Follow your heart but take your brain with you.

Courage is not an ability one either possess or lacks. Courage is the willingness to engage in a risk-taking behavior regardless of whether the consequences are unknown or possibly adverse. We are capable of courageous behavior provided we are willing to engage in it. Given that life offers few guarantees, all living requires risk-taking.

To all those who walk the path of human cooperation war must appear loathsome and inhuman.

Every individual acts and suffers in accordance with his peculiar teleology, which has all the inevitability of fate, so long as he does not understand it.

Death is really a great blessing for humanity, without it there could be no real progress. People who lived for ever would not only hamper and discourage the young, but they would themselves lack sufficient stimulus to be creative.

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.

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.