MATHEMATICAL DISCOVERY. 49 



in his memory. Every good mathematician should 

 also be a good chess player and vice versa, and 

 similarly he should be a good numerical calculator. 

 Certainly this sometimes happens, and thus Gauss 

 was at once a geometrician of genius and a very 

 precocious and very certain calculator. 



But there are exceptions, or rather I am wrong, 

 for I cannot call them exceptions, otherwise the excep- 

 tions would be more numerous than the cases of con- 

 formity with the rule. On the contrary, it was Gauss 

 who was an exception. As for myself, I must confess 

 I am absolutely incapable of doing an addition sum 

 without a mistake. Similarly I should be a very bad 

 chess player. I could easily calculate that by playing 

 in a certain way I should be exposed to such and 

 such a danger ; I should then review many other 

 moves, which I should reject for other reasons, and 

 I should end by making the move I first examined, 

 having forgotten in the interval the danger I had 

 foreseen. 



In a word, my memory is not bad, but it would be 

 insufficient to make me a good chess player. Why, 

 then, does it not fail me in a difficult mathematical 

 argument in which the majority of chess players 

 would be lost ? Clearly because it is guided by the 

 general trend of the argument. A mathematical 

 demon.stration is not a simple juxtaposition of syl- 

 logisms ; it consists of .syllogisms placed in a certain 

 order, and the order in which these elements are 

 placed is much more important than the elements 

 themselves. If I have the feeling, so to speak the 

 intuition, of this order, .so that I can perceive the 

 whole of the argument at a glance, I need no longer 



(1,777) ^ 



