MATHEMATICS AND PRACTICAL LIFE 79 



importance in many directions, as various sciences 

 reach those more advanced stages in which they 

 present more opportunities than formerly for exact 

 methods of treatment. The consideration of these 

 matters will naturally lead up to some discussion 

 of the educational problems connected with the 

 provision of the necessary outfit of Mathematical 

 knowledge and skill required by those who are to 

 carry out various parts of the mental and practical 

 work of the nation. 



Mathematical thought, in a more or less explicit 

 form, pervades every department of human activity. 

 Certain fundamental parts of Mathematics, em- 

 bodied in the processes and notation of Arithmetic, 

 have become part of the ordinary mental outfit of 

 civilized man. There is perhaps no other branch 

 of science of which this can be asserted with such 

 definiteness. The grocer, when he weighs out his 

 sugar, makes use of Mathematical conceptions 

 which were developed only by a long process of 

 evolution. When he enters his receipts in his 

 books, the notation he employs embodies an 

 invention which, as a mode of economizing labour, 

 must be regarded as one of the triumphs of our 

 race. So simple does our system of numeration 

 seem to us that it requires an effort to realize the 

 fact that the Greeks, with their unsurpassed 

 capacity for abstract thinking, failed to discover 

 it. The navigator, when he uses his logarithmic 

 tables, is utilizing the great invention of John 



