A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment.

It is by logic we prove. It is by intuition we discover.

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

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.

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

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.