Both my grandmothers had upright pianos and I just knew how to play since I was a child. Nobody taught me. I sounded like a grown-up and then I learned how to read music. I played so well by ear I could fool the teacher to believe I could play the notes. She'd make the mistake of playing the song once and I could play it.
Mathematics are the result of mysterious powers which no one understands and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.