Music and arithmetic (by G.W. Leibniz)

This year marks the 300th anniversary of Leibniz’s death. For this reason, the IMUS, in partnership with the Faculty of Mathematics, has dedicated this year’s “Year of …” to him – a series of lectures dedicated each year to one of the great mathematicians who have left their mark on history, taking advantage of one of the anniversaries. But we did not want to miss the opportunity to dedicate at least one pill to him in this blog. It will necessarily be a kind one, given that Leibniz was essentially a good human being -as would say Antonio Machado-, naïve at times, and rarely lost his temper, although he sometimes did -for example, during the ugly, long and to some extent nasty dispute he had with Newton over priority in the discovery of infinitesimal calculus-. With his proverbial clairvoyance, Leibniz was able to illuminate the relationship between music and numbers – discovered many centuries earlier by the Pythagoreans – in this famous quote:

Music is an unconscious arithmetical exercise in which the mind does not know that it calculates.