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SCIENCE 



[N. S. Vol. XLII. No. 1089 



"the remotest past reaches out its skeletal 

 fingers and grapples both present and fu- 

 ture in its iron grip." And there is the 

 conservation of energy and that of mass — 

 both of them, again, doctrines prefigured 

 in the thought of ancient Greece — and nu- 

 merous other so-called natural laws, simple 

 and complex, familiar and unfamiliar, all 

 posing as permanent forms of reality — as 

 natural invariants under the infinite sys- 

 tem of cosmic transformations — and thus 

 together constituting the enlarging con- 

 tribution of natural science towards the 

 slow vindication of a world that has 

 seemed capricious, lawless and imperma- 

 nent. 



Such, then, is a conspectus, suggested 

 rather than portrayed, of the results which 

 the great allies of mathematics, operating 

 through the ages, have achieved in their 

 passionate endeavor to transcend the 

 tragic vicissitudes and limitations of life 

 in an "ever-growing and perishing" uni- 

 verse and to win at length the freedom, the 

 dignity and the peace of a stable world 

 where order and harmony reign and spir- 

 itual goods endure. If we are to arrive at 

 a really just or worthy sense of the hu- 

 man significance of mathematics, it is in 

 relation with those great results of her 

 sister enterprises that the achievements of 

 this science must be appraised. Immense 

 indeed and high is the task of criticism as 

 thus conceived. How diverse and mani- 

 fold the doctrines to be evaluated, what 

 depths to be plumbed, what heights to be 

 scaled, how various the relationships and 

 dignities to be assigned their rightful place 

 in the hierarchy of values. In the pres- 

 ence of such a task what can we think or 

 say in the remaining moments of the hour 1 

 If we have succeeded in setting the prob- 

 lem in its proper light and in indicating 

 the sole eminence from which the matter 

 may be rightly viewed, we ought perhaps 



to be content with that as the issue of the 

 hour, for it is worth while to sketch a 

 worthy program of criticism even if time 

 fails us to perform fully the task thus set. 

 And yet I can not refrain from inviting 

 you to imagine, before we close, a few at 

 least of the things that one who essayed 

 the great critique would submit to his 

 auditors for mediation. And what do you 

 imagine the guiding lines and major 

 themes of his discourse would be? 



I fancy he would say: The question be- 

 fore us, ladies and gentlemen, is not a 

 question of weighing utilities nor of count- 

 ing applications nor of measuring mate- 

 rial gains ; it is a question of human ideals 

 together with the various means of pur- 

 suing them and the differing degrees of 

 their approximation ; we are occupied with 

 a question of appreciation, with the prob- 

 lem of values. I am, he would say, ad- 

 dressing you as representatives of man, and 

 in so doing, I am not regarding man as a 

 mere practician, as a hewer of wood and 

 drawer of water, as an animal content to 

 serve the instincts for shelter and food and 

 reproduction. I am contemplating him as 

 a spiritual being, as a thinker, poet, 

 dreamer, as a lover of knowledge and 

 beauty and wisdom and the joy of har- 

 mony and light, responding to the lure of 

 an ideal destiny, troubled by the mystery 

 of a baffling world, conscious subject of 

 tragedy, yearning for stable reality, for 

 infinite freedom, for perpetuity and a 

 thousand perfections of life. As represent- 

 atives of such a being, you, he would say, 

 and I, even if we be not ourselves produ- 

 cers of theology or philosophy or science or 

 jurisprudence or art or mathematics, are 

 nevertheless rightful inheritors of all this 

 manifold wisdom of man. The question is : 

 What is the inheritance worth? We are 

 the heirs and we are to be the judges of 

 the great responses that time has made to 



