Beauty is the first test: there is no permanent place in the world for ugly mathematics.

A mathematician, like a painter or a poet, is a maker of patterns.

When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."

Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism".

In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.