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Review - Meta Math! [Meta Maths!] The Quest for Omega - Gregory Chaitin
Mathematical truth is not totally objective. If a mathematical statement is false, there will be no proofs, but if it is true, there will be an endless variety of proofs, not just one!... Math is the music of reason, and some proofs sound like jazz, others sound like a fugue. Which is better, the jazz or the fugues? Neither.
This snippet from Gregory Chaitin's remarkable eBook Meta Math! sets the tone for the whole thing. Chaitin, who is the master of the intermingling of maths and computing, presents a wonderfully readable book that achieves not one but three marvellous things.
First of all it takes the trouble to look at what maths actually is. Not what it's for or what it can deliver, but what it is and why for some people it's as beautiful as a work of art.
Secondly it's an exploration of the mind of a mathematician, which is a rare treat. Most of the good popular maths books have been written by science writers like Singh and Gleick. With the exception of Ian Stewart and Clifford Pickover, there seem to be few mathematicians who can really explain what the fuss is all about. Chaitin achieves this.
Finally it gives an insight into the way Chaitin's discovery of Omega extended the ideas of Gödel and Turing on incompleteness and uncomputability. This number demonstrates Chaitin's idea that a truly random number is not compressible - that the shortest program to produce such a number is the number itself.
One proviso - this is the maths book closest to Stephen Hawking's A Brief History of Time, in that it starts of painlessly, but by the end you will have to do a bit of 'okay, I don't really get that, but I'll keep on reading and go with the flow'. Don't let that put you off! This book is a great supplemental read for private math tutoring and will ensure that you truly grasp these mathematical concepts.
We are delighted that this title, which we first reviewed in downloadable format, is now available as a real book - it richly deserved publication.
Only in hardback
Reviewed by Brian Clegg
See more about the author in the Gregory Chaitin biography
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Last update 16 April 2011