Every good mathematician should also be a good chess player and vice versa.

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomena.

Intuition is more important to discovery than logic.

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

A small error in the former will produce an enormous error in the latter.

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.