1869.] Mathematical and Phijsical Science. 587 



those of life transcend, as I have endeavoured to infer, those of 

 chemistry and molecular attractions, or as the laws of chemical 

 afl^ity in their turn transcend those of mere mechanics. Science 

 can be expected to do but Httle to aid us here, since the instrument 

 of research is itself the object of investigation. It can but enlighten 

 us as to the depth of our ignorance, and lead us to look to a higher 

 aid for that wluch most nearly concerns our well-being." 



Mathematical and Physical Science. (Section A.) 



The meetings of this Section were opened on August 19 th, by 

 the President, Professor Sylvester, who, in his addi'ess confined 

 himself mainly to combating the view advanced by Professor 

 Huxley, that " mathematical training is almost purely deductive. 

 The mathematician starts with a few simple propositions, the proof 

 of which is so obvious that they are caUed self-evident, and the rest 

 of his work consists of subtle deductions from them." And again 

 that " mathematics is that study which knows nothing of observa- 

 tion, nothing of experiment, nothing of induction, nothing of 

 causation." These statements were shown to be opposite to the 

 facts of the case, and many instances were adduced to show that 

 mathematical analysis is unceasingly caUing forth the faculties of 

 observation and comparison; that one of its leading featm-es is 

 induction ; that it has frequently recourse to experimental trial and 

 verification ; and that it affords a boundless scope for the exercise 

 of the highest efforts of imagination and invention. Kieman wrote 

 a thesis to show that the basis of our conception of space is purely 

 empirical, and our knowledge of its laws the result of observation ; 

 that other kinds of space might be conceived to exist, subject to 

 laws different from those which govern the actual space in which 

 we are immersed. Gauss called mathematics a science of the eye ; 

 and this great man was used to say that he had laid aside several 

 questions which he had treated analytically, and hopal to apply 

 to them geometrical methods in a future state of existence, when 

 his conceptions of space should have become amphfied and extended ; 

 for as we can conceive beings (like infinitely attenuated book- worms 

 in an infinitely thin sheet of j^aper) which have only the notion 

 of space of two dimensions, so we may imagine beings caj^able of 

 reahzing space of four or a greater number of dimensions. 



Most, if not aU, of the great ideas of modern mathematics have 

 had their origin in observation. For instance, one gigantic out- 

 come of modern analytical thought, itself, too, only the precursor 

 and progenitor of a future still more heaven-reaching theory, which 

 will comprise a complete study of the interoperation of algebraic 



