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.
Science is facts.
Just as houses are made of stones, so is science made of 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.
It is through science that we prove, but through intuition that we discover.
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 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.
The mind uses its faculty for creativity only when experience forces it to do so.