8 president's address. 



when he tries to play chess, lose the game because we make the wrong 

 move. Do we not all remember how, after the announcement of a 

 new fact or generalization, there are always many who claim to have 

 had, and perhaps vaguely expressed, the same idea ? They put it down 

 to bad luck that they have not pursued it, but they have failed precisely 

 in what, accoi'ding to Poincar^, is the essence of inventive power. It 

 may be bad luck not to have had a good idea, but to have had it and 

 failed to appreciate its importance is downright incapacity. 



An objection may be raised on the ground that before a selection can 

 be made the ideas themselves must appear, and that, even should they 

 arrive in sufficient numbers, the right one may not be among them. It 

 may even be argued that Poincar6 gives his case away by saying that 

 ' the sterile combinations do not even present themselves to the mind of 

 the inventor, ' expressing in a negative form what may be the essence of 

 the matter. Moreover, a fertile mind like that of Poincar^ would be apt 

 to place too low a value on his own exceptional 'gifts. Nevei-theless, 

 if Poincar^'s more detailed exposition be read attentively, and more 

 especially the description of how the discoveries which made him 

 famous among mathematicians originated in his mind, it will be found 

 that his judgment is well considered and should not be lightly set 

 aside. New ideas seldom are born out of nothing. They most fre- 

 quently are based on analogies, or the recollection of a sequence of 

 thoughts suggested by a different branch of the subject, or perhaps by a 

 different subject altogether. It is here that the memory comes in, which 

 is not a memory of detail, but a memory of premises with their con- 

 clusions, detached from the particular case to which they were originally 

 applied. Before we pronounce an adverse opinion on Poincar6's judg- 

 ment, we must therefore investigate what constitutes novelty in a new 

 idea ; but the subject is too vast to be dealt with here, nor can I attempt 

 to discuss whether an essential distinction exists between mathematical 

 invention and that more practical form of invention with which, for 

 instance, the engineer has to deal. 



If Poincar^, by this introspective analysis of his own powers, has 

 dimmed the aureole which, in the eyes of the public, surrounds the 

 mathematician's head, he removes it altogether by his definition of 

 mathematics. According to him, ' mathematics is the art of calling two 

 different things by the same name. ' It would take me too far were I 

 to try to explain the deep truth expressed in this apparently flippant 

 form: physicists, at any rate, will remember the revolution created in 

 the fundamental outlook of science by the application of the term 

 ' energy ' to the two quite distinct conceptions involved in its sub- 

 divisions into potential and kinetic energy. 



Enough has been said to show that the peculiar powers necessary 



