MATHEMATICS 

 Earle Raymond Hedrick 

 Professor of Mathematics 



INTRODUCTION 



The difficulties of such a lecture as this are many. Par- 

 ticularly in the treatment of mathematics, the immensity of 

 the subject-matter makes it quite impossible to do justice to 

 the topic, though the same may perhaps be said of many other 

 general subjects in this University. Mathematics, however, 

 as I shall point out, consists of a great variety of somewhat 

 isolated fields joined together by one broad principle of which 

 I shall speak. The diversity of its subject-matter and the 

 great length of its history make for such a voluminous litera- 

 ture as scarcely exists in any other science. 



Moreover, there are in this audience several classes of 

 listeners. To some of you my remarks will seem trite, while 

 to others the same remarks may seem abstruse. I shall at- 

 tempt to say something to each class of listeners, and I shall 

 trust that one class will not grow impatient as I turn my atten- 

 tion temporarily to the other. 



Again, a lecture by Professor Keyser of Columbia Uni- 

 versity, a former student and teacher in this University, was 

 heard here last year in this same room. His lecture — of great 

 length and extensive forethought — was heard by many of you. 

 To those who heard it I can add little. To those who did 

 not hear it what I say may carry something of the inspira- 

 tion which many of us received from him. 



I am about to attempt what the committee has justly said 

 might be impossible, or at least exceedingly difficult: namely, 



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