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39 of 41 people found the following review helpful
5.0 out of 5 stars Clear and concise overview of mathematical concepts
Professor Gowers explains the key concepts of mathematics in this accessible and well-constructed book. Written for a general audience (although some basic scientific knowledge is an advantage), this book avoids the popularisation of mathematics, but instead focuses instead on the central ideas of abstraction and axiomisation which underpin all of modern mathematics...
Published on 29 April 2003 by simonstrong

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2 of 3 people found the following review helpful
3.0 out of 5 stars A book providing some insight into the world of mathematics
I had expected this to be a book outlining some of the advanced theories and formulae of mathematics. On the contrary, it was largely concerned with rather fundamental aspects of maths, such as what is meant by numbers, the concept of infinity, how to handle multiple dimensions, geometry, etc. I found this unexpected approach to be quite refreshing and informative. It...
Published 12 months ago by Roger


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39 of 41 people found the following review helpful
5.0 out of 5 stars Clear and concise overview of mathematical concepts, 29 April 2003
Professor Gowers explains the key concepts of mathematics in this accessible and well-constructed book. Written for a general audience (although some basic scientific knowledge is an advantage), this book avoids the popularisation of mathematics, but instead focuses instead on the central ideas of abstraction and axiomisation which underpin all of modern mathematics.
After an introductory chapter on mathematical models in the sciences, Professor Gowers covers topics including numbers, limits, dimension and approximation in six short chapters. A final chapter gives thought-provoking answers to questions such as what are the connections between mathematics and music, and what is beauty in mathematics. The format inevitably means that some topics are omitted due to lack of space - there is little background on the history of mathematics for example - but that does not detract from the central theme of the book.
Professor Gowers' enthusiasm for his subject comes across on every page.
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21 of 22 people found the following review helpful
5.0 out of 5 stars Fascinating, 23 Dec 2003
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I have bought several books in the "Very Short Introduction..." series all of which have been excellent and this one in particular is extremely clear and interesting. The book is aimed at the intelligent layperson and gives a general introduction to what maths really is and how professional mathematicians think about it. This approach is in contrast to most people's experience in school where tedious and repetitive calculation is the norm (which is a real shame). Various areas in maths are looked at and the ideas behind them are explained rather than the reader being hit with big formulae and funny looking symbols.
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33 of 36 people found the following review helpful
5.0 out of 5 stars Insightful, Lucid, and Thought-Provoking, 30 Sep 2002
By A Customer
It is amazing how Tim Gowers, one of the greatest mathematicians
of our time, managed to convey the spirit and content of math to the general reader, and not only. Even professional mathematicians will learn a lot from his insightful remarks.
This ``little'' book is destined to become a classic of popular
science writing.
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5 of 5 people found the following review helpful
5.0 out of 5 stars The best introduction to math out there, 26 April 2011
By 
Dr. Bojan Tunguz (Indiana, USA) - See all my reviews
(TOP 500 REVIEWER)    (REAL NAME)   
The world of mathematics elicits many different emotions, from fear to reverence, from apprehension to fascination. On a surface this may seem surprising, since mathematics is supposed to deal rational thought, and should be as removed from emotional considerations as it gets. And yet, it is precisely this dispassionate rationality that makes those unaccustomed to mathematical thinking recoil, and those with a mathematical bend of mind rub their hands in glee. For the truth is, mathematical thought relies heavily on emotions, and mathematicians are fascinated with beauty and elegance of mathematical creations.

