PROBLEMS OF MODERN SCIENCE 



have a beauty of their own. But I offer them as 

 a justification for my own action in including 

 some of the outstanding problems of the * purest ' 

 Mathematics in my lecture, even when I can 

 give no evidence directly that they will ever 

 come strictly into the purview of Pure or 

 Applied Science. In fact, I should like to define 

 Mathematics as Quantitative Science, either of 

 the present or perhaps of the future excluding 

 the actual registering of a formula which describes 

 a phenomenon, but including any logical deduc- 

 tion of that formula from a general principle. 

 In this way it plays a part in unexpected sciences. 

 It has, for instance, succeeded in giving an account 

 of the development of deposits of silica on sponge- 

 spicules, following a suggestion of Professor Dendy, 

 and it has made its way strongly into Physiology 

 in regard to the various actions associated with 

 muscles in the body. These instances could be 

 multiplied, though I propose to say no more 

 regarding its applications to sciences other than 

 Physics or Chemistry, beyond giving this mere 

 indication that such applications exist. If the 

 special branch of Mathematics which deals with 

 statistical questions is considered even casually, a 

 host of problems from every branch of Science 

 come into its scope in fact, all problems regarding 

 which information may be obtained from a con- 

 sideration of the probabilities of occurrence of the 

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