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. Apologies 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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