Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.

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.

Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

There is always more in one of Ramanujan's formulae than meets the eye, as anyone who sets to work to verify those which look the easiest will soon discover. In some the interest lies very deep, in others comparatively near the surface; but there is not one which is not curious and entertaining.

... Philosophy proper is a subject, on the one hand so hopelessly obscure, on the other so astonishingly elementary, that there knowledge hardly counts.

Most people can do nothing at all well

As Littlewood said to me once [of the ancient Greeks], they are not clever school boys or "scholarship candidates," but "Fellows of another college."