It seems to us unwise to have insisted on teaching geometry to the younger Dionysius, tyrant of Syracuse, in order to make him a good king, but from Plato's point of view it was essential. He was sufficiently Pythagorean to think that without mathematics no true wisdom is possible.

Thought is merciless to privilege, established institutions, and comfortable habit.

Love and knowledge led upwards to the heavens.

Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.

Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in inferring that he is an inexact man. Every careful measurement in science is always given with the probable error ... every observer admits that he is likely wrong, and knows about how much wrong he is likely to be.

The fundamental principle in the analysis of propositions containing descriptions is this: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted.

Vanity is a motive of immense potency.