“Mathematical discoveries, like all others, may come from the need to solve practical problems. But a more important motive is the pure delight some individuals take in invention and discovery.
“A mathematician tries to extend his powers. He knows a trick which allows him to solve one sort of problem – but might there not be other sorts that can be solved in the same way? He tries to find out how his tricks work, to group problems in families, to classify them. When a new problem comes up he will often be able to see immediately what family it belongs to, and what methods are likely to solve it.
“In this book I have tried to arouse this active state of mind, to encourage mental adventurousness.
“If my readers have come to share this feeling for the subject my objective has been attained.”