THE STUDY OF MATHEMATICS 59 



key to open the doors of the temple ; though they spend 

 their lives on the steps leading up to those sacred doors, 

 they turn their backs upon the temple so resolutely that 

 its very existence is forgotten, and the eager youth, who 

 would press forward to be initiated to its domes and 

 arches, is bidden to turn back and count the steps. 



Mathematics, perhaps more even than the study of 

 Greece and Rome, has suffered from this oblivion of its 

 due place in civilisation. Although tradition has decreed 

 that the great bulk of educated men shall know at least 

 the elements of the subject, the reasons for which the 

 tradition arose are forgotten, buried beneath a great 

 rubbish-heap of pedantries and trivialities. To those 

 who inquire as to the purpose of mathematics, the usual 

 answer will be that it facilitates the making of machines, 

 the travelling from place to place, and the victory over 

 foreign nations, whether in war or commerce. If it be 

 objected that these ends all of which are of doubtful 

 value are not furthered by the merely elementary 

 study imposed upon those who do not become expert 

 mathematicians, the reply, it is true, will probably be 

 that mathematics trains the reasoning faculties. Yet 

 the very men who make this reply are, for the most part, 

 unwilling to abandon the teaching of definite fallacies, 

 known to be such, and instinctively rejected by the un- 

 sophisticated mind of every intelligent learner. And the 

 reasoning faculty itself is generally conceived, by those 

 who urge its cultivation, as merely a means for the avoid- 

 ance of pitfalls and a help in the discovery of rules for 

 the guidance of practical life. All these are undeniably 

 important achievements to the credit of mathematics ; 

 yet it is none of these that entitles mathematics to a place 

 in every liberal education. Plato, we know, regarded the 

 contemplation of mathematical truths as worthy of the 



