20 of 20 people found the following review helpful
I can't praise this book highly enough. I just wish I had more time to "mine" its depths.
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.
10 of 10 people found the following review helpful
on 20 October 1998
I found this an enthralling book. The style of writing makes it easy to read, while still being very clear and precise. It covers an intriguing range of topics and would, I feel, be of interest to anyone with reasonable level of mathematical knowledge.
3 of 3 people found the following review helpful
on 1 May 2012
A great book exploring mathematics as a living & exciting subject. A sort of cross between a pop-science book & a textbook.
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.
10 of 11 people found the following review helpful
on 28 April 2000
A great book. Korner shows how mathematics has been applied to many areas of study with practical, fascinating results. If you have got as far as reading this review, you will love this book. Enjoy!
13 of 19 people found the following review helpful
on 8 April 2003
No question, this is a five star book, it is a nice tutorial overview of applied maths, the high point being a presentation of Turing's analysis of the Enigma cypher at Bletchley, which I had never read before.
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.