MATHEMATICS 



occurs in the problem. It is often very difficult to 

 find, though many valuable ones have been found 

 recently, and are still being found, by quite new 

 methods of considerable generality. A period 

 of rapid development in mathematical physics will 

 necessarily follow. 



I must perforce, from the mere limitation of 

 space, disregard several lines of present-day progress 

 in Mathematics, and many interesting problems 

 awaiting solution. A majority of these are naturally, 

 in their present form, not very capable of anything 

 like a popular exposition, and I do not pretend to 

 give any general review of the subject as a whole, 

 for its ramifications are very vast, and involve 

 many totally different types of thought as dif- 

 ferent in kind at least as, for instance, pure geometry 

 and the analysis of the properties of whole numbers 

 connected only by the special form of logic, 

 whose nature has been so much discussed, which 

 runs through the whole. Otherwise I should have 

 wished for space to mention, with a certain amount 

 of detail, such matters as the Theory of Transfinite 

 Numbers, with which the names of Whitehead 

 and Russell, after Cantor, are mainly associated- 

 capable of loose description as the Theory of the 

 Infinite the general advance in decisiveness of 

 our conceptions of such fairly simple processes as 

 integration, due to Lebesgue, and recent rapid 

 progress in such matters as the theory of the tides, 



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