the fetters of their own ever-changing desires. It impels those of keener sensibility out of their personal existences into the world of objective perception and understanding. It is a motive force of like kind to that which drives the dweller in noisy confused cities to restful Alpine heights whence he seems to have an outlook on eternity. Associated with this negative motive is the positive motive which impels men to seek a simplified synoptic view of the world conformable to their own nature, overcoming the world by replacing it with this picture. The painter, the poet, the philosopher, the scientist, all do this, each in his own way.” Spengler has elaborately argued that there is a perfect identity of physics, mathematics, religion, and great art.[54] We might fairly be allowed to point to Einstein as a lofty embodiment of that identity. Here, where we reach the sphere of mathematics, we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is here that the artist has the fullest scope for his imagination. “Mathematics,” says Bertrand Russell in his “Mysticism and Logic,” “may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” We are in the imaginative sphere of art, and the mathematician is engaged in a work of creation which resembles music in its orderliness, and is yet reproducing on another plane the order of the universe, and so becoming as it were a music of the spheres. It is not surprising that the greatest mathematicians have again and again appealed to the arts in order to find some analogy to their own work. They have indeed found it in the most various arts, in poetry, in painting, in sculpture, although it would certainly seem that it is in music, the most abstract of the arts, the art of number and of time, that we find the closest analogy. “The mathematician’s best work is art,” said Mittag-Lefler, “a high and perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch each other.” And Sylvester wrote in his “Theory of Reciprocants”: “Does it not seem as if Algebra had attained to the dignity of a fine art, in which the workman has a free hand to develop his conceptions, as in a musical theme or a subject for painting? It has reached a point in which every properly developed algebraical composition, like a skilful landscape, is expected to suggest the notion of an infinite distance lying beyond the limits of the canvas.” “Mathematics, rightly viewed,” says Bertrand Russell again, “possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture.... The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.”