SIR JAMES JEANS 243 



with which the pure mathematician works are taken 

 directly from his experience of nature. An obvious 

 instance is the concept of quantity; but this is so fun- 

 damental that it is hard to imagine any scheme of 

 nature from which it was entirely excluded. Other 

 concepts borrow at least something from experience; 

 for instance multi-dimensional geometry, which clearly 

 originated out of experience of the three dimensions 

 of space. If, however, the more intricate concepts 

 of pure mathematics have been transplanted from the 

 workings of nature, they must have been buried very 

 deep indeed in our sub-conscious minds. 



This very controversial possibility is one which 

 cannot be entirely dismissed, but in any event it can 

 hardly be disputed that nature and our conscious 

 mathematical minds work according to the same laws. 

 She does not model her behaviour, so to speak, on 

 that forced on us by our whims and passions, or on 

 that of our muscles and joints, but on that of our 

 thinking minds. This remains true whether our 

 minds impress their laws on nature, or she impresses 

 her laws on us, and provides a sufficient justification 

 for thinking of the designer of the universe as a 

 mathematician. 



Personally I feel that this train of thought may, very 

 tentatively, be carried a stage further, although it is 

 difficult to express it in exact words, again because 

 our mundane vocabulary is circumscribed by our mun- 

 dane experience. The terrestrial pure mathematician 

 does not concern himself with material substance, 

 but with pure thought. His creations are not only 

 created by thought but consist of thought, just as the 



