” A page of sheet music represents a piece of music; the music itself is what you get when the notes on the page are sung or performed on a musical instrument. It is in its performance that the music comes alive and becomes part of our experience; the music exists not on the printed page, but in our minds. The same is true for mathematics, the symbols on a page are just a representation of the mathematics. When read by a competent performer (in this case, someone trained in mathematics), the symbols on the printed page come alive – the mathematics leaves and breathes in the mind of the reader like some abstract symphony.
[…] Though only someone well trained in music can read a musical score and hear the music in her head, if that same piece of music is performed by a competent musician, anyone with the sense of hearing can appreciate the result. It requires no musical training to experience and enjoy music when it is performed.
[…] however, the only way to appreciate mathematics was to learn how to ‘sight-read’ the symbols. Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent of a pair of ears. Mathematics can be ‘seen’ only with the ‘eyes of the mind’. It is as if we had so sense of hearing, so that only someone able to sight-read musical notation would be able to appreciate the patterns and harmonies of music. ”
(KEITH DEVLIN – “THE LANGUAGE OF MATHEMATICS: MAKING THE INVISIBLE VISIBLE”)