PEESIDEXT’S ADDEESS — SECTION A. 
17 
Prom the beauty of mere statuesque form to that of the most complex 
masterpiece performed by a grand orchestra, all forms of beauty have 
their analogues in the field of mathematics. 
Do you laugh when it is said that a mathematician in any but a 
ludicrous sense experiences the feeling of despair? Have you never 
felt a sickening sense of incapacity to grasp some fleeting image which 
it is your unhappy power to know the existence of? You are certain 
that it contains some special truth for you, but your powers just fall 
short of making it reveal itself. Can you not therefore understand that 
the mathematician, with his specialised opportunities of instinctively 
realising the near presence of some idea which, if caught, would be 
fruitful beyond conception, should sometimes despair of the puny 
power of the human mind ? 
Ask a pure mathematician to analyse his feelings of delight 
mixed with painful struggle, his feelings of wonder at the harmony 
that reigns among his symbols, his awe of the vast regions of truth 
touched bv his simplest formula — regions of which he knows that he 
himself only perceives a minute fraction — the analysis is quite beyond 
him. Why by many is the poet regarded as the fortunate possessor 
of a greater share of truth than any other? Is it not because he has 
the faculty of so choosing his words that they shall cover a greater 
portion of truth than ordinary words, indeed cover a greater portion 
than he is himself aware of? Is it not; that he refuses to believe 
that formal logic is our only guide, and so throws himself for much 
of his guidance on his instincts ? It is hard for those not behind the 
scenes to understand how exactly these words describe some of the 
moods of the pure mathematician. Glaisherl think it was who said 
that it would no doubt be a brilliant exaggeration to say that no 
mathematician understood any other mathematician. It would 
scarcely be a greater exaggeration to say that no mathematician 
understood himself. And by this I do not mean that he fails like 
everybody else to gauge himself as a social unit, but that he sees only 
a small part; of the meaning of his own mathematics, that he struggles 
ever to bring the mathematics into harmony with nature, but he never 
properly realises how much is left inharmonious. He only has dim 
feelings that in such a direction lie is almost certainly right, and in 
this other direction there is still something wanting. Sometimes be 
lias a nearly definite, sometimes a faint notion, and sometimes none at 
all of what is wanting, but there is always something wanting. 
And yet the popular fancy, fostered perhaps by misapprehension 
of the meaning of “ exact science,” is that the mathematician, by 
putting pen to paper, is enabled to turn a mental handle, whereupon, 
with unerring precision, some particular execrable barrel-organ tune 
bursts forth. 
There is another oft-mentioned but rarely understood aspect of 
the mathematician's work. A smile of derision is usually all that is 
bestowed upon the propounder of the statement that the imagination 
of the mathematician is closely akin to that of the poet. The mathe- 
matician is frequently compelled to travel leagues ahead of his 
symbols, and centuries ahead of his facts. He makes a plausible 
guess, but be is convinced that it is something more. His quick 
thought pursues the suggestion into a thousand ramifications. He 
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