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Page:Popular Science Monthly Volume 73.djvu/327

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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 developments. 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 l'Index du répertoire is much superior. In fact, the last number of the Revue semestrielle des publications mathématiques, which follows this index, classifies the publications under about seven hundred headings, and, as 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 literature 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 Müller's Mathematisches Vocabularium contains more than ten thousand technical terms used in pure and applied mathematics 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-