Occasionally I am asked if there is some field I might have cared to go into instead of mathematics. Though there is a rival area that has strongly pulled on me, the conviction that I would have done so much more poorly in it than in mathematics makes the answer a definite “No.” Not only that, but I had already become dedicated to mathematics. That other area is music. My desires there would have been too high for me to attain, for I would want to compose outstanding symphonies—that, or nothing at all. So I content myself to listening to great symphonies rather than trying in vain to write them.

There is certainly a strong kinship between music and mathematics. J. J. Sylvester had a keen sense of this. In a paper of his, “On Newton's rule for the discovery of imaginary roots,” he exclaims in a footnote:

“May not Music be described as the Mathematic of sense, Mathematic as Music of the reason? the soul of each the same! Thus the musician feels Mathematic, the mathematician thinks Music,—Music the dream, Mathematic the working life—each to receive consummation from the other when human intelligence, elevated to its perfect type, shall shine forth glorified in some future Mozart-Dirichlet or Beethoven-Gauss—a union already indistinctly foreshadowed in the genius and labours of Helmholtz!”

During my Harvard years I had great opportunity to enjoy fine music, for just across the Charles River in Boston was the world-famous Boston Symphony Orchestra, conducted at that time by the incomparable Serge Koussevitzky.