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

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.

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

The public does not need to be convinced that there is something in mathematics.

They [formulae 1.10 - 1.12 of Ramanujan] must be true because, if they were not true, no one would have had the imagination to invent them.

Mathematics may, like poetry or music, "promote and sustain a lofty habit of mind."

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