Intuition is more important to discovery than logic.

Experiment is the sole source of truth.

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

How is error possible in mathematics?

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.