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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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VII.13 Mathematics and Music

Catherine Nolan

1 Introduction and Historical Overview

Music is the pleasure the human mind experiences from counting without being aware that it is counting.

This intriguing remark of LEIBNIZ [VI.15], from a 1712 letter to fellow mathematician CHRISTIAN GOLDBACH [VI.17], suggests a serious connection between mathematics and music, two subjects—one a science, the other an art—that may at first seem very different from each other. Leibniz was perhaps thinking of the longstanding historical and intellectual association of the two disciplines that date back to the time of PYTHAGORAS [VI.1], when the subject of music was part of an elaborate classification scheme of knowledge in the mathematical sciences. This scheme ...

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