September 12, 1913] 



SCIENCE 



349 



most commonly, not of set purpose — but 

 lies at the mercy of the response which the 

 mind may make to the opportunities of its 

 experience. When the response proves to 

 be of permanent interest — and for how 

 many centuries have mathematical ques- 

 tions been a fascination? — we do well to re- 

 gard it. Let us compare another case which 

 is,. I think, essentially the same. It may be 

 that early forms of what now is specifically 

 called art arose with a view to applications : 

 I do not know. But no one will deny that 

 art, when once it has been conceived by us, 

 is a worthy object of pursuit; we know by 

 a long trial that we do wisely to yield our- 

 selves to a love of beautiful things, and to 

 the joy of making them. Well, pure mathe- 

 matics, as such, is an art, a creative art. If 

 its past triumphs of achievement fill us 

 with wonder, its future scope for invention 

 is exhaustless and open to all. It is also a 

 science. For the mind of man is one: to 

 scale the peaks it spreads before the ex- 

 plorer is to open ever new prospects of 

 possibility for the formulation of laws of 

 nature. Its resources have been tested by 

 the experience of generations; to-day it 

 lives and thrives and expands and wins the 

 life-service of more workers than ever be- 

 fore. 



This, at least, is what I wanted to say, 

 and I have said it with the greatest brevity 

 I could command. But may I dare attempt 

 to carry you further? If this seems fanci- 

 ful, what will you say to the setting in 

 which I would wish to place this point of 

 view ? And yet I feel bound to try to indi- 

 cate something more, which may be of 

 wider appeal. I said a word at starting as 

 to the relations of science to those many to 

 whom the message of our advanced civili- 

 zation is the necessity, above all things, of 

 getting bread. Leaving this aside, I would 

 make another reference. In our time old 

 outlooks have very greatly changed; old 



hopes, disregarded perhaps because un- 

 doubted, have very largely lost their sanc- 

 tion, and given place to earnest question- 

 ings. Can any one who watches doubt that 

 the courage to live is in some danger of 

 being swallowed up in the anxiety to ac- 

 quire ? May it not be, then, that it is good 

 for us to realize, and to confess, that the 

 pursuit of things that are beautiful, and 

 the achievement of intellectual things that 

 bring the joy of overcoming, is at least as 

 demonstrably justifiable as the many other 

 things that fill the lives of men? May it 

 not be that a wider recognition of this 

 would be of some general advantage at 

 present? Is it not even possible that ta 

 bear witness to this is one of the uses of the- 

 scientific spirit? Moreover, though the 

 pursuit of truth be a noble aim, is it so new 

 a profession ; are we so sure that the ardor 

 to set down all the facts without extenua- 

 tion is, unassisted, so continuing a purpose? 

 May science itself not be wise to confess to 

 what is its own sustaining force ? 



Such, ladies and gentlemen, in crude, 

 imperfect phrase, is the apologia. If it 

 does not differ much from that which work- 

 ers in other ways would make, it does, at 

 least, try to represent truly one point of 

 view, and it seems to me specially appli- 

 cable to the case of pure mathematics. But 

 you may ask: What, then, is this subject? 

 What can it be about if it is not primarily 

 directed to the discussion of the laws of 

 natural phenomena? What kind of things 

 are they that can occupy alone the thoughts 

 of a lifetime? I propose now to attempt 

 to answer this, most inadequately, by a bare 

 recital of some of the broader issues of pres- 

 ent interest — though this has difficulties, 

 because the nineteenth century was of un- 

 exampled fertility in results and sugges- 

 tions, and I must be as little technical as 

 possible. 



