The Pleasures of Counting Paperback – 5 Dec 1996
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'This is real mathematics, not the watered down versions served in 'maths for liberal arts' courses … Not just maths lovers, but a much larger audience, should enjoy Körner's witty prose and enlightening comments, numerous historical passages and anecdotes. I would particularly recommend the book to all maths teachers.' Arturo Sangalli, New Scientist
'… a glorious celebration of mathematics as a way of getting to grips with the world around us, employing a seamless mix of history, abstract thought and applications.' Ian Stewart, New Scientist
'… a real gem of a book … I don't recommend a book this strongly very often - if you have any interest in maths at whatever level and for any reason go out and buy a copy!' Computer Shopper
'… delightful.' Douglas Quadling, The Magazine of the Cambridge Society
'This is a marvelous book which I commend to all mathematicians and students of mathematics.' C. M. Elliott, Mathematics Today
'If you have ever wondered what it is that mathemeticians do and why they do it then this may be the book for you.' L'Enseignement Mathématique
' … well-researched book … It is aimed at anyone who is willing to remember school mathematics. A cracking good tale: buy it for your children and read it yourself.' Mathematika
What is the connection between the outbreak of cholera in Victorian Soho, the Battle of the Atlantic and the design of anchors? They all show how a little mathematics can shed light on the world around us. If you have ever wondered what mathematicians do, then read on. Mathematicians wanting to explain to others how they spend their working days (and nights) should seek inspiration here.
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The subject matter is maths, of course. But the approach puts the maths into the context of how it is used to solve real-world problems - giving an insight into the development of applied mathematics - often mistaken as mechanics and stats.
Korner's description of the people behind the maths, particularly Richardson, is very warm and helps you feel how particular problems were tackled.
The style is "literary" and the exercises, which are scattered throughout, "emerge" from the text. This provides real motivation for the problems - and motivates the reader to learn something by attempting them. It reminded me of Polya's classic "How to Solve It" (now that's an ABSOLUTE must).
I think Korner's target of a bright teenager is a bit ambitious. I feel the intended reader would have to be a pretty serious minded individual destined for the "premier division" maths departments to get much out of the book - but I may be underestimating the potential of the readers.
I was surprised at some of the things cited (the first chapter on operational research in the first world war is not, shall we say, deep) and some of those that do not get cited, but de gustibus non disputandem est. And I would have to say that in general the contents were surprising in the best way, by being ofbeat, and that is good.
Nevertheless, I have a list of quibbles; here are some:
First, he makes some foolishly dismissive - to be kind - remarks about economics, which reveal only that he does not seem to know a lot about the subject.
Second, he makes some foolish jokes about masters and servants; he glosses his description of Halmos's Naive set theory as a gentlemans guide by explaining that a gentleman should know how to drive, but probably prefers to let his chauffeur do it most of the time. He makes similar remarks about valets and algorithms (an algorithm is something that your valet could perform). One gets the feeling he would have been on the prosecutions side over lady Chatterley's Lover.
When I was doing my PhD, I remember one of the other students attempted to cultivate a gentleman's attitude to the computer on which he did his research. This was not as endearing a pose as he thought.
Third, maybe less aristocratic disdain about foundations would have improved the final dialogue about the axiomatic method, where complex technical issues are simply brushed under the rug without mention. Yes, the standard axioms for addition and multiplication, plus induction, do define the natural numbers up to isomorphism, but not in a standard first-order language. Surely such a point is germane to the discussion (or reason to have another discussion instead, if you do not want to confuse a beginner with end extensions and non-standard models).
But a nice book, and I look forward to reading bits of it more carefully sometime soon.
Be warned: It takes no prisoners. You don't need any mathematical background to begin it. But you must be willing to do maths if you're going to get the most from this book.
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