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

Problems cannot be solved by thinking within the framework in which the problems were created.

In my view, it is the most important function of art and science to awaken this feeling and keep it alive in those who are capable of it.

The individual must not merely wait and criticize, he must defend the cause the best he can. The fate of the world will be such as the world deserves.

The series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences.

Although I am a typical loner in my daily life, my awareness of belonging to the invisible community of those who strive for truth, beauty, and justice has prevented me from feelings of isolation.

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.