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4.6 out of 5 stars
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4.6 out of 5 stars
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on 5 November 2008
I received a copy of this book for my birthday this year, and was immediately drawn towards the material on algebra with which I was most familiar. The most striking thing about the book as a whole, both in the bits I know well, and the bits I don't know much about, is the way in which it combines large portions of accessible text with substantial mathematical content - it is the lack of actual serious content which frustrates me most about popular books about maths (Fermat's Last Theorem and the Riemann Hypothesis have received the popular treatment with limited content). But in this companion there are clues to enable an enthusiast to engage with the material.

It is right to say, as the introduction does, that there is material in this book which will require some knowledge beyond what you might learn at school. But do not let that put you off (it is no more daunting than the physical size of the book, which mirrors only its extensive coverage). For the genius of this companion is in the way that it engages with real mathematics and how it is actually done by real mathematicians. It is not simply a presentation of particular subject matter (as in a text book) nor is it an encyclopedia of mathematics, for it seeks to convey an understanding of the nature and importance of pure mathematics, rather than simply definitions of the component parts - and through disciplined editing and clear exposition it sets a standard which will not easily be matched.

There is a huge amount which will challenge and excite a good A-level student. My one observation is that the suggested further reading is sometimes a great deal more demanding than the component articles of the Companion (which is partly a reflection of just how good these articles are) - but more consistency, or a scheme for marking references accessible at or just beyond A-level is the only improvement I could think of.

If this book had been in my school library when I was 17 ... well every school with a 6th form should have one. And anyone with a true interest in mathematics should have it to browse (and will want to read it).
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on 6 January 2011
I hesitated before buying this book, thinking that there would be little that I would understand. I have a degree in mathematics from Cambridge, but that was achieved 50 years ago and although I have kept my interest and read a number of popular books on the subject, I have never continued my studies and have forgotten most of what I once knew.

The book is a delight. Look inside and you will find a wide range of topics, ranging from a series of introductory articles to biographical and historical sections and including descriptions of the branches of the subject currently under investigation and the impact of mathematics on the practical world.

If you have an interest in mathematics and are tempted, do seriously consider buying this book. There will be (almost certainly) some parts that you find very difficult but there will be very many that give you a fascinating insight and great pleasure.
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on 7 October 2010
This review applies only to the Kindle version.

The print edition of this book is a fantastic, weighty tome and is well worth every penny. Unfortunately the same cannot be said of the Kindle edition. For such a huge text, the failure to take advantage of hyperlinks makes browsing the book a frustrating experience. In addition, mathematical graphics and equations are rendered in low resolution and are virtually unreadable. As the Kindle device is perfectly capable of rendering high quality graphical content, this lapse is unforgiveable in an ebook costing this much.

Disappointing.
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on 16 April 2016
For the first-time ever, in my 65 years on this planet Timothy Gowers has enabled me to understand and appreciate a mathematical concept i.e. Algebraic geometry. I am so overjoyed, by what, many wiser heads, would take in their stride.
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on 13 January 2014
My formal maths education ended 30 years ago with university level mathematics for engineering. A renewed interest had me looking for a book that explains how the many topics within mathematics are linked together, in a way that limits the use of the formal language of maths. The search is over....this is the book.

It is not a textbook, and you won't earn a college degree by reading it, but anyone reading part 1 will understand fundamentals which will make textbooks much easier to read. Part 2 is also a good path to understanding the history of mathematics, and both why and how it was developed to solve real problems that man has faced down the years.
Further sections explain key concepts in language as close to laymans's terms as possible, and give more detailed guides to major subtopics, significant contemporary questions, prominent figures, applications to other area of science and life as a mathematician.

The book is not 'light' reading in any sense. Maths can be inherently difficult, and the contents of the Companion are essays without illustrations. The hard copy is also physically daunting, which is why I would recommend the digital kindle version for each of access and use.

Nonetheless, if you have an interest in mathematics and have some level of maths education then, whether you use it as a guide to the subject or as a companion to deeper study, this is a book you should have.
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on 23 August 2009
This is a great book. Its entries are well written by recognisable experts and at a high enough level so that people attempting research may use them as a starting point or even as a guide to the main people in the field. It can be read by the amateur too. Other good points are: the quality and depth of coverage, the connections made between fields, and the broad perpective it provides on the subject.
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on 12 June 2013
This is a true companion - someone you'd welcome on a trip or sharing an exploration of mathematics. The articles are written by people who are both clear writers and excellent teachers. It helps both the mathematical 'day-tripper' as well as the student of mathematics, as a comprehensive reference.
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on 24 March 2015
This is a brilliant book, everyone who loves maths should own it, and everyone who is curious about whether they could love maths (i.e. recovering from a disasterous experience at school) should read it.
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on 30 June 2013
This is a truly excellent books that I find myself dipping into whenever I have a spare moment. A fair proportion of the material requires a reasonable mathematical background to fully appreciate. Wonderfully insightful articles from world class mathematics.

Many times I read an article and was enlightened about the history, links with other areas or sometimes even the real point of the theory. It reminds me of some sessions with my PhD supervisor when you would come away thinking - Wow! I wish I could think like that!
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on 27 December 2013
A wonderful kaleidoscope of a marvellous discipline. Not what you'd call light reading, though; the book is far too massive to read in bed!
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