All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.

In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?

It is not order only, but unexpected order, that has value.

Often when works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, long or short, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind.

In the old days when people invented a new function they had something useful in mind.

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.