MATHEMATICS IN ENGLISH SCHOOLS 163 



they are mastering the elements. They should be brought 

 to the stage from which a broad undetailed view may be 

 obtained over the country of applied mathematics : and they 

 may be shown the beginnings of a few of the roads that lead 

 through this country. A public must be created able to realise 

 what science and mathematics are doing for the world and 

 to form some general conception of the means used. 



In England we have a ruling class whose interests are 

 sporting, athletic and literary. We might easily have a worse 

 set of masters : but they do not know or if they know do not 

 realise that the Western civilisation on which they are parasitic 

 is based on applied mathematics. This defect will lead to 

 difficulties ; it is curable and the place for curing it is school. 

 The study of science in public schools will do much to put 

 this right ; but science has not the privileged position that 

 mathematics enjoys : it has not the same opportunities. Mathe- 

 matics was a well-established subject of instruction in public 

 schools before science was heard of. During many generations 

 English boys have learnt mathematics but the subject has not 

 been taught in such a way as to cultivate a mathematical 

 outlook on the world. It has not justified its privileged 

 position. Partly this is due to the aristocratic theory of 

 education. We have to break this down and think of the 

 average boy ; the clever boy will take care of himself and 

 there is no fear of his interests being forgotten so long as 

 scholarships are so powerful a lever in education. The aristo- 

 cratic theory has been the bane of education in all subjects; 

 the specialist teacher wants to make a man in his own image : 

 the non-specialist, who might be expected to sympathise with 

 average wits, lacks either the courage or the originality to 

 strike out a line of his own. It is to the specialists that we 

 must look for improvement. They must be persuaded that 

 it is not necessarily deplorable for their pupils to remain 

 ignorant of dodges and bits of knowledge that they themselves 

 cherish from long familiarity. 



But apart from the aristocratic theory the main reason why 

 the average boy leaves school with no mathematical outlook 

 is that the cultivation of such an outlook has not been accepted 

 as a main object of mathematical instruction. Why not ? There 

 is no glory to be won from slaying the slain and I am tempted 

 to remain silent on the subject of examinations. Examination 



