have never done anything “useful.” No discovery of mine has made or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world. . . . Judged by all practical standards, the value of my mathematical life is nil, and outside mathematics it is trivial anyhow. . . . I have added something to knowledge and helped others to add more; and these somethings have a value that differs in degree only, and not in kind, from that of the creations of the great mathematicians, or any of the other artists, great or small, who have left some kind of memorial
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