The result of teaching small parts of a large number of subjects is the passive reception of disconnected ideas, not illumed with any spark of vitality.

It is not paradox to say that in our most theoretical moods we may be nearest to our most practical applications.

The world is shocked, or amused, by the sight of saintly old people hindering in the name of morality the removal of obvious brutalities from a legal system.

In a living civilization there is always an element of unrest, for sensitiveness to ideas means curiosity, adventure, change. Civilized order survives on its merits and is transformed by its power of recognizing its imperfections.

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.

All practical teachers know that education is a patient process of mastery of details, minute by minute, hour by hour, day by day.

The study of mathematics is apt to commence in disappointment.