The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.

Chance ... must be something more than the name we give to our ignorance.

Sociology is the science with the greatest number of methods and the least results.

I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry.

Mathematical discoveries, small or great are never born of spontaneous generation.

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.

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.