THE CLASSIFICATION OF MATHEMATICS 323 



mathematics into exactly four grand divisions, yet a small number of 

 divisions offers advantages by furnishing names which will generally be 

 remembered and by emphasizing the connection between extensive de- 

 velopments. It is true that the names of these grand divisions do not 

 have a very definite meaning, but they have some meaning, and they 

 exhibit something of the tenor of the various branches whose names 

 are too numerous and appear too erudite to the average educated man. 

 Instead of simply saying that one is working on Ausdehnungslehre it 

 may be some satisfaction to add for the benefit of the uninitiated that 

 this is a kind of algebra, and thus established language contact even if 

 thought contact is out of question. 



A question of more general interest is the number of parts into 

 which mathematics is divided in the final classifications. The answer 

 to this question gives some idea of the fractional part of the entire 

 literature which must be examined by one who is seeking all that is 

 known along a particular line. The last issue of the International 

 Catalogue contains only about two hundred headings, so that one 

 would have to look over one two-hundredth of the total publications 

 of the year in order to find all that had been written during the year 

 on a subject comprised under a single heading. In this respect Vlndex 

 du repertoire is much superior. In fact, the last number of the Revue 

 semestrielle des publications matliematiques, which follows this index,. 

 classifies the publications under about seven hundred headings, and, a& 

 a large number of headings have no entries during one of the periods 

 of six months, it would frequently be possible to get at all the literature 

 which appeared on a particular subject during a period of years by 

 examining less than a thousandth part of the total mathematical litera- 

 ture of the period. 



The preceding paragraph relates to the classification of current 

 literature. The classification of the total literature is in a much less 

 satisfactory condition. The magnitude of this work may be inferred 

 from the facts that Muller's Mathematisches Vocabularium contains 

 more than ten thousand technical terms used in pure and applied mathe- 

 matics and that it is not exhaustive. As most of these terms relate to 

 concepts which either are or may become the centers of a series of 

 closely related developments, we can predict no limit to the number of 

 headings under which the mathematics of the future will be treated. 

 In fact, if we adopt the view that mathematics consists of creations as : 

 well as of discoveries, considerations as to limits become very vague 

 even if they do not lack interest. 



Professor Sylvester once called himself the mathematical Adam in 

 the proud consciousness of having named a large number of algebraic 

 concepts and that these names had become more or less current among 

 his colleagues. While technical terms are useful for the sake of classi- 



