How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?
Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
The creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
Imagination is more important than knowledge.
Pure mathematics is, in its way, the poetry of logical ideas.