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
paul@paul-brown.com
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 researchedof
the books 386 pages 127 are composed
of appendices and endnotes and many are
an interesting read in their own right
(though surprisingly theres no index!).
However, theres 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
Im 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
theres a missed opportunity to compare
Pixar founderEd Catmulls
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. Theres
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"andCERN
is "the centre of the universe for
determining the contents of the universe
in its 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
subjectthe man himself. But
even here theres 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"orthe
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.