In considering mathematics in relation to the beautiful, the range of possibility is so vast that a brief article like this can hardly be expected even to list the salient points of contact. The field might properly include all that we designate as the fine arts or, to use the more expressive phrase of the French, the beaux arts. Painting, for example, might be considered with reference to the works of that great genius in science, in mathematics, and in art—Leonardo da Vinci. Sculpture might equally well be included because of the mathematical principles employed by that majestic user of ponderous masses, Michelangelo. Architecture might have place with reference to the works of that Oxford professor of mathematics, Sir Christopher Wren, who rebuilt ecclesiastical London; engraving, with reference to that gifted artist of Niirnberg, Albrecht Diirer, who published the first modern work on curves; music, with reference to the fact that it always ranked as a branch of mathematics until the sixteenth century; decoration, with reference to the geometric designs found in all ages and reaching their highest degree of perfection in the works of the Moslems; and literature, with reference to the mathematics of poetry, and the poetry of mathematics. Indeed, we might properly include the beauties of nature, where mathematics plays a part of which we are usually quite unconscious.