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Page:Popular Science Monthly Volume 73.djvu/323

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THE CLASSIFICATION OF MATHEMATICS

THE CLASSIFICATION OF MATHEMATICS
By Professor G. A. MILLER

UNIVERSITY OP ILLINOIS

HERR VALENTIN, of Berlin, who has been working on a general mathematical bibliography for more than twenty years, estimates 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 classification this vast store of knowledge would have little value from the difficulty of finding what is wanted. Before entering upon a description 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 published almost simultaneously in German and French includes determinants under arithmetic, while the International catalogue of scientific

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