The study of mathematics is apt to commence in disappointment.

It is natural to think that an abstract science cannot be of much importance in affairs of human life, because it has omitted from its consideration everything of real interest.

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. "Necessity is the mother of invention" is a silly proverb. "Necessity is the mother of futile dodges" is much closer to the truth. The basis of growth of modern invention is science, and science is almost wholly the outgrowth of pleasurable intellectual curiosity.

Art heightens the sense of humanity. It gives an elation to feeling which is supernatural...A million sunsets will not spur us on towards civilization. It requires Art to evoke into consciousness the finite perfections which lie ready for human achievement.

The preternatural solemnity of a good many of the professionally religious is to me a point against them.

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.

It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery - Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.