Just as houses are made of stones, so is science made of facts.

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.

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

All of mathematics is a tale about groups.

Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?

Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.

Just as houses are made of stones, so is science made of facts.