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on 5 September 2012
When learning Maths at secondary school in the UK, one learns theorems, equations, mathematical methods, learns how to apply them, answers questions on them in class and in exams and stops there. Maths done. Finished.

Ian Stewart sees this gap between the Maths people know and the uses of this Maths both historically and in our present-day societies. An example is his chapter on logarithms. Many have heard of logarithms and know the basic logarithmic rules of addition, subtraction, multiplication and division. What Stewart does, as he does with the other 16 equations, formulas and mathematical ideas, is to give the historical development of logarithms, describes how they function, describe how they are useful and describes their various important applications in our daily lives.

Stewart is a great ambassador for Maths and has done a great deal to make the subject seem less stuffy and more approachable to the reader. If students were introduced to the applications, meanings and ideas behind the Maths they are taught at school at an earlier age via Stewart's book then maybe there would be a greater passion developed amongst adolescents to study it further and realise its importance in understanding the world around us.
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on 10 March 2012
The difficulty with a book devoted to the important equations is that there is a lot of very complex mathematics which underpins those equations. To understand a lot of the equations in this book it would be helpful to know something about calculus or other higher level maths. Since nowadays you can do an A level in Physics without studying calculus it seems that this book can only be aimed at undergraduate students or people who have studied these interesting areas. Nevertheless, this book is a great inspiration to those who have an understanding of maths and want to develop it further beyond what they know.

These equations have had a remarkable impact on our lives and our understanding of the universe so it is great that someone is willing to sit down and explain them to us in a way that is not too abstract and technical. Like with most popular science books it is not important that the reader understand all the logical implications of maths, but to get some understanding of the general nature of these equations. When trying to understand these equations we have to start from somewhere and this book is a good place to start.
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VINE VOICEon 3 June 2014
Ian Stewart has been in the forefront of popular mathematics writing for over 20 years. In that time I would say that most of his books have been good books, especially the collections of his Scientific American columns and Fearful Symmetry come to mind. But then there have been the odd aberrations such as his Very Short Introduction on Symmetry which was aimed at far too high a mathematical level.

This book falls somewhere in between good Stewart and bad Stewart. In the first half of the book he tries to explain where the maths comes from as well as its context. For formulae such as those of Euclid and Fourier this can be a very demanding exercise and this part of the book is not for the maths phobic. Where the book improves is when you get to the more advanced equations where the derivation is no longer possible to explain in lay terms and so the development of the equations are only sketched. Then the focus is on their implications to provide context. So once you get to Relativity it is a fairly easy ride after that. His take down of the entire field of economics in the Black-Scholes chapter is particularly worth the cover price. It just shows how all those experts are fooled by their equations. So there are gems and some chapters that are excellent but the first half is at times painful.
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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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on 6 February 2013
Really great and interesting book, that inspired me to start learning calculus properly. Strongly recommended to any science fan, as it has a fascinating exploration of some really important science (and maths).

I would have given it five stars had the Schrödinger and the entropy chapters not been so unusually poor and misleading. Theyre probably not worth reading, especially the Quantum Mechanics one, but they're definitely worth learning about elsewhere.
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on 3 June 2012
Ian Stewart is one of those rare writers whose familiarity with esoteric topics facilitates his ability to communicate it to us lesser mortals rather than widen the gap. He's not alone in this regard, but this book is better than most.

I've read a few books written along similar lines, all commendable, but 17 Equations that Changed the World pretty well fulfils its brief. The virtue of this book over others is how Stewart deftly explains the relevance between truly serious mathematics and the real world - a connection that eludes most people.

I expect that some of the mathematical exposition will be beyond the ability of many readers, but it's worth persevering just to appreciate how much the Western civilization that we all take for granted is grounded in pure mathematics.

To give some snippets: the relationship between the second law of thermodynamics and time; how Maxwell's equations gave us modern communication; how the Fourier transform allows us to compress digital photographs; how Newton's theory of gravity predicts `tubes' for gravitational travel around the solar system; why the relationship between quantum mechanics and physical reality is a conundrum yet gives us all our electronic toys; how chaos theory predicts that there's no such thing as a stable population; how cracking codes is related to the sphere-packing problem in higher dimensions; how mathematics gives credence to human-generated climate change; and how mathematics can deceive us into thinking that investing virtual money in virtual commodities doesn't have consequences in the real world yet gave us the GFC.
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on 21 April 2012
I am not a mathematician but have really enjoyed this book. Some parts are quite challenging but well worth trying to get your head round.
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on 20 January 2013
Ian Stewart has written a most readable and interesting book, which on occasion almost becomes a page turner as you wait to see how some esoteric but important problem will be solved. And he brings to life some of the greatest names in science, making them flesh and blood - Newton, Descartes, Poincare, so that we care about them and their fates. To do all this in between some of the most abstruse equations some of us will ever see is quite an achievement.
He also mentions some of the lesser known characters, people in the wings who don't get their share of the fame. Also he is fair with his spreading out of the honours, letting many have the praise when there was multiple creators of some invention, ignoring the usual fight over who was first past the post.
Then there are those equations. I must say I am surprised that so many seemed so happy with them, esoteric as they are. I would have thought that for anyone not keeping up with maths or physics they would have been a major stumbling block, but it seems not, which is great. I would warn less up-to-date readers though that the science is full on and you had better be prepared to skip those bits. In fact I don't think Stewart explains some of those areas very adequately at all for a book supposedly to be about popularizing science - sometimes he seems to be conversing as though he were in the senior common room instead.
However overall a great read and very educational.
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on 17 August 2012
Britain will I should declare but I have a degree in mathematics so my review is likely to be coloured by that. This book takes you through 17 equations, giving a short introduction to the equations, a description of why they are important and then for each one a lovely rambling story of occasions where the equation might be important or higher was discovered with a little bit of mathematical history thrown in. Like many popular books on mathematics the narrative often brings you to the point of deepening your understanding, but then pulls away. So from the book was a little disappointing. However I would recommend that for anyone who has an interest in mathematics but maybe not much training, and who wants to improve their mathematical literacy. The best thing about book is the broad range of topics covered in the various chapters.
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on 16 July 2014
This is a book which takes some major mathematical equations and explains how they have affected the development of our world, from Pythagoras's theorem to the Black-Scholes equation for pricing financial instruments. Like some other books by Ian Stewart, it does not attempt to explain all the maths to the uninitiated, nor does it describe the technicalities of how the equations have been used in e.g. modern technology: the more mathematically-minded reader may prefer to have a fuller exposition of the maths. What the book does, though, is give a feel for the relationship between the equations and their application in the real world. I found it readable, interesting, and occasionally provocative (especially in the final main chapter, which is centred on the recent financial crash), but would have preferred a deeper technical exposition.
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