I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming . . . and a little mad.

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.

Without adventure civilization is in full decay. ... The great fact [is] that in their day the great achievements of the past were the adventures of the past.

Wisdom alone is true ambition's aim, wisdom is the source of virtue and of fame; obtained with labour, for mankind employed, and then, when most you share it, best enjoyed.

The motive of success is not enough.

Everyone is a philosopher. Not everyone is good at it.

Our rate of progress is such that an individual human being, of ordinary length of life, will be called on to face novel situations which find no parallel in his past. The fixed person, for the fixed duties, who, in older societies was such a godsend, in the future will be a public danger.