It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

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

Geometry is the art of correct reasoning from incorrectly drawn figures.

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.

It is not order only, but unexpected order, that has value.

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