What is courage? Courage is the willingness to risk failure...There is only one danger I find in life, and that, indeed, is a real one. You may take too many precautions.

Each generation has its few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing.

Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms.

Exaggerated sensitiveness is an expression of the feeling of inferiority.

More important than innate disposition, objective experience, and environment is the subjective evaluation of these. Furthermore, this evaluation stands in a certain, often strange, relation to reality.

There is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material-these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative-a spirit of disciplined search for adventures of the intellect. Only as adventurer can really tell of adventures.

Every pampered child becomes a hated child.... There is no greater evil than the pampering of children.