Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Any pleasure that does no harm to other people is to be valued.

3 is prime, 5 is prime, 7 is prime, 9 is a paradox; as is a paradox why the number 1 is not prime if it has no other divisors besides himself.

...I am afraid that education is conceived more in terms of indoctrination by most school officials than in terms of enlightenment. My own belief is that education must be subversive if it is to be meaningful. By this I mean that it must challenge all the things we take for granted, examine all accepted assumptions, tamper with every sacred cow, and instill a desire to question and doubt. Without this the mere instruction to memorise data is empty. The attempt to enforce conventional mediocrity on the young is criminal.

The reason is, and by rights ought to be, slave to the emotions.

The man who suffers from a sense of sin is suffering from a particular kind of self-love. In all this vast universe the thing that appears to him of most importance is that he himself should be virtuous. It is a grave defect in certain forms of traditional religion that they have encouraged this particular kind of self-absorption.

Right discipline consists, not in external compulsion, but in the habits of mind which lead spontaneously to desirable rather than undesirable activities.