METHODS OF SCIENCE; NUMBERS 19 



elephant family, but to no existing species. He 

 sketches a hypothetical creature and calls it a 

 mammoth. Then, as more bones are found, not 

 only the complete skeleton is deduced, but also 

 much information regarding the position and 

 size of muscles. Thus the mammoth is recon- 

 structed, although there may be many disputes 

 as to detail. Later, caves of the old stone age 

 are found, with accurate drawings of the self- 

 same creature. Finally, in the northern sea an 

 iceberg is seen, enclosing the complete carcass 

 of a mammoth thus preserved for thousands of 

 years in cold storage for the confirmation of 

 the work of the palaeontologist and the archaeol- 

 ogist. Somewhere in the course of these several 

 discoveries the mammoth has changed from a 

 speculation to a reality, and we file it away 

 among our verities. 



In every new and growing science there are 

 many working hypotheses that never attain to 

 any sort of reality. On the other hand, in the 

 old and abstract sciences of mathematics, where 

 it is hard to tell how much is mere definition or 

 convention, the problem of reality is not so 

 much doubtful as it is meaningless. A branch 

 of mathematics may be interesting and satisfy- 

 ing to some of our aesthetic desires; it may be 



