Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages. If a being with such a mind existed, we could play no game of chance with him; we should always lose.

How is error possible in mathematics?

Need we add that mathematicians themselves are not infallible?

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

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.

A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we say that this effect is due to chance.