By G. H. Hardy
A Mathematician's Apology is the recognized essay by means of British mathematician G. H. Hardy. It matters the aesthetics of arithmetic with a few own content material, and offers the layman an perception into the brain of a operating mathematician. certainly, this booklet is frequently one in every of the simplest insights into the brain of a operating mathematician written for the layman.
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Extra resources for A Mathematician's Apology
But solicitors and stockbrokers and bookmakers often lead comfortable and happy lives, and it is very difficult to see how the world is richer for their existence. Is there any sense in which I can claim that my life has been less futile than theirs? It seems to me again that there is only one possible answer: yes, perhaps, but, if so, for one reason only: I have never done anything ‘useful’. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.
Haldane, Callinicus: a Defence of Chemical Warfare (1924). 44 horrible than the warfare of pre-scientific times; that bombs are probably more merciful than bayonets; that lachrymatory gas and mustard gas are perhaps the most humane weapons yet devised by military science; and that the orthodox view rests solely on loos-thinking sentimentalism19. It may also by urged (though this was not one of Haldane’s theses) that the equalization of risks which science was expected to bring would be in the long range salutary; that a civilian’s life is not worth more than a soldier’s, nor a woman’s more than a man’s; that anything is better than the concentration of savagery on one particular class; and that, in short, the sooner war comes ‘all out’ the better.
Thus the idea of an ‘irrational’ is deeper than that of an integer; and Pythagoras’s theorem is, for that reason, deeper than Euclid’s. Let us concentrate our attention on the relations between the integers, or some other group of objects lying in some particular stratum. Then it may happen that one of these relations can be comprehended completely, that we can recognize and prove, for example, some property of the integers, without any knowledge of the contents of lower strata. Thus we proved Euclid’s theorem by consideration of properties of integers only.
A Mathematician's Apology by G. H. Hardy