THE CLASSIFICATION OF MATHEMATICS 3*9 



THE CLASSIFICATION OF MATHEMATICS 



By Professor G. A. MILLER 



UNIVERSITY OP ILLINOIS 



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HERR VALENTIN", of Berlin, who has been working on a general 

 mathematical bibliography for more than twenty years, esti- 

 mates that the total number of different mathematical works is about 

 35,000 and that about 95,000 mathematical articles have appeared in 

 the various periodicals. 1 The present rate of growth of this literature 

 is so rapid that, without increasing the amount per year, the next 

 fifty years would produce more than the total produced from the 

 earliest records to the present time. Without some means of classifica- 

 tion this vast store of knowledge would have little value from the 

 difficulty of finding what is wanted. Before entering upon a de- 

 scription of any details of classification I shall make a few remarks 

 on some of the terms of classification which are familiar to all; viz., 

 arithmetic, algebra and geometry. 



About three years ago Sir Oliver Lodge published an unusual work 

 under the unusual title " Easy mathematics, chiefly arithmetic, being 

 a collection of hints to teachers, parents, self-taught students, and 

 adults; and containing a summary or indication of most things in 

 elementary mathematics useful to be known." This title is followed 

 by a no less unusual preface, whose tenor may be inferred from the 

 following quotation : " The mathematical ignorance of the average 

 educated person has always been complete and shameless, and recently 

 I have become so impressed with the unedifying character of much of 

 the arithmetical teaching to which ordinary children are liable to be 

 exposed that I have ceased to wonder at the widespread ignorance, and 

 have felt impelled to try and take some step towards supplying a 

 remedy." The main reason for referring to this work in this connection 

 is to call attention to what appears to be a very common use of the 

 word arithmetic, as including most but not all of the mathematics 

 which the average educated man should know. 



Efforts to arrive at a much more accurate definition of the term 

 arithmetic are apt to meet with disappointment. On the one hand, we 

 meet with contradictory classifications among works of the highest 

 authority. The great mathematical encyclopedia which is being pub- 

 lished almost simultaneously in German and French includes determi- 

 nants under arithmetic, while the International catalogue of scientific 



1 Felix Mueller, Bibliotheca Mathematica, Vol. 7 (1907), p. 416. 



