Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in inferring that he is an inexact man. Every careful measurement in science is always given with the probable error ... every observer admits that he is likely wrong, and knows about how much wrong he is likely to be.

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

What hunger is in relation to food, zest is in relation to life.

But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

We may say, in a broad way, that Greek philosophy down to Aristotle expresses the mentality appropriate to the City State; that Stoicism is appropriate to a cosmopolitan despotism; that stochastic philosophy is an intellectual expression of the Church as an organization; that philosophy since Descartes, or at any rate since Locke, tends to embody the prejudices of the commercial middle class; and that Marxism and Fascism are the philosophies appropriate to the modern industrial state.

It appeared that after first contemplating a book on some subject, and after giving serious preliminary attention to it, I needed a period of subconscious incubation which could not be hurried and was if anything impeded by deliberate thinking.... Having, by a time of very intense concentration, planted the problem in my subconsciousness, it would germinate underground until, suddenly, the solution emerged with a blinding clarity, so that it only remained to write down what happened as if in a revelation.

War grows out of ordinary human nature.