It can be said with complete confidence that any scientist of any age who wants to make important discoveries must study important problems. Dull or piffling problems yield dull or piffling answers. It is not enough that a problem should be "interesting".

Deductivism in mathematical literature and inductivism in scientific papers are simply the postures we choose to be seen in when the curtain goes up and the public sees us. The theatrical illusion is shattered if we ask what goes on behind the scenes. In real life discovery and justification are almost always different processes.

It is a common failing-and one that I have myself suffered from-to fall in love with a hypothesis and to be unwilling to take no for an answer. A love affair with a pet hypothesis can waste years of precious time. There is very often no finally decisive yes, though quite often there can be a decisive no.

The art of research [is] the art of making difficult problems soluble by devising means of getting at them.

Science is the art of the solvable.

Simultaneous discovery is utterly commonplace, and it was only the rarity of scientists, not the inherent improbability of the phenomenon, that made it remarkable in the past. Scientists on the same road may be expected to arrive at the same destination, often not far apart.

To abdicate from the rule of reason and substitute for it an authentication of belief by the intentness and degree of conviction with which we hold it can be perilous and destructive. Religious beliefs give a spurious spiritual dimension to tribal enmities.