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SCIENCE 



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



be said that not all this has been done by 

 mathematics alone. Far from it. It is, of 

 course, the joint achievement of many sci- 

 ences and arts, but — and just this is the 

 point — the contributions of mathematics 

 to the great work, direct and indirect, have 

 been indispensable. And it will require no 

 great skill in our speaker to show to his 

 audience, if it have a little imagination, 

 that, as I have said elsewhere, if all these 

 mathematical contributions were by some 

 strange spiritual cataclysm to be suddenly 

 withdrawn, the life and body of industry 

 and commerce would suddenly collapse as 

 by a paralytic stroke, the now splendid 

 outer tokens of material civilization would 

 quickly perish, and the face of our planet 

 would at once assume the aspect of a ruined 

 and bankrupt world. For such is the 

 amazing utility, such the wealth of by- 

 products, if you please, that come from a 

 science and art that owes its life, its con- 

 tinuity and its power to man's love of in- 

 tellectual harmony and pleads its inner 

 charm as its sole appropriate justification. 

 Indeed it appears — contrary to popular be- 

 lief — that in our world there is nothing 

 else quite so practical as the inspiration of 

 a muse. 



But this is not all nor nearly all to which 

 our applied mathematician will wish to in- 

 vite attention. It is only the beginning of 

 it. Even if he does not allude to the quiet 

 service continuously and everywhere ren- 

 dered by mathematics in its role as a norm 

 or standard or ideal in every field of 

 thought whether exact or inexact, he will 

 yet desire to instance forms and modes of 

 application compared with which those we 

 have mentioned, splendid and impressive 

 as they are, are meager and mean. For 

 those we have mentioned are but the more 

 obvious applications — those, namely, that 

 continually announce themselves to our 

 senses everywhere in the affairs, both great 



and small, of the workaday world. But 

 the really great applications of mathemat- 

 ics — those which, rightly understood, best 

 of all demonstrate the human significance 

 of the science — are not thus obvious; they 

 do not, like the others, proclaim themselves 

 in the form of visible facilities and visible 

 expedients everywhere in the offices, the 

 shops, and the highways of commerce and 

 industry; they are, on the contrary, almost 

 as abstract and esoteric as mathematics 

 itself, for they are the uses and applica- 

 tions of this science in other sciences, es- 

 pecially in astronomy, in mechanics and in 

 physics, but also and increasingly in the 

 newer sciences of chemistry, geology, min- 

 eralogy, botany, zoology, economics, statis- 

 tics and even psychology, not to mention 

 the great science and art of architecture. 

 In the matter of exhibiting the endless and 

 intricate applications of mathematics to the 

 natural sciences, applications ranging from 

 the plainest facts of crystallography to the 

 faint bearings of the kinetic theory of 

 gases upon the constitution of the Milky 

 Way, our speaker's task is quite as hope- 

 less as we found the pure mathematician's 

 to be; and he, too, will have to compro- 

 mise; he will have to request his auditors 

 to acquaint themselves at their leisure with 

 the available literature of the subject and 

 especially to read attentively the great 

 work of John Theodore Merz dealing with 

 the "History of European Thought in the 

 Nineteenth Century," where they will find, 

 in a form fit for the general reader, how 

 central has been the role of mathematics 

 in all the principal attempts of natural 

 science to find a cosmos in the seeming 

 chaos of the natural world. Another many- 

 sided work that in this connection he may 

 wish to commend as being in large part in- 

 telligible to men and women of general edu- 

 cation and catholic mind is Bnriques's 

 "Problems of Science." 



