10 president's address — SECTION A. 



If the average man were asked what a mathematician is, he might 

 answer that he is a being possessed of a strange aptitude for, and a 

 curious delight in, numerical calculation. Some there might be who 

 would echo the old saying — 



Purus mathematicus, purus asinus : 

 but most people would agree that the mathematician is a lucky sort 

 of fellow with a good head for figures. 



It cannot be repeated too often that this idea of the mathematical 

 mind is quite wrong. The mathematician is not merely a glorified 

 chess player, who can carry the moves of a prolonged calculation in 

 his head and be relied upon in the end to return a correct numerical 

 answer. Certainly there have been mathematicians possessing this- 

 faculty. Gauss had it, but Gauss was the exception, not the rule. 



We read that Newton, " though so deep in Algebra and Fluxions 

 could not readily make up a common account ; and when he was 

 Master of the Mint used to get somebody to make up his accounts for 

 him." 



Poisson once remarked to Madame Biot that he could net add as 

 well as his cook ; neither did he understand how Gauss and Bessel 

 could be at the same time expert calculators and skilled analysts. 



Poincare was not ashamed to say that he was absolutely incapable 

 of doing an addition sum correctly, and that he was an equally bad 

 chess player. He could calculate well enough that in making a certain 

 move he would get into trouble. He would pass in review other 

 possible moves and give them up for the same reason. Then in the 

 end he would probably play the move .which he had first put aside, 

 having forgotten the dans'er which he had then loreseen. 



• Such instances could be multiplied indefinitely ; and we see 

 that it is not necessarily a good head for figures and a prodigious 

 memory that make the mathematician. Mathematics and Arithmetic 

 are not identical. If they Avere, Mathematics would, in the opinion 

 of some of us, be a dry and arid science. 



A mathematical demonstration is not simply a collection of 

 syllogisms. It is a series of syllogisms in a certain order, and the order 

 in which they come is almost as important as their content. The 

 mathematical mind seems to have an intuitive perception of this 

 order ; it takes in at a glance the whole of the reasoning, and has no 

 fear of forgetting the elements. These appear to fall into their places 

 without any special effort of memory. With this mathematical sense 

 or taste, there is associated the idea of mathematical beauty and 

 elegance. Only the mathematician appreciates it ; probably he alone 

 would admit its existence ; but for it we claim a reality just as actual 

 as the beauty of the picture, the statue, or the poem. 



If this statement of the nature of the mathematical mind be 

 correct, it is not surprising that the mathematical faculty frequently 



