These days, mathematics books tend to be awash with symbols, but mathematical notation no more
is mathematics than musical notation is music. 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 lives and breathes in the
mind of the reader like some abstract symphony.
- excerpt from What is mathematics?
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