But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.

The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.

Point set topology is a disease from which the human race will soon recover.

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

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.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.