60 MYSTICISM AND LOGIC 



Deity ; and Plato realised, more perhaps than any other 

 single man, what those elements are in human life which 

 merit a place in heaven. There is in mathematics, he 

 says, " something which is necessary and cannot be set 

 aside . . . and, if I mistake not, of divine necessity ; for 

 as to the human necessities of which the Many talk in 

 this connection, nothing can be more ridiculous than such 

 an application of the words. Cleinias. And what are these 

 necessities of knowledge, Stranger, which are divine and 

 not human ? Athenian. Those things without some use 

 or knowledge of which a man cannot become a God to 

 the world, nor a spirit, nor yet a hero, nor able earnestly 

 to think and care for man " (Laws, p. SiS). 1 Such was 

 Plato's judgment of mathematics ; but the mathe- 

 maticians do not read Plato, while those who read him 

 know no mathematics, and regard his opinion upon this 

 question as merely a curious aberration. 



Mathematics, rightly viewed, possesses not only truth, 

 but supreme beauty a beauty cold and austere, like 

 that of sculpture, without appeal to any part of our 

 weaker nature, without the gorgeous trappings of paint- 

 ing or music, yet sublimely pure, and capable of a stern 

 perfection such as only the greatest art can show. The 

 true spirit of delight, the exaltation, the sense of being 

 more than man, which is the touchstone of the highest 

 excellence, is to be found in mathematics as surely as in 

 poetry. What is best in mathematics deserves not merely 

 to be learnt as a task, but to be assimilated as a part of 

 daily thought, and brought again and again before the 

 mind with ever-renewed encouragement. Real life is, to 

 most men, a long second-best, a perpetual compromise 

 between the ideal and the possible ; but the world of 

 pure reason knows no compromise, no practical limita- 



1 This passage was pointed out to me by Professor Gilbert Murray. 



