586 GEOMETRY 



out in the near future: what is the most general mode of setting up 

 a correspondence which associates with every Jordan curve another 

 Jordan curve? Such discussions are aspects of geometry with an 

 infinite number of dimensions. 



After a review of the kind given in this paper, one is tempted to 

 ask: What is it which influences the mathematician in selecting 

 certain (out of an infinite number of equally conceivable) problems 

 for investigations? It is true, of course, that his subject is ideal, 

 self-created, and that " Das Wesen der Mathematik liegt in. ihrer 

 Freiheit." Georg Cantor would indeed replace the term pure mathe- 

 matics by free mathematics. This freedom, however, is not entirely 

 caprice. The investigators of each age have always felt it their 

 duty to deal with the unsolved questions and to generalize the re- 

 sults and conceptions inherited from the past, to correlate with 

 other fields of contemporaneous thought, to keep in contact, as far 

 as possible, with the whole body of truth. This is not all, however. 

 The influence of aesthetic considerations, though less subject to 

 analysis, has been, and still is, of at least equal importance in guiding 

 the course of mathematical development. 



