PROBLEMS OF MODERN SCIENCE 



imaginable branch of Pure Mathematics, however 

 pure, will not at some time become the foundation 

 of much that can only be classed, without any 

 reservation, as Science. And this is true even of 

 geometry. The geometry of four dimensions, 

 worked out very completely, at least on its analytical 

 side, very much in the spirit of a mathematical 

 curiosity, came into its own in Science, in the hands 

 of Minkowski, as a fine framework for the restricted 

 Principle of Relativity. Elliptic and hyperbolic 

 geometries, associated with the names of Lobat- 

 chewsky and Bolyai and others, were mathematical 

 curiosities until one of them was found almost 

 infinitely simpler than Euclidean geometry in 

 giving an account of the ultimate laws of Physics in 

 space. But geometry at present is not a subject 

 which may be said to be expanding rapidly, or to 

 contain serious fundamental problems which many 

 mathematicians are trying to solve attention, as 

 for instance in the notable work of Dr Robb, 

 being mainly confined to its ultimate postulates 

 and foundations generally so that I propose to 

 leave it at this point. 



Let us turn our attention to some of the matters 

 on which our own leading school of Pure Mathe- 

 maticians is at present mainly engaged. These 

 matters lie in a region in which progress is very 

 difficult, which bristles with fundamental problems 

 of types which can be stated quite simply some 

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