Innovation is not the product of logical thought, even though the final product is tied to a logical structure.

In two weeks the sheeplike masses of any country can be worked up by the newspapers into such a state of excited fury that men are prepared to put on uniforms and kill and be killed, for the sake of the sordid ends of a few interested parties. Compulsory military service seems to me the most disgraceful symptom of that deficiency in personal dignity from which civilized mankind is suffering today.

I know that it is a hopeless undertaking to debate about fundamental value judgements. For instance, if someone approves, as a goal, the extirpation of the human race from the earth, one cannot refute such a viewpoint on rational grounds. But if there is agreement on certain goals and values, one can argue rationally about the means by which these objectives may be obtained.

What I seek to accomplish is simply to serve with my feeble capacity truth and justice, at the risk of pleasing no one.

But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed.

The world as we see it is only the world as we see it. Others may see it differently.

The human mind has first to construct forms, independently, before we can find them in things.