We make a living by what we get, but we make a life by what we give. The inherent vice of capitalism is the unequal sharing of blessings; the inherent virtue of socialism is the equal sharing of miseries. We contend that for a nation to tax itself into prosperity is like a man standing in a bucket and trying to lift himself up by the handle. The whole history of the world is summed up in the fact that, when nations are strong, they are not always just, and when they wish to be just, they are no longer strong.

The most frightful of all spectacles is the strength of the civilization without its mercy.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

Heresy would like to think of itself as 'invented Truth'. But of course, all Reason and Logic would agree that no man can ever create Truth; he can only discover it. If heresy were ever at all beneficial, God would use it really to bring one right back to Truth, as countless 'inventions' have brought men to discovery.

Mathematics is one of the major modern mysteries. Perhaps it is the leading one, occupying a place in our society similar to the religious mysteries of another age. If we want to know something about what our age is all about, we should have some understanding of what mathematics is, and of how the mathematician operates and thinks.

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.