Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as a sensible intelligible world.

Experience has taught me a technique for dealing with such people [...] I counter the devotees of the Great Pyramid by adoration of the Sphinx; and the devotee of nuts by pointing out that hazelnuts and walnuts are as deleterious as other foods and only Brazil nuts should be tolerated. But when I was younger I had not yet acquired this technique, with the result that my contacts with cranks were sometimes alarming.

It will be said that the joy of mental adventure must be rare, that there are few who can appreciate it, and that ordinary education can take no account of so aristocratic a good. I do not believe this. The joy of mental adventure is far commoner in the young than in grown men and women. ...It is rare in later life because everything is done to kill it during education.

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.

In a democracy it is necessary that people should learn to endure having their sentiments outraged.

One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision.

While the dogmatist is harmful, the sceptic is useless ...; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or of ignorance. Knowledge is not so precise a concept as is commonly thought. Instead of saying 'I know this', we ought to say 'I more or less know something more or less like this'. ... Knowledge in practical affairs has not the certainty or the precision of arithmetic.