Thought is only a flash between two long nights, but this flash is everything.

[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.

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

Geometry is not true, it is advantageous.

What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

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.