MATHEMATICS 



haps fifty or more years later, turned out to be 

 just the material necessary for clarifying some 

 group of natural phenomena and welding them 

 into a compact whole. We have a striking instance 

 at the present day in regard to Einstein's Theory, 

 which I select as an illustration, not because many 

 more equally striking, or even more so, could not 

 readily be given, but only because Einstein's 

 Theory is so prominent everywhere that I do not 

 think a single one of my readers can have failed to 

 pick up some information about it. Many years 

 ago Riemann and Christoffel worked out what, 

 until only just before the War, seemed to be per- 

 haps one of the most * useless ' developments of 

 Mathematics which the mind could conceive, from 

 the point of view of ultimate application to anything 

 in Nature I mean the Theory of Tensors, whose 

 only recommendation was then that it was very 

 general and involved some interesting analysis of 

 a new type, fundamental only as a contribu- 

 tion to mathematical logic. But this analysis 

 has nevertheless turned out to be just what Ein- 

 stein wanted for the development of his theory, 

 and may well be described as its backbone. I 

 shall quote at least one other similar instance 

 later. 



Such considerations are in no sense a 'justifica- 

 tion ' of Pure Mathematics it does not need any, 

 like all other logical creations of the mind, which 



