TEE CLASSIFICATION OF MATHEMATICS 3*5 



mathematics does not generally involve the concept of derivative, which 

 was introduced into French secondary instruction in 1902, and has 

 proved successful in that country as well as in some others where it 

 has been tried. From a historical point of view analysis is merely an 

 extension of algebra. It has already been observed that for Newton, 

 Euler and Lagrange analysis and algebra were synonyms, and the 

 present significance of the term analysis may be inferred from the 

 fact that the most familiar subjects that are now generally comprised 

 under it are differential and integral calculus and the theory of func- 

 tions. „ 



It may be desirable to add that the aim of the present article was to 

 convey some idea of the extent and nature of the modern mathe- 

 matical developments, from the standpoint of classification. While 

 this standpoint reveals only the outside yet this side is worth knowing 

 and is apt to awaken some thoughts in regard to what may be within. 

 As the use of machines has revolutionized the material world, so the 

 use of mathematics has revolutionized the efficiency of thought in re- 

 gard to problems whose solution is sufficiently elementary to come 

 under known developments. As these developments proceed they pro- 

 vide for greater efficiency and wider applications. The analogy between 

 mathematics as a machine of thought and an ordinary labor saving 

 device known as a machine can be traced through many points of 

 interest. It should, however, be emphasized that the real mathe- 

 matician is the inventor of such machines, but not the machine itself. 



