Section A.— ASTRONOMY, MATHEMATICS, PHYSICS, 

 METEOROLOGY, GEODESY, SURVEYING, ENGIN- 

 EERING, ARCHITECTURE, AND GEOGRAPHY. 



President of the Section — Prof. W. N. Roseveare, M.A. 



MONDAY, JULY 2. 



The President delivered the following address : — 



Mathematical Analysis and Science. 



We need not enter on a discussion of the meaning of 

 '■ Science " generally — ^I will ask you to think rather in our 

 every-day terms of " the Sciences." By a Science of any specified 

 kind— Astronomy, Chemistry, Botany — we mean, I suppose, the 

 systematic study of a group of facts and phenomena connected 

 by some link of similarity. The aim of the system of study 

 must be, as Mach says, " the completest possible presentment 

 of facts ivlth the least possible expenditure of thought." The 

 various Sciences, as we know them, seem to have a regular law 

 of development : first, the bare collection of facts which present 

 some likeness or common tendency ; then, after the sifting out 

 of extraneous matter, the cumulative evidence of this body of 

 facts to some laws, some links of cause and effect, which distin- 

 guish one body of facts from others; next, the discovery and 

 clear logical statement of the laws ; and finallx-, the creation of 

 a symbolic language b}- which these laws are expressed with the 

 utmost brevity and economy of thought. By means of this 

 specialized shorthand, efifects can be prophesied from a given set 

 of causes; the continued collection of facts {i.e., making of ex- 

 periments ) serves to check the results, to suggest new ideas 

 (needing new symbols), and to confirm or reject ideas arising, 

 n(^t from experience, but from suggestive grouping or develop- 

 ment of the accepted symbols. To my mind, this Science lan- 

 guage, in all its various forms, is mathematics ; or, at least, it is 

 the form into which mathematics has developed, and in which it 

 will continue to develo]). From this point of view mathematics is 

 not a Science in itself, in so far as it does not originate in phy- 

 sical facts. All its attributes are those of language — the lan- 

 guage in which the only verb form is " is equal to." Like other 

 languages, it lends itself to literary development — to the use 

 of words as words, of forms as forms : this may be regarded as 

 its artistic side — Pure Mathematics. This development is often 

 regarded by the eager Scientist as futile, as waste of ingenuity, 

 yet. historically and logically, this artistic work is of the greatest 

 service to the scientific branch ; ingenious a priori combinations 

 of symbols, worked out without any aim at ulterior representa- 

 tion of facts, have repeatedly been found useful and suggestive 

 in scientific applications. Gill's tale of the voluminous pure 

 mathematical author, Sylvester, who " thanked God he had 



