Music Is A Hidden Arithmetic Exercise

This remark appears in a letter Gottfried Wilhelm Leibniz wrote to the mathematician Christian Goldbach in April 1712. Leibniz was himself a major musical theorist as well as a mathematician, and he saw music as a model of unconscious mathematical order — the soul counts intervals and rhythms without being consciously aware that it is doing arithmetic. The idea influenced later thinkers including Arthur Schopenhauer, who cited a version of it in his account of music as the purest expression of will.