In talking about the relations of mathematics and culture or, rather, about the cultural value of mathematics, I think it advisable that I should first say a little about what I suppose the word “culture” to mean. In its general use it contains, I think, two ingredients, as it were. It refers to information and it refers to sensibility An ignorant man, however refined his natural sensibilities may be, is not regarded as cultured. And a man who has amassed an immense knowledge of facts, but is quite unable to distinguish between what is valuable and what is not valuable in his information, is not regarded as cultured. Of these two elements, I am inclined to think that sensibility is the more important. What the old writers on aesthetics used to call taste is, I think, more important than knowledge for the formation of a cultured outlook.