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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.

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Keith Devlin













Thank you for watching.

