“Mathematics rightly viewed possesses not only truth but supreme beauty.”

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.”

“Truth is for the gods; from our human point of view, it is an ideal, towards which we can approximate, but which we cannot hope to reach.”

“Since this craving (for material possessions) is in the nature of competition, it only brings happiness when we outdistance a rival, to whom it brings correlative pain.”

“Philosophy, for Plato, is a kind of vision, the 'vision of truth' ... Everyone who has done any kind of creative work has experienced, in a greater or less degree, the state of mind in which, after long labour, truth or beauty appears, or seems to appear, in a sudden glory – it may only be about some small matter, or it may be about the universe ... I think most of the best creative work, in art, in science, in literature, and in philosophy, has been the result of such a moment.”

“Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.”

“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 in poetry.”