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maticians of our time have abandoned the former attempt, and therefore 
speak a language absolutely without meaning to the average man. Often 
the use of symbols and technical terms is not even a matter of choice. 
It is a necessity, for the ideas sought to be conveyed can be expressed in 
no other language. The mathematician, therefore, often labors on with 
no understanding or appreciation of his work or its results on the part of 
the general public. His subject is dumped into the same class with the 
dead languages. Latin, Greek and mathematics must form an unnatural 
alliance in a fight for recognition. Too frequently the mathematician is 
grudgingly given but a tithe of what he claims, and even then he is asked 
why he should cumber the ground and impede the way to higher and more 
useful pursuits. Before Latin had a literature, mathematics ius. _ Now, 
when the conviction is rapidly gaining ground and in all progressive in- 
stitutions being put into practice, that a smattering of Greek and Latin 
soon forgotten are not essentials in education, mathematics have entered 
new fields and conquered new territory. Their cultivation has gone for- 
ward in the last generation in leaps and bounds, their advance has kept 
pace with and in a large measure conditioned, both on the material and 
intellectual side, the tremendous and unexampled progress of civilization 
in that period. 
There are three general aspects in which mathematics can be viewed: 
First. As a disciplinary study. 
Second. As a cult. 
Third. As a tool. 
These three general grounds for consuming time and effort in culti- 
vating this science are not mutually exclusive. Their territory frequently 
overlaps and the determination of the stronger incentive often depends 
upon the point of view of the individual or his environment. 
As a disciplinary study, mathematics are present in some form in all 
the curricula of colleges, high schools and the grades. In the grades, 
however, we must recognize as the principal reason for time and effort, 
the thorough mastery of number and the development through drawing 
of the form perception for the practical every-day business of life’s activi- 
ties. At this point it has seemed to me that a serious error is quite com- 
monly committed, Too often instructors imbued with that philosophy of 
education which unduly idealizes every subject taught, make a premature 
attempt to develop logical processes at the expense of an intimate knowl- 
