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1、A Mathematicians ApologyG. H. HardyFirst Published November 1940 As fifty or more years have passed since the death of the author, this book is now in the public domain in the Dominion of Canada. First Electronic Edition, Version 1.0 March . Published by the University of Alberta Mathematical Scienc
2、es Society Available on the World Wide Web at http:/www.math.ualberta.ca/mss/To JOHN LOMAS who asked me to write itPrefaceI am indebted for many valuable criticisms to Professor C. D. Broad and Dr C. P. Snow, each of whom read my original manuscript. I have incorporated the substance of nearly all o
3、f their suggestions in my text, and have so removed a good many crudities and obscurities.In one case, I have dealt with them differently. My 28 is based on a short article which I contributed to Eureka (the journal of the Cambridge Archimedean Society) early in the year, and I found it impossible t
4、o remodel what I had written so recently and with so much care. Also, if I had tried to meet such important criticisms seriously, I should have had to expand this section so much as to destroy the whole balance of my essay. I have therefore left it unaltered, but have added a short statement of the
5、chief points made by my critics in a note at the end.G. H. H.18 July 19401It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about
6、what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who expl
7、ain. Exposition, criticism, appreciation, is work for second-rate minds.I can remember arguing this point once in one of the few serious conversations that I ever had with Housman. Housman, in his Leslie Stephen lecture The Name and Nature of Poetry, had denied very emphatically that he was a critic
8、; but he had denied it in what seemed to me a singularly perverse way, and had expressed an admiration for literary criticism which startled and scandalized me.He had begun with a quotation from his inaugural lecture, delivered twenty-two years beforeWhether the faculty of literary criticism is the
9、best gift that Heaven has in its treasures, I cannot say; but Heaven seems to think so, for assuredly it is the gift most charily bestowed. Orators and poets, if rare in comparison with blackberries, are commoner than returns of Halleys comet: literary critics are less commonAnd he had continuedIn t
10、hese twenty-two years I have improved in some respects and deteriorated in others, but I have not so much improved as to become a literary critic, nor so much deteriorated as to fancy that I have become one.It had seemed to me deplorable that a great scholar and a fine poet should write like this, a
11、nd, finding myself next to him in Hall a few weeks later, I plunged in and said so. Did he really mean what he had said to be taken very seriously? Would the life of the best of critics really have seemed to him comparable with that of a scholar and a poet? We argued the questions all through dinner
12、, and I think that finally he agreed with me. I must not seem to claim a dialectical triumph over a man who can no longer contradict me, but Perhaps not entirely was, in the end, his reply to the first question, and Probably no to the second.There may have been some doubt about Housmans feelings, an
13、d I do not wish to claim him as on my side; but there is no doubt at all about the feelings of men of science, and I share them fully. If then I find myself writing, not mathematics, but about mathematics, it is a confession of weakness, for which I may rightly be scorned or pitied by younger and mo
14、re vigorous mathematicians. I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job.2I propose to put forward an apology for mathematics; and I may be told tha
15、t it needs none, since there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true: indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher
16、 in popular estimation. A mathematician need not now consider himself on the defensive. He does not have to meet the sort of opposition describe by Bradley in the admirable defence of metaphysics which forms the introduction to Appearance and Reality. A metaphysician, says Bradley, will be told that metaphysical knowledge is wholly impossible, or that even if possible to a certain degree, it is practically no knowledge worth the name.
