82 MATHEMATICS 



has given great prominence to the formal aspect of 

 the subject and to a technique requiring effort 

 and aptitude for its acquirement to any considerable 

 degree of success. In other branches of Science 

 the disentanglement of the relevant aspects of the 

 phenomena concerned is a process of greater com- 

 plexity than in the case of Mathematics, and con- 

 sequently the process of reduction to a schematic 

 form is in every case in a much less advanced stage. 

 Some branches have as yet advanced but little 

 beyond the purely classificatory stage. It is a 

 matter for speculation how far the various branches 

 of Science may be expected to proceed along the 

 same path as in the case of Mathematics, the end 

 of which is a purely rationalized representation 

 of the phenomena concerned in a schematic form. 

 One of our most prominent Biologists has been 

 heard to assert, at a scientific gathering, that the 

 ultimate goal of Biological Science consists in its 

 reduction to Pure Mathematics. The case of 

 Geometry affords the most striking example of a 

 science reduced to the purely deductive stage ; 

 originally developed by induction from spatial 

 observations it has no longer need to have recourse 

 to observation for its further development. It 

 may be regarded as the type towards which each 

 department of science tends to conform as it becomes 

 more rationalized, that is as it becomes less depen- 

 dent at every point on purely empirical elements. 

 Completely rationalized Physics and Chemistry 



