56 



nothing which, was not latent in the original statement. 

 Mathematics cannot tell us whether there be or be 

 not limits to time or space ; but to her they are both 

 of indefinite extent, and this in a sense which neither 

 affirms nor denies that they are either infinite or finite. 

 Mathematics cannot tell us Avhether matter be con- 

 tinuous or discrete in its structure; but to her it is 

 indifierent whether it be one or the other, and her 

 conclusions are independent of either particular hypo- 

 thesis. Mathematics can tell us nothing of the origin of 

 matter, of its creation or its annihilation ; she deals 

 only with it in a state of existence ; but within that 

 state its modes of existence may vary from our most 

 elementary conception to our most complex experience. 

 Mathematics can tell us nothing beyond the problems 

 which she specifically undertakes ; she will carry them 

 to their limit, but there she stops, and upon the great 

 region beyond she is imperturbably silent. 



Conterminous with space and coeval with time is the 

 kingdom of Mathematics ; within this range her dominion 

 is supreme ; otherwise than according to her order 

 nothing can exist ; in contradiction to her laws nothing 

 takes place. On her mysterious scroll is to be found 

 written for those who can read it that which has been, 

 that which is, and that which is to come. Everything 

 material which is the subject of knowledge has number, 

 order, or position ; and these are her first outlines for a 

 sketch of the universe. If our more feeble hands cannot 

 follow out the details, still her part has been drawn with 

 an unerring pen, and her work cannot be gainsaid. Bo 

 wide is the range of mathematical science, so indefi.^ 

 nitely may it extend beyond our actual powers of 

 manipulation, that at some moments we are inclined to 

 fall down with even more than revereiice before her 



