What is best in mathematics deserves not merely to be learnt as a task, but to assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.

No man can be a good teacher unless he has feelings of warm affection toward his pupils and a genuine desire to impart to them what he believes to be of value.

All exact science is dominated by the idea of approximation.

Science tells us what we can know but what we can know is little and if we forget how much we cannot know we become insensitive of many things of very great importance. Theology, on the other hand induces a dogmatic belief that we have knowledge where in fact we have ignorance and by doing so generates a kind of impertinent insolence towards the universe. Uncertainty in the presence of vivid hopes and fears is painful, but must be endured if we wish to live without the support of comforting fairy tales.

Even in the most purely logical realms, it is insight that first arrives at what is new.

When we perceive any object of a familiar kind, much of what appears subjectively to be immediately given is really derived from past experience.

The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself.