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SCIENCE 



[N. S. Vol. XXXII. No. 821 



in the names of himself and Lady Hug- 

 gins, remains as a monumental record of 

 their joint labors. 



The names of the great departments of 

 science, mathematics, physics, astronomy, 

 meteorology, which are associated with Sec- 

 tion A, are a sufficient indication of the vast 

 range of investigation which comes under 

 the purview of our section. An opinion 

 has been strongly expressed in some quar- 

 ters that the time has come for the erection 

 of a separate section for astronomy and 

 meteorology, in order that fuller oppor- 

 tunities may be afforded than hitherto for 

 the discussion of matters of special inter- 

 est to those devoted to these departments 

 of science. I do not share this view. I be- 

 lieve that, whilst the customary division 

 into sub-sections gives reasonable facilities 

 for the treatment of questions interesting 

 solely to specialists in the various branches 

 with which our section is concerned, a 

 policy of disruption would be injurious 

 to the wider interests of science. The close 

 association of the older astronomy with 

 mathematics, and of the newer astronomy 

 with physics, forms strong presumptions 

 against the change that has been sug- 

 gested. Meteorology, so far as it goes be- 

 yond the purely empirical region, is, and 

 must always remain, a branch of physics. 

 No doubt, the more technical problems 

 which arise in connection with these sub- 

 jects, though of great importance to 

 specialists, are often of little or no interest 

 to workers in cognate departments. It ap- 

 pears to me, however, that it is unwise, in 

 view of the general objects of the British 

 Association, to give too much prominence 

 in the meetings to the more technical as- 

 pects of the various departments of sci- 

 ence. Ample opportunities for the full 

 discussion of aU the detailed problems, the 

 solution of which forms a great and neces- 

 sary part of the work of those who are ad- 



vancing science in its various branches, are 

 afforded by the special societies which 

 make those branches their exclusive con- 

 cern. The British Association will, in my 

 view, be performing its functions most 

 efficiently if it gives much prominence to 

 those aspects of each branch of science 

 which are of interest to a public at least in 

 some degree larger than the circle of spe- 

 cialists concerned with the particular 

 branch. To afford an opportunity to work- 

 ers in any one department of obtaining 

 some knowledge of what is going on in 

 other departments, to stimulate by means 

 of personal intercourse with workers on 

 other lines the sense of solidarity of men 

 of science, to do something to counteract 

 that tendency to narrowness of view which 

 is a danger arising from increasing special- 

 ization, are functions the due performance 

 of which may do much to further that su- 

 preme object, the advancement of science, 

 for which the British Association exists. 



I propose to address to you a few re- 

 marks, necessarily fragmentary and in- 

 complete, upon the scope and tendencies of 

 modern mathematics. Not to transgress 

 against the canon I have laid down, I shall 

 endeavor to make my treatment of the sub- 

 ject as little technical as possible. 



Probably no other department of knowl- 

 edge plays a larger part outside its own 

 narrower domain than mathematics. Some 

 of its more elementary conceptions and 

 methods have become part of the common 

 heritage of our civilization, interwoven in 

 the every-day life of the people. Perhaps 

 the greatest labor-saving invention that the 

 world has seen belongs to the formal side 

 of mathematics ; I allude to our system of 

 numerical notation. This system, which, 

 when scrutinized, affords the simplest il- 

 lustration of the importance of mathe- 

 matical form, has become so much an indis- 

 pensable part of our mental furniture that 



