Mozart was not only a prodigy. Yes, music came miraculously easy to him. He showed gifts as early as 3; he wrote his first three symphonies at the age of 8 and his first opera a couple of years later; he could "steal" complex choral and orchestral works, writing down the scores note-for-note as he listened. But he also was painfully sensitive to human emotions.
He was a prodigy who had a true aha! moment: the discovery that ease could reside within difficulty, profound clarity within profound complexity.
Hold that thought.
A prodigy is a young person with uncannily advanced skills. There are some fields, such as literature, in which you almost never see prodigies - and some that are very pastures for them. Mathematics is one; music is another. I recall a 10-year-old completing a bachelor's degree in math at my college; he was brilliant and had no one to play with.
The knack of "seeing into" the interplay of numbers is probably closely related to the same knack for notes. (Jay Greenberg of New York City is now 14; he had written five full-length symphonies by the time he was 12.) As neurobiology burgeons, such mysteries may unfold petal by petal. What's sure is that the history of music - like those of math and physics - is studded with prodigies, from Mozart to Felix and Fanny Mendelssohn to Stevie Wonder.
But prodigy status does not a Mozart make. Most prodigies lack his flare for melody, and for poignant sensitivity to human predicaments, especially in the characters and themes of his operas. He absorbed from the great musicians and composers he met - including George Frideric Handel and Johann Sebastian Bach.