MATHEMATICS IN ENGLISH SCHOOLS 165 



geometrician be expert in putting his finger on the fallacies 

 in a mathematical argument, is not this mainly because he 

 knows the kind of thing he has to look out for? The fallacy 

 may arise from a bad figure, from the neglect of an alternative 

 root to an equation, from assuming" that an infinite series must 

 diverge and so forth ; all these are old friends. I do not know 

 that a mathematician would be quicker than another man to 

 unveil the fallacies of a free trade or protectionist argument, 

 unless the argument were of a mathematical nature ; the weak- 

 nesses of political arguments usually arise from erroneous 

 historical premises. If a training in geometry were of palpable 

 value in fortifying the logical faculty (assuming that such a 

 thing exists), it ought to be easy to find definite instances in 

 which it might be said, " So-and-so would not have made this 

 mistake if he had learnt Euclid." But is it easy ? 



We are very much in the dark-, about these questions. 

 I should be unwilling to go to the stake in defence of the state- 

 ment that Euclid has made me logical. Even if mathematicians 

 do exhibit certain well-marked characteristics in their habits 

 of thought and behaviour, we have at least two hypotheses 

 before us : the characteristics may be due to their course of 

 study ; or on the other hand these may be innate characteristics 

 which led their possessors to choose the study of mathematics. 

 Even if we adopt the former hypothesis, we have to remember 

 that the fully fledged mathematician has made a very intense 

 and concentrated study of his subject. He has probably studied 

 nothing else during at least three years at the university and 

 very likely during two years before ; and he may have been 

 engaged in mathematical work and teaching an indefinite 

 number of years before he comes under our observation. An 

 ordeal of this duration does undoubtedly tend to colour the 

 whole mental and moral character. But what we are concerned 

 to ask is rather this, Does a comparatively superficial study 

 of mathematics (or any other subject), such as may be made 

 by a schoolboy not specially gifted in this direction — does such 

 a study as this affect seriously his general mental qualities ? 

 Such a study may do much for a boy. It may give him definite 

 knowledge, it may give him interests, it may give him ideas 

 and modes of thought about form and quantity that will shape 

 his way of looking at all sorts of subjects ; it may give him 

 outlook and intelligent appreciation of things going on round 



