It belongs to the self-respect of intellect to pursue every tangle of thought to its final unravelment.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise

The factor in human life provocative of a noble discontent is the gradual emergence of a sense of criticism, founded upon appreciation of beauty, and of intellectual distinction, and of duty.

Culture is activity of thought, and receptiveness to beauty and humane feeling. Scraps of information have nothing to do with it. A merely well informed man is the most useless bore on God's earth.

The vigour of civilised societies is preserved by the widespread sense that high aims are worth while. Vigorous societies harbour a certain extravagance of objectives, so that men wander beyond the safe provision of personal gratifications. All strong interests easily become impersonal, the love of a good job well done. There is a sense of harmony about such an accomplishment, the Peace brought by something worth while. Such personal gratification arises from aim beyond personality.

The only use of a knowledge of the past is to equip us for the present. The present contains all that there is. It is holy ground; for it is the past, and it is the future.