542 REPORT— 1897. 



It appears, however, from the practice of the Council and the General Committee, 

 to be their policy that mathematicians belonging to the extreme right (if the phrase 

 may be used) shall from time to time be nominated to the presidency of the Section. 

 It is, I think, the case that this Section has always had assigned to it the subjects 

 of Mathematics and Physics. In their development, pure mathematics has con- 

 tinued to be associated with applied mathematics, and applied mathematics with 

 physics. So far as I know, there is no substantial reason why any change sliould 

 be made, and so far as I have been able to observe, there is a strong consensus 

 of opinion that no change by way of separation need be tried. Wide as is the 

 range of our discussions, distracting as is the occasional variety in the matter of 

 the papers we receive, the complexity of our Section, if in any respect a disadvantage, 

 does not appreciably discount the advantages it otherwise secures. Specialisation 

 in all our subjects has become almost a necessity for progress; but e.xcessive 

 obedience need not be paid to that necessity. On the one hand, there will be 

 danger of impei'fect appreciation if a subject is so completely restricted to a few 

 specialists that it is ignored by all but them ; and, on the other hand, there will be 

 danger of unsound growth if subject and thinkers alike become isolated, and cease 

 to take an active interest in the methods, the processes, and the results other than 

 those which directly concern them. Accordingly, I think that our group of 

 sciences, which form a continuous range, are better united than divided. 



Aristotle declared that it is unbecoming to praise the gods. Observing his 

 canon, I shall say nothing as to the wisdom and the justice of our Executive in 

 sometimes selecting a pure mathematician to preside over this Section. I shall 

 only appeal to your indulgence in accepting the opportunity they have thus given 

 me of speaking more specially about my own subject. 



I make this appeal the more earnestly, for two particular reasons. One of 

 these is based upon the conflicting views, popularly held and sometimes summarily 

 expressed, about the subject and those who are addicted to it. It is true that the 

 day has gone by, when it is necessary to give serious consideration to attacks upon 

 mathematical studies, and particularly upon analysis, such as were made by 

 the metaphysician Hamilton : attacks no longer thought worthy of any answer. 

 Feelings of hostility, if ever they were widely held, have given way to other 

 feelings, which in the mildest form suggest toleration and acquiescence, and in the 

 most extreme form suggest solemn respect and distant wonder. By common con- 

 sent, we are allowed without reproach to pursue our aims; though those aims 

 sometimes attract but little sympathy. It is not so long since, during one of the 

 meetings of the Association, one of the leading English newspapers briefly de- 

 scribed a sitting of this Section in the words, 'Saturday morning was devoted to 

 pure mathematics, and so there was nothing of any general interest ' : still, such 

 toleration is better than undisguised and ill-informed hostility. But the attitude 

 of respect, I might almost say of reverence, is even more trying : we mathema- 

 ticians are supposed to be of a different mould, to live far up the heights above 

 the driving gales of controversy, breathing a rarer intellectual atmosphere, serene 

 in impenetrable calm. It is difficult for us to maintain the gravity of demeanour 

 proper to such superior persons ; and perhaps it is best to confess at once that we 

 are of the earth, earthy, that we have our differences of opinion and of judgment, 

 and that we can even commit the Machiavelian crime of making blunders. 



The other of my reasons for claiming your indulgence is of a graver character, 

 and consists in the difficulty of framing general explanations about the subject. 

 The fact is that mathematics do not lend themselves readily to general exposition. 

 Clifford, it is true, could lecture and enchant his audience : and yet even his 

 lectures ranged about the threshold of the temple of mathematical knowledge and 

 made no attempt to reveal the shrines in the sanctuary. The explanation of this 

 initial difficulty is, however, at hand. Our vocabulary is highly technical, per- 

 haps as teclmical as is that of moral philosophers : and yet even the technicality 

 of a vocabulary can be circumvented by prolixity of statement. But the ideas 

 and the subject-matter in any branch of our study, when even only moderately 

 developed, are so abstract as to demand an almost intolerable prolixity of state- 

 ment if an attempt is made to popularise them. Moreover, of the many results 



