1 68 SCIENCE PROGRESS 



the development has been on lines divergent from the lines 

 of schoolwork. The form of mathematics that is being intro- 

 duced nowadays into so many departments of thought is the 

 infinitesimal calculus. For general purposes, though the techni- 

 calities and machinery of the calculus are not needed, the language, 

 notation and ideas of the calculus are of all-pervading utility. 

 Leaving aside the definitely mathematical sciences of physics 

 and engineering, we find the calculus entering into studies such 

 as chemistry, biology, economics and statistics. Lectures on 

 these subjects are apt to be unintelligible to an audience 

 brought up on school mathematics, for want of a nodding 

 acquaintance with the calculus ; at some universities it is 

 found desirable to arrange special mathematical lectures in 

 order that students may be able to follow the instruction 

 in other subjects, a kind of deathbed repentance for those who 

 have wasted their mathematical time at school through no 

 fault of their own. And let it be noted that this simple form 

 of calculus does not grow out of the summit of school mathe- 

 matics but branches off low down the stem and it is independent 

 of formal geometry ; a vigorous pruning of school algebra 

 and arithmetic would in no wise prejudice the growth we 

 want to encourage. 



The infinitesimal calculus has now been before the world 

 during two and a half centuries. It is the fundamental form 

 in which mathematics are applied to the affairs of modern 

 life. We must recognise as a law of development in educational 

 affairs that matter which in one century occupies the attention 

 of the foremost philosophers finds its way in a subsequent 

 century into the elementary curriculum. If the infinitesimal 

 calculus was the high-water mark for the seventeenth century, 

 so was ^the geometry of Euclid to the third century b.c, the 

 Arabic notation (in Europe) for the twelfth century a.d., the 

 method of long division for the fifteenth and so forth. The 

 quality of the human brain does not alter, presumably, from 

 one century to another; how then has it been possible to make 

 the schoolboy of one generation assimilate matter that has 

 puzzled the best brains of earlier times? 1 The answer is 

 simply this : Teachers come to know more, simpler methods 

 of presentation are discovered and it is seen more clearly how 



1 Wallis, Newton's forerunner, was very doubtful whether he might write 

 V8 as 2 sj2. 



