540 



SCIENCE 



[N. S. Vol. XLVII. No. 1222 



is not only no end but no very evident diminu- 

 tion. The phenomenon is interesting, espe- 

 cially in view of the gravity of the times so 

 Tinfavora'ble to the customary pursuits of schol- 

 ars. No doubt the explanation involves a wide 

 variety of considerations. One of these is the 

 purely commercial competition among pub- 

 lishers who invite cooperation of teachers in 

 the making of books. Another is the fact of a 

 certain inertia acquired before the war : for 

 example, no less than four of the above-listed 

 volumes belong to series of publications initi- 

 ated in times of peace or at all events prior to 

 the entry of the United States into the world 

 conflict. A third consideration relates to num- 

 bers: the number of persons in the country 

 who are devoted to the teaching of mathematics 

 or to mathematical research or to both is large ; 

 it is absolutely large and it is large relatively 

 to the number of those similarly engaged a 

 generation or two ago; the membership of the 

 American Mathematical Society includes more 

 than seven hundred; that of the recently or- 

 ganized Mathematical Association of America, 

 more than a thousand; and there are in various 

 sections of the country other flourishing asso- 

 ciations of teachers of mathematics: it goes 

 without saying that where there are many per- 

 sons competent to write books many books will 

 be written. 



ISTo doubt the more intimate personal mo- 

 tives to the writing of mathematical text-books 

 are various. The hope of pecuniary reward is 

 probably not very effective, at least not effec- 

 tive with many, if by hope we are to under- 

 stand desire plus expectation. What may be 

 called the reputational motive is doubtless 

 more powerful: there is a general expectation 

 that college and university instructors will be 

 productive scholars; owing to a variety of cir- 

 cumstances the production of text-books is 

 apt to seem an easier, albeit a less effective, 

 way to meet such expectation than is the way 

 of research. Then there is the altruistic mo- 

 tive — the impulse to serve; it is certain that 

 this motive is frequently present and some- 

 times dominant : mathematical text-books are 

 sometimes vsritten to advance the cause 

 of mathematical education. It is probable 



that the principal motive to the kind of 

 activity in question is really hedonic, con- 

 sisting in the peculiar pleasure that is felt 

 in trying to perform an approved task of great 

 difficulty or — to view the matter in another 

 aspect — in trying to win, in competition, an 

 exceedingly difficult game. Surely there is 

 here ample room for the play of that motive, 

 for it is not easy to imagine an undertaking 

 more beset with difficulties than is the writing 

 of a mathematical text-book that is to be at 

 once excellent in quality and successful in its 

 appeal for public approval. The suffrages of 

 teachers must be won. But teachers vary 

 enormously in respect of scientific competence. 

 The extremes are widely sundered. One of 

 them is represented by the reactionaries, by 

 those whose knowledge is less a knowledge of 

 subject-matter than of traditional ways of pre- 

 senting it and who are naturally opposed to 

 every innovation of theme or of method. The 

 other extreme is represented by the fadist, the 

 ultra modern, the clamorous reformer whose 

 creed is that whatever is is bad, who confuses 

 the novel with the good, and pursues the new, 

 because it is new, with irrational zeal. 

 Another difficulty is the question of size: how 

 big ought the book to be? The question is 

 puzzling because in our schools there is no 

 uniformity of standard or of practise regard- 

 ing the amount of time devoted to a given 

 subject. A yet 'more perplexing question is 

 that of presuppositions: what degree of intel- 

 lectual maturity and what degree of scientific 

 preparation ought to be presupposed in the 

 pupils for whom the book is designed? Such 

 is our lack of uniformity of standards that an 

 answer that is right for one institution or one 

 locality will be wrong for another, and so the 

 author is obliged to guess and to compromise. 

 Not the least interesting part of the game, and 

 a part that is especially fascinating, because it 

 can never be managed quite successfully, is the 

 part requiring the author to minister at once 

 to the culture interests and the efficiency in- 

 terests of his readers; for the two interests 

 can not be harmonized nor made identical by 

 the easy device of stoutly denying their dif- 

 ference. Again, the necessity of adjusting the 



