Preface xvii
I tried to place a photograph of a particular person in
tion of the book where his/her views had some impact on my writ-
ing. The responsibility for my writing is my own, and including a
photograph of a person should not be construed as his or her tacit
endorsement of my views.
This book may need more than one preface, and
in the end there would still remain room for doubt
whether anyone who had never lived through
similar experiences could be brought closer
to the experience of this book by means of prefaces.
Friedrich Nietzsche
I hope that the reader will forgive me that the book reflects
my personal outlook on mathematics. To preempt criticism of my
sweeping generalizations (and of the even greater sin of using in-
trospection as a source of empirical data), I quote Sholom Aleichem:
Man’s life is full of mystery, and everyone tries to compare it
to something simple and easier to grasp. I knew a carpenter,
and he used to say: “A man is like a carpenter. Look at the
carpenter; the carpenter lives, lives and then dies. And so
does a man.”
And to ward off another sort of criticism, I should state clearly
that I understand that, by writing about mathematics instead of
doing mathematics, I am breaking a kind of taboo. As G. H. Hardy
famously put it in his book A Mathematician’s Apology [45, p. 61]:
The function of a mathematician is to do something, to
prove new theorems, to add to mathematics, and not to
talk about what he or other mathematicians have done.
Statesmen despise publicists, painters despise art-critics,
and physiologists, physicists, mathematicians have similar
feelings; there is no scorn more profound, or on the whole
justifiable, than that of the men who make for the men
who explain. Exposition, criticism, appreciation is work for
second-rate minds.
Having broken a formidable taboo of my own tribe, I can only
apologize in advance if I have disregarded, inadvertently or through
ignorance, any sacred beliefs of other disciplines and professions.
To reduce the level of offence, I ask the discerning reader to treat
my book not so much as a statement of my beliefs but as a list of
that sec-
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