end, that the cellular automata famously championed by Stephen Wolfram do a better job of explaining the universe than equations do, and maybe algorithms are going to be more important than equations. His engrossing book, showing the vital importance of equations not just for explanation but as causation of historic and social change, makes clear that it will be a long time before any other modeling becomes more important.
16 of 16 people found the following review helpful
5.0 out of 5 stars Important Equations: Their History and Meaning April 7 2012
By G. Poirier - Published on Amazon.com
Format:Hardcover
As a quick glance through this book will indicate, some of the equations presented are well-known and simple whereas others can look awfully intimidating. A given reader may be intimately familiar with several of these equations while at the same time be totally unaware of some of the others or their significance. The author does not provide mathematical derivations of these equations. Instead, he describes how they came about, explains their meanings and applications and then discusses their legacy. Several fields are covered in this fascinating book: physics, engineering, mathematics, statistics, information theory, chaos and economics.

The author writes very clearly and in a friendly, lively and engaging style. In some sections the author seems to assume very little or no pertinent knowledge on the part of the reader and as a result is very careful and detailed in his explanations, e.g., logarithms, calculus. In other cases, the discussions are much more challenging, and although new terms are briefly defined, the discussions may still result in some head scratching, e.g., quantum mechanics, Black-Scholes equation. Consequently, it is difficult to determine at what population this book is aimed. Science buffs may be bored by some of the more elementary discussions but find themselves more challenged by the topics on which they know very little. On the other hand, a younger (or less-informed) reader may learn quite a bit from the elementary discussions but get lost in some of the other sections.

Overall, I think that it is safe to say that this book has something for everyone. Although I did find some sections rather challenging, I must admit that I thoroughly enjoyed it.
32 of 37 people found the following review helpful
2.0 out of 5 stars Sitck with the Facts! Aug. 13 2012
By Amazon Customer - Published on Amazon.com
Format:Hardcover|Verified Purchase
While I enjoyed the stories and anecdotes about the history of the equations, I found that the author often punctuated his discussions with his own opinions about...nearly everything. When I purchased the book, I didn't expect to get an op-ed on Mr. Stewarts stances on politics and the environmet.

For example, at least half of the chapter on the Navier-Stokes equations - one of the fundamental tools for thermo-fluid scientists - is devoted to the author's position on global warming. As a practicing thermo-fluid scientist, I was terribly disappointed that the opportunity to share the wonders of this relationship were lost.
6 of 6 people found the following review helpful
4.0 out of 5 stars Inspiring but occasionally challenging look at the maths behind the modern world May 30 2012
By Andrew Johnston - Published on Amazon.com
Stephen Hawking wrote A Brief History of Time with only a single equation, accepting that more might "scare the punters off". Bill Bryson wrote A Short History of Nearly Everything with neither equations nor pictures. Ian Stewart is therefore being very brave writing a popular science book which explains the mathematical basis for our modern world, unashamedly focusing on the key equations themselves.

That said, the equations are used more as milestones than intensively studied subjects. This is not a "book full of maths", and each chapter is largely a textual exploration around the subject starring the featured equation, explaining what it means, and what it led to.

The scope is vast, from Pythagoras through to the underpinnings of quantum theory, chaos and derivatives trading, taking in key scientific developments and their mathematical explanations along the way. Stewart does a remarkable job of compacting this scope into just 17 chapters and about 300 pages.

If you're a skilled mathematician you will gloss over the maths and still take value from the following discussions. If, however, your maths is more limited or, like mine, rather rusty, you'll find you don't need to follow all the mathematical details. You don't need to really understand about grads, divs and curls, for example, to appreciate the similarity in "shape" between the key equations in several different areas of science. The author does a very fine job of both explaining this structure, and also where the reader must understand, and where detailed understanding is less important.

Some of the explanations are quite complex, especially where Stewart is exploring the most recent applications of older ideas. I did get lost a couple of times and had to re-read short sections, but overall I came away thinking that I had built a decent grasp.

The book has an admirable focus on the practical applications of science, but some of this is presented with such limited detail that in a couple of places it devolves into lists of applications rather than real explanations. As well as positive stories, Stewart is not afraid to show where mis-interpretation of the mathematics or its limitations has failed us, most notably in the last chapter on financial derivatives and how their abuse has caused the current crises.

Although eminently readable and often amusing, this book is best read in chunks of a couple of chapters at a time, allowing the ideas to sink in. Do so, and invest a little effort, and you'll be well rewarded.
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