Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.

One does not ask whether a scientific theory is true, but only whether it is convenient.

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.

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 feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

Geometry is not true, it is advantageous.

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