To be out of harmony with one's surroundings is of course a misfortune, but it is not always a misfortune to be avoided at all costs. Where the environment is stupid or prejudiced or cruel, it is a sign of merit to be out of harmony with it.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty-a beauty cold and austere ... yet sublimely pure and capable of stern perfection such as only the greatest art can show.

Dr. Arnold . . . the admired reformer of public schools, came across some cranks who thought it a mistake to flog boys. Anyone reading his outburst of furious indignation against this opinion will be forced to the conclusion that he enjoyed inflicting floggings.

Mathematics is only the art of saying the same thing in different words.

A habit of finding pleasure in thought rather than action is a safeguard against unwisdom and excessive love of power, a means of preserving serenity in misfortune and peace of mind among worries. A life confined to what is personal is likely, sooner or later, to become unbearably painful; it is only by windows into a larger and less fretful cosmos that the more tragic parts of life become endurable.

HELL: A place where the police are German, the motorists French and the cooks English.

We may say, in a broad way, that Greek philosophy down to Aristotle expresses the mentality appropriate to the City State; that Stoicism is appropriate to a cosmopolitan despotism; that stochastic philosophy is an intellectual expression of the Church as an organization; that philosophy since Descartes, or at any rate since Locke, tends to embody the prejudices of the commercial middle class; and that Marxism and Fascism are the philosophies appropriate to the modern industrial state.