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on 29 October 2008
Mathematics is a topic than can easily overwhelm a novice with its esoteric lingo, abstract notations and complex ideas. Tony Crilly manages to explain the most important mathematical concepts in a clear, concise way. Every idea receives a four page explanation, which in most cases is enough to give you a clear understanding of the concept and how it applies to the real world.

The book has a few flaws though. Some concepts could do with a little more material, as sometimes the brevity of the explanation leaves one puzzled and unfulfilled. Also, the writer assumes the reader has a firm grip on the very basics of mathematics, which may not be the case for everyone. And lastly sometimes the way a concept applies to real world situations isn't made sufficiently clear.

Nonetheless this is a great book, recommended for everyone who has an interest in mathematics and wants a clear, no-nonsense, plain language explanation of all those fantastic ideas that you see in TV shows like Numb3rs, but who lack the time and inclination to wrestle their way through inaccessible tomes of mathematical knowledge. This book is very much accessible and a joy to read.
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on 11 March 2009
I approached this book with three questions in mind. Being mathematically trained I was curious about whether these really were ideas I didn't know about and needed to. On the other hand I thought about my past students embarking on their training - could they benefit from knowing these 50 ideas? Finally, I wondered if this book might inspire someone to begin to study mathematics, much in the way I was inspired as a novice by trying to read about relativity and finding myself staring into the face of a strange and enticing mystery. The answers were appealingly affirmative, which made me wonder what else it is about this little book that makes it so attractive. Yes, the layout is good with topics mainly restricted to bite-size 4-page spreads. Yes, the hand drawn diagrams give the book a friendly feel and, yes, 50 is a nice round number. But its real appeal lies in the way the author slowly wins the reader's trust and confidence. The author, as tour guide, is friendly and humorous, knows his stuff and communicates it well. In fact, the book is a Pandora's box of delights ranging across an extraordinary wide set of ideas. For instance, ideas 23 to 28 are listed as `Topology', `Dimension', `Fractals', `Chaos', `The parallel postulate' and `Discrete geometry', to list just a few of the enticing mysteries on offer. It is the sort of book I will return to again and again to extract new gems of mathematical insight or historical perspective. But it seems to work also at many levels - I have even had 14-year-old students read and enjoy parts of it. Remarkably, age and experience do not seem to be barriers, though I am always bound to look at it through possibly more practised eyes. Still, I feel completely confident in recommending it, especially to students either setting out on their mathematical studies or thinking about doing so.
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on 3 July 2010
this is the 3rd "50 ... You Really Need to Know" book I've read in a row - I've enjoyed the series so far, I bought the Genetics (very good) and the Economics one before this. Of the 3 I'd say this one was the least interesting. Its not bad, but you really really need to be into maths to enjoy it. I studied mathematics at university so some of the chapters were familiar, however if you are an average person who doesn't use calculus, geometry, rings and groups for a living, then you might find it a bit boring. If you are a mathematics student then this probably is of interest to you.
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on 25 March 2009
This well-written book works on many levels - I have thoroughly enjoyed it as it includes many of the interesting concepts (and sometimes proofs) that I covered, but had since forgotten, during my mathematics degree 15 years ago. But this book is not just for maths students, my wife who normally has no interest in this sort of thing has picked it up and found many of the ideas interesting - as too has my 10 year old neice.

So it has something for everyone and is written in a way that is not too dry.
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on 23 June 2009
This little book encapsulates the essence of 50 mathematical ideas which are of great interest to many although a lot of people would not realise it.

Each idea presented here gives the germs of background which clearly the author hopes will take root in the conciouness of the reader suffice for them to go and examine more for themselves.

I suspect that the target audience would be young students of pre-university age, perhaps taking up some quantative methods courses to support their chosen subject as well as some older, yet educated readers who may have not got so far into their mathematical development but who wish to aquaint them selves with the basics.

Each chapter offers a taste, a tidbit of knowledge which whets the appetite for more and urges the reader on to consider the subject matter as a whole, underpinning other sciences and physical subjects such as engineering, while seeking to broaden the mind with the mathematical universe.

An open mind can lead to imaginary constructions which sees the puzzles contained within the book as part of a unified theory of mathematics which connects them all together: just think of theories of multi-dimensional constructs and the neuron net just glows.

I really like this book. The lack of detail serves to offer a clear perspective for thinking about the general nature of each puzzle although the limitations of only four pages can result in some zealous editing. Still it is a fun filled and exciting book which I am happy to recommend as an essential addition to any home library.
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on 23 March 2009
I haven't studied maths in 20 years and found this a great way to remind myself of some key concepts (and learn new ones). Each section is short, clearly written and presented in a way that non-mathematical people like me will find easy to understand. Definitely worth reading.
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on 25 December 2008
This is a great book; It goes into sufficient detail on all the topics, and introduced and explained to me to a few new topics.

It gives each topic 4 pages of clear, interesting and thorough analysis.

The ideas lead very clearly from one to another, but you will most likely be able to understand the next idea even if you haven't grasped the previous one fully.

I definatly recommend it.
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50 Mathematical Ideas you really need to know, by Tony Crilly, Quercus Publishing, London, 2007, 210 ff.

The fun of mathematics!!
By Howard Jones

`Mathematical ideas you really need to know'? Well, not really. But if you are at all interested in maths, or like to do puzzles, or you want to engage in sophisticated chat around the dinner table telling your fellow diners about the Riemann hypothesis or how Fermat's theorem was solved, or you are one of those who, like Francis Bacon, think that pure maths isn't really of any use to anyone, then this the book for you. It is profusely illustrated on almost every double-page opening and was written by the Reader in Mathematical Sciences at Middlesex University in the U.K.

Perhaps in school you wondered about Diophantine equations, and I'm sure you must have met the Fibonacci series and Pascal's triangle, but I wonder if you've heard of the Leibniz triangle with fractions instead of integers? Bayes' theorem and chaos theory were never part of the maths syllabus when I was in school, but now they are - and for the very good reason that they are applied in many aspects of our everyday lives, as the author tells us. In fact, it is the most entertaining and easily accessible `mathematics for everyone' book I have ever read.
As someone who has taught maths to A-level for the past 50 years, I would unhestitatingly recommend this book. It concludes with a Glossary of some of the more technical terms and an Index.

Dr Howard A. Jones is the author of The Thoughtful Guide to God (2006) and The Tao of Holism (2008), both published by O Books of Winchester, U.K.; and The World as Spirit published by Fairhill Publishing, Whitland, West Wales, 2011.

Chaos: Making a New Science
Statistics without Tears: An Introduction for Non-Mathematicians (Penguin Science)
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on 17 December 2010
Got this as present last year. Thought 'someone has bought me - a graduate in mathematics - this???'
However, once I got into it, I found the material not as simple as I expected, and was pleased the see the breadth and material was well chosen - they are great mathematical ideas - and well explained by TC. Yes, it leaves mathematicians wanting to see more proofs and more detail, but the title doesn't claim any more than an introduction, and further material is always available for those who want it.

So - great little book, didn't put it down all last Christmas. Definitely one for younger sparks too.

Oh, and yes, the pictures / graphics were also pretty but helpful (e.g. hypercubes)

JB
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on 3 April 2009
There are not many books which really manage to describe mathematical ideas straightforwardly. The great classic, I believe, is Calculus Made Easy by the great Sylvanus P Thompson. But Tony Crilly has written one which is fit to stand alongside it.

If any serious number of bankers had bothered to read it, the world economy might not be in such a mess.
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