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ByM. F. Cayleyon 11 August 2014

Ian Stewart is a fairly prolific author of books popularising maths. This is one of his best. He takes the reader through 14 major mathematical problems, and along the way explains some advanced maths in comprehensible language. Where the maths is too complicated to expound in detail, he gives enough of a feel for what it is about for the layman to perceive the essence. There are passages one needs to read slowly and carefully, but only a basic knowledge of maths is assumed. Besides the maths itself, there are fascinating glimpses into how professional mathematicians think and how new major mathematical insights come about. Thoroughly recommended.

13 people found this helpful

ByMacboyon 29 April 2013

I'm a bit of a fan of Ian Stewart but this time he hasn't quite hit the mark. He does indeed deal with the great mathematical problems but he seems to have trouble finding the right level of difficulty and detail. So he does the historical perspective well but becomes confusing in the mathematical perspective. Sometimes there is an explanation and sometimes he simply admits that it's too advanced and pushes on. This approach left me wanting fewer great problems and more extended and clearer explanations.

ByM. F. Cayleyon 11 August 2014

Ian Stewart is a fairly prolific author of books popularising maths. This is one of his best. He takes the reader through 14 major mathematical problems, and along the way explains some advanced maths in comprehensible language. Where the maths is too complicated to expound in detail, he gives enough of a feel for what it is about for the layman to perceive the essence. There are passages one needs to read slowly and carefully, but only a basic knowledge of maths is assumed. Besides the maths itself, there are fascinating glimpses into how professional mathematicians think and how new major mathematical insights come about. Thoroughly recommended.

ByMacboyon 29 April 2013

I'm a bit of a fan of Ian Stewart but this time he hasn't quite hit the mark. He does indeed deal with the great mathematical problems but he seems to have trouble finding the right level of difficulty and detail. So he does the historical perspective well but becomes confusing in the mathematical perspective. Sometimes there is an explanation and sometimes he simply admits that it's too advanced and pushes on. This approach left me wanting fewer great problems and more extended and clearer explanations.

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ByMr Ron 26 April 2013

Following an introductory chapter of a general nature we are treated to 15 chapters exhibiting well-chosen and wide-ranging examples, including the well-known Goldbach conjecture, and squaring the circle, through to the so-called Millennium Problems. Don't expect a rehash of other authors' accounts of these problems: Stewart injects rare enthusiasm, vitality, and fresh insights throughout. Particularly spellbinding are the chapters on the Mordell Conjecture, Fermat's Last Theorem (yes, I realise it has been flogged to death in recent years, but this chapter is truly refreshing), and the Riemann Hypothesis. The Hodge Conjecture is perhaps overambitious; but the real coup is the last chapter, entitled 'Twelve for the future', and I defy anyone to read that without a frisson of excitement! Some of these are immediately accessible (the Collatz Conjecture, and the 'Lonely Runner Conjecture') and the final and irresistible ABC Conjecture will have you searching the internet.

Prospective undergraduates cannot fail to be inspired by this book: it is the best inducement to study mathematics that I've seen in some time, so every school should have at least one copy on the library shelves. Pupils will find perfectly intelligible accounts of extensions of number systems (rings without unique factorisation), elliptic curves, and much more. Of course, many graduates are familiar with Stewart's university texts (Galois Theory, Algebraic Number Theory...)

Just one or two oversights. for example, I didn't think much of the phrase on page 216, which talks of forces generated by a particle's acceleration (it's the other way round). Misprints are mercifully few: eg on page 167 we read of Titchmarsh working in 1986 (long after his demise).

This must be Ian Stewart's most attractive book on popular mathematics.

Prospective undergraduates cannot fail to be inspired by this book: it is the best inducement to study mathematics that I've seen in some time, so every school should have at least one copy on the library shelves. Pupils will find perfectly intelligible accounts of extensions of number systems (rings without unique factorisation), elliptic curves, and much more. Of course, many graduates are familiar with Stewart's university texts (Galois Theory, Algebraic Number Theory...)

Just one or two oversights. for example, I didn't think much of the phrase on page 216, which talks of forces generated by a particle's acceleration (it's the other way round). Misprints are mercifully few: eg on page 167 we read of Titchmarsh working in 1986 (long after his demise).

This must be Ian Stewart's most attractive book on popular mathematics.

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Byrosy44on 10 July 2013

I found this book exceeded my expectations of "popular" books on mathematics and physics topics. The explanations are comprehensive putting the problems into historical and mathematical contexts which give the reader a very good insight into why they are "great" rather than simply a bit of a puzzle. Also the author manages make the stories readable by successfully treading the fine line between being lightweight and being too rigorous to be readable. I would recommend this book to anyone wanting to know about the sorts of problems mathematicians wrestle with.

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ByWillon 15 February 2016

As a retired academic (maths & computer science), I enjoyed reading this book very much, at least most of it.

Personally, I am not, and never have been interested in what is known as applied mathematics, and therefore I have skipped

a number of chapters, such as the Navier-Stokes equations, the Quantum Conundrum, and also the Poincare conjecture, as well as

the Hodge conjecture (never studied cohomlogy!) One cannot be interested in absolutely everything. However, the prolific author, Ian Stewart , obviously, is.

And he presents the material very clearly.

Having been written only some two years ago there are references to recent discoveries in a number of areas that were new to me.

Personally, I am not, and never have been interested in what is known as applied mathematics, and therefore I have skipped

a number of chapters, such as the Navier-Stokes equations, the Quantum Conundrum, and also the Poincare conjecture, as well as

the Hodge conjecture (never studied cohomlogy!) One cannot be interested in absolutely everything. However, the prolific author, Ian Stewart , obviously, is.

And he presents the material very clearly.

Having been written only some two years ago there are references to recent discoveries in a number of areas that were new to me.

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ByNitaon 31 March 2016

Unclear exposition of almost everything except Kepler conjecture and Three-body problem. Even in the end when the author "introduces" 12 unsolved problems of his own selection, he seems to be confused about what the actual problems are and what the actual conjectures say. No matter how many times you read the poorly-written chapters and section, you won't gain clear insight into the problems. 2 stars only because the chapters on Kepler conjecture and Three-body problem are fairly clear, should actually deserve 1.

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ByBirtleBoyon 9 January 2015

I have A level maths and found it utterly beyond me. Don't purchase unless you have a degree in maths and need stimulus.

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ByMr. G. Saxbyon 11 November 2013

Beautifully written; no oversimplifying and no condescending, and with the odd touch of wry humour, too. This is not a book for the mathematically underprivileged, though.Although the author puts all his material in the most straightforward way, it isn't all easy going. If you are halfway to a maths or physics degree and find number theory fascinating, this book will be exactly what you want.

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ByPaul Bakeron 15 July 2013

Ian Stewart at his very best yet. It shouldn't be underestimated just what a demanding task Professor Stewart sets himself in this book. The problems are mostly easy enough to express but to outline the historical progress made with each problem in a meaningful but accessible way that leaves the reader educated in the mathematical approach taken and to identify and tie together the deeper over-arching principles that human progress through difficult maths problems have often shared - that is tough and he does it quite brilliantly. A real masterpiece, the product of many long hours of careful thought on approach I suspect, and a super book for all gifted GCSE or A Level pupils to help the budding love of the subject blossom.

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ByChristopher Mathewson 28 April 2013

...my enthusiastic endorsement of this exceptional book. Ian Stewart never dilutes his mathematics, but always makes it accessible & interesting for everyone.

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