In the book "Mathematics: A Very Short Introduction" the author Timothy Gowers tries to convey some of this beauty. This is a very readable and intelligent short introduction, and probably the best short introduction to mathematics out there. It takes reader through some basic mathematical problems, and showcases the methods and procedures that mathematicians use in their work. If you are math-phobic, you will not have to deal with any complicated mathematical equations, and all of the problems and proofs that are offered in the book are straightforward and intuitive, and require a very minimal level of mathematical knowledge. The fact that the book attempts to "do" mathematics, as opposed to just tell about it, is one of its more rewarding aspects. It makes this an intelligent read, and rewarding no matter whether you are a complete mathematical "outsider" or someone with an advanced degree in a math-intensive field.
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12 of 13 people found the following review helpful
5.0 out of 5 stars Great book, 28 Dec 2004
This book demystifies puzzling concepts such as infinity, curved space, n-dimensional space and fractional dimensions. His emphasis on the abstract method - the focus on what mathetical objects DO rather than what they really ARE - as the key to understanding all these concepts is amazingly powerful, truly an eye-opener.
A basic knowledge of mathematics is an advantage
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22 of 25 people found the following review helpful
5.0 out of 5 stars Pragmatic Mathematics, 26 Sep 2005
By 
Peter Reeve (Thousand Oaks, CA USA) - See all my reviews
(VINE VOICE)    (REAL NAME)   
An introduction to mathematics could be just that; elementary arithmetic and geometry, or it could be an outline history or finally, it could introduce the philosophical aspects of the subject. Gowers does none of those, although he does touch on the history and philosophy of mathematics. This is really an introduction to higher mathematics, for readers who have reached what in Britain is GCSE standard, roughly eleventh grade in the US.
Philosophically, Gowers is a pragmatist. To him, problematic concepts like infinity and irrational numbers have meaning in as much as they are useful, and are true in as much as they give true results. As a European, Gowers credits Wittgenstein with these ideas. An American author would have credited William James. Gowers sidesteps rather than resolves philosophical problems, thus giving reassurance to mathematicians and irritation to philosophers.
The book is a random selection of topics rather than a continuous narrative, but succeeds because each topic is fascinating and the writing is clear throughout.
Under "Further Reading", Gowers includes his own website address, where you can find sections that did not make it into the book. What a good idea! The site is as full of good stuff as the book, and gives links to further sites that will give you as much mathematics as you will ever want.
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8 of 9 people found the following review helpful
5.0 out of 5 stars A Very Very Good Introduction, 7 Jan 2004
I've recently gotten interested in Mathematics again (after finding it very difficult and boring at school) and was looking for a good general book to serve as an introduction. I really don't think I could have done any better than this. If you have even the slightest interest/curiosity about maths - you should buy this book.
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2 of 2 people found the following review helpful
4.0 out of 5 stars Back to school, 12 Feb 2013
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I have already a growing number of "very short introduction.." on my bookshelf and quite enjoy reading them.
I think its a very good series except for the text font and layout which I am not a big fan. I find them hard to read sometimes but they do have the advantage of being pocket size so handy.

This one on Mathematics brought be back to my young age at school. I would have been so pleased to have a math teacher such as Mr Gower.

He has a talent to explain complex things simply. Some worked examples may be a bit derouting for some of us who dont use maths every day but you honnestly do not have to read everything. I read this book with a relaxed attitude, trying to enjoy more than to learn. The book is also loaded with diagrams which helps you further to understand some key concepts.

What I found fascinating was that some maths conjectures are still not resolved to this date. Finally, the last sections on "FAQ" is very useful and instructive.

7/10
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2 of 2 people found the following review helpful
5.0 out of 5 stars A good take on the subject, 5 Jan 2011
It's well known that some concepts in mathematics can be utterly mind-bending - concepts such as curved space, higher dimensional geometry, infinity, and more besides. To be able to work with any of these, you often need to let go of the urge to visualise something and instead settle for merely conceptualising it. You need, in other words, to feel comfortable thinking in a thoroughly abstract way. This book is an introduction to that way of thinking. It's not one of those books that joyously recaps all the rules and syntax you'd forgotten since leaving school. Rather, its aim is simply to give you the means to grapple with core aspects of advanced mathematics.

While this book doesn't overwhelm with technicalities (a British GCSE or equivalent in the subject should be sufficient prior knowledge for most readers), the rules and processes are not ignored, and there are brief introductions/reminders of topics such as Euclidean geometry, irrational numbers and so on. However the author's aims and emphasis are decidedly more psychological and philosophical. Why should we accept the axioms proposed by mathematicians? What exactly is a number? What does mathematical proof actually mean? These questions first need to be explored before embarking on the path to more esoteric concepts such as multi-dimensional geometry and manifolds (incidentally, useful for anyone interested in string theory).

The chapters are sensibly structured and Gowers's enthusiasm for the subject radiates from each page without ever sinking into that patronising "Hey kids, maths is fun!" style of writing. The last chapter contains a selection of genuinely interesting FAQs, including some good suggestions as to why so many people seem to strongly dislike mathematics, compared with say biology or English literature (about which the non-enthusiast may just feel indifferent). Overall I found this more interesting that expected; a useful take on the subject that lays the groundwork for some of the more advanced areas of mathematics.
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6 of 7 people found the following review helpful
5.0 out of 5 stars Making Sense of Mathematics, 28 July 2008
By 
C. Johnson "Clive Johnson" (Brighton, UK) - See all my reviews
(REAL NAME)   
I have become addicted to the "Very Short Introduction" series, offering the knowledge-hungry layman a great way to gain insight into a wide variety of topics. For me, mathematics is a subject which I was happy to close the book on in upper school, and it seems I was not alone in lacking enthusiasm for the subject which was impressed upon hapless students as being so important (why maths is so dreaded by many is a question this book seeks to answer, amongst many other "FAQ's" of this kind).

Rather than presenting a mass of complex formulae to prove various points, the book takes the approach of explaining the practical applications of mathematics, such as why modelling is relevant in many different situations, and how an understanding of patterns can be of value. Teaching mathematics from such a practical stand-point is a trick modern school education may be missing, yet the book suggests this might be the key for a new generation to understand what's being taught and actually getting excited about the subject.

Rather than being a dry read best left for boffins and insomniacs, this is a book which provokes thought and puts this fascinating subject in a whole new light.
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