When George Berkeley published his famous Treatise he was only twenty-five years old. And David Hume was twenty-nine when his Treatise of Human Nature was published. These were their most important philosophical works, although they lived until sixty-eight and sixty-five respectively. Should the youth of these philosophers at the time of such important works be surprising? Why should it, since Newton discovered what is now called the binomial theorem when he was twenty-three and within a year had developed principles of Integral Calculus and worked out much of his theory of gravitation. And Mozart wrote all his lovely violin concerti when he was nineteen. As for important work later in life, Newton did not do it, but Mozart in his few years developed amazingly.

Yet we should be surprised by Berkeley and Hume, for great philosophy is not usually a youthful accomplishment, although great mathematics and music are. Mathematicians, however, rarely do major work beyond their early years; musicians often do. A reasonable hypothesis to explain these phenomena is that a priori, intellectual and manipulative abilities are native, and appear early in life, needing only the tools that society provides. Mathematics is the prime example of these skills. When experience is required for one's work, or genuine emotional growth and maturity, even the same skills can seldom be put to use until emotion and experience ripen. Music is mathematical enough that quite brilliant compositions can be written young, like the sixteen-year-old Mendelssohn's incidental music to A Midsummer Night's Dream. But maturity is necessary for the power, range and depth of greater music.