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King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry

by Siobhan Roberts
Walker & Company, New York, 1996
368 pp., illus. b/w, col. Trade, $27.95
ISBN: 13 978-0-8027-1499-2.

Reviewed by Paul Brown
Artist and Writer
Sunshine Coast, Australia


Donald Coxeter is recognised as one of the 20th centuries most important mathematicians. He chose at an early age to specialise in classical geometry at a time that when it was already considered unfashionable (some even thought it was closed) and then throughout his long life defended it against the attacks of the algebraic school centred on the work of the Bourbaki collective.

This book is assiduously researched——of the book’s 386 pages 127 are composed of appendices and endnotes and many are an interesting read in their own right (though surprisingly there’s no index!). However, there’s a definite suspicion that this almost obsessive scholarship is an attempt by the author to disguise her own lack of understanding of many of the concepts she is trying to explain. For example, she confuses the field of Computer Aided Design with a specific software program and later credits John Horton Conway with the observation that successive terms in the Fibonacci series equal the golden ration, whereas I’m pretty confident that what Conway was trying to explain was the concept of approximation and limit.

Some sections, like the one on computer animation company Pixar, appear gratuitous and little more than an opportunity of adding some fashionable and attractive material to what might otherwise be considered a book about a "dry" individual with poor sales potential. And even here there’s a missed opportunity to compare Pixar founder——Ed Catmull’s subdivision with the methods used by Buckminster Fuller (which are described earlier in the book) who used polygonal subdivision to convert the regular polyhedra into his famous dome structures. There’s so much of this extraneous material (Jeff Weeks, we are told, prefers pen to pencils because "pens make darker, firmer lines than pencils, he finds"——and——CERN is "the centre of the universe for determining the contents of the universe in it’s first trillionth of a second"——this latter a part of the explanation of string theory) that there is a real sense of relief when the author returns to her subject——the man himself. But even here there’s no real glimpse of the real Coxeter, and I finished the book with a lack of fulfilment made all the worse by my original high expectations of learning more about a man who has been a major inspiration to me throughout my life.

Biographies fall into two categories. The almost fictionalised version that emotionally engage the reader … "Continuing on and on with his passion for geometry was at the top of his mind by the end of the Budapest conference"——or——the scholarly pedantically researched version that aims to engage with intellect. This books attempts to be both and, sadly, fails to be either.

Nevertheless, anyone who would like to get a glimpse of this important figure will want to read this book. There is a wealth of material there despite its failings. And so gently reader I will recommend this book to you, if only for the subject himself who stood alone for a major part of the 20th century defending the gates of geometry from the continental hordes.




Updated 1st March 2007

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