What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?- Henri Poincare
To invent is to discern, to choose.
To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.
Thus, they are free to replace some objects by others so long as the relations remain unchanged.
Thought is only a flash between two long nights, but this flash is everything.
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.
The mind uses its faculty for creativity only when experience forces it to do so.
The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.
Science is facts.
Science is built up of 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.
Point set topology is a disease from which the human race will soon recover.
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.
No more than these machines need the mathematician know what he does.
Need we add that mathematicians themselves are not infallible?
Mathematics is the art of giving the same name to different things.
