60 



DISCUVIOHY 



gave new energy to Greek art ami tlioiiglit. .Eschylus 

 no less than Herodotus is moved by the new geography. 

 Travellers' tales from the ends of the world now took 

 the place of the early sailors' yarns. Sc3'lla was no 

 longer to be met with round the Mediterranean coasts 

 as in the Bronze Age or in the days of Homer..' But 

 though the boundaries of the world had been pushed 

 back, travellers had still tales to tell of their remoter 

 edges. Above the Issedonians, Herodotus tells us 

 simply, dwell the Arimaspians, who have only one eye, 

 and the gryphons who guard the gold. Or, as typical of 

 the new type of wonder-tale, take his account of cinna- 

 mon. " We Greeks," he says, " get our cinnamon from 

 the Phoenicians, but it is originally collected by the 

 Arabians. There is an enormous bird in Arabia, 

 which builds its nests of mud and cinnamon logs on 

 the tops of inaccessible precipices. The Arabians get 

 at them in this way. They put out whole carcases of 

 o.xen, which the bird carries off to the nest ; the added 

 weight is too much for the structure ; down falls the 

 nest, and the ingenious Arabians pick up the debris. 

 And that is how we get our cinnamon." 



Neglected Aspects of 

 Mathematics 



By C. A. Stewart, M.A. 



Lecturer in Malhemalics in the University o/ Slie/Jicld 



Of those who do not understand Pure Mathematics, 

 some are respectful as if entering a shrine ; but others, 

 of the baser sort, are contemptuous. These have found 

 the way of progress dark and difficult. Their guides, 

 perhaps, have not inspired them, and symbolism seems 

 far removed from the needs of ordinary human life. 

 They deny that it can have an ideal, that it can have 

 any claim to beauty. They admit that it has some 

 purpose in its application to the practical affairs of life, 



' Homer. Odyssey, ix -xii, with its cannibals, sirens, clashing 

 rocks, and the western end of the world where dwell the dead, 

 is a collection of sailors' yarns. In a narrow strait between two 

 cliffs on the one hand was a whirlpool, and on the other a sheer 

 precipice halfway up which was a hole so deep and high that 

 an arrow would not reach. Here lurked Scylla. " Her voice, 

 indeed, is no greater than the voice of a new-born puppy, but 

 a dreadful monster is she, nor would any look on her gladlv, 

 not if he were a god that met her. Verily she hath twelve feet 

 all dangling down, and six necks exceeding long, and on each a 

 hideous head, and therein three rows of teeth set thick and close 

 full of black death. Up to her middle is she sunk far down in 

 the hollow cave, but forth she holds her heads from the dreadful 

 gulf, and there she fishes, swooping down from the rock for dol- 

 phin or sea-dogs, or whatsogrcater beast she may anywhere take, ' ' 

 Sir Arthur Evans has pubhshed a clay scaling of the Bronze 

 Age which depicts a man in a boat being attacked by a dog- 

 headed sea-monster. Journal of Hellenic Studies, xxxii, p. 291. 



but tliat it can have an end in itself is incomprehensible. 

 It is associated in the minds of some with the removing 

 of interminable brackets, and with the chasing of 

 elusive unknowns. Since it deals usually with the 

 variable and not with the particular, and since it is 

 concerned more with deductions from data than with 

 the truth of these data, it has been described as the 

 subject " in which we never know what we are talking 

 about, nor whether what we are saying is true." ' It 

 is usually considered unwise to express lack of apprecia- 

 tion of the works of a great painter or sculptor or poet, 

 but there have been men of intellect who not only have 

 expressed ignorance of scientific method, but have also 

 been inclined to exaggerate that ignorance. The 

 questions that such a criticism of the subject naturally 

 raises are : Is this hostility justified ? Can it be wholly 

 attributed to feebleness of insight ? For it is possible 

 that although Mathematics need not fail to supply the 

 necessary stimulus to intellectual thoughts and aspira- 

 tions, yet its exponents maj? fail in the interpretation 

 and expression of its ideals ; and it must be admitted 

 that the way of mathematical learning can be, and 

 often is, a dull and cheerless one, especially for him 

 whose aptitude is weak. The inherent beaut\- of 

 mathematical reasoning may be marred by methods 

 that are brutal, and its outlook warped by unduly 

 insisting on the necessity of the moment. 



My object in this article is to consider the position 

 of the mathematician in two of his possible moods — 

 during his moments of leisure and during his moments- 

 of reflection. Are there pleasant bypaths of mathe- 

 matical thought and speculation for him to wander 

 in during his hour of freedom ? Are there fields of 

 activity within its sphere that can fitly be described 

 as inherently attractive ? And is there scope in 

 mathematical teaching for the occasional introduction 

 of what is distinctly recreative or amusing ? He has. 

 too, his moments of weakness, his hours of doubt, when 

 he is oppressed by the feebleness of his efforts, the 

 apparent uselcssness of all his endeavour and the 

 emptiness of his outlook. Is there sufficient purpose 

 in what mathematicians have achieved to provide him 

 solace at these times ? Has the use of Mathematics 

 been so beneficial in the interests of humanity as to 

 strengthen him in the continuation of his task ? It 

 is then that his mind becomes receptive of a higher 

 conception of his subject. In contemplating its 

 strength and greatness, its permanence and beauty, 

 he recognises that it has defined his attitude to the 

 world and has guided him in the art of living. 



This, then, is the first consideration : Is Mathematics 



interesting or not ? — one not unimportant in the view 



of the modern trend of education;il method. Can the 



subject be made attractive not merely to those who 



' Bertrand Russell, Mathematics and Metaphysics. 



