Posted by: Alexandre Borovik | July 31, 2011

Mathematics is the music of the reason

I discovered that this nowadays famous formula (popularised in Paul Lockhart’s essay A Mathematician’s Lament) was coined by James Joseph Sylvester in 1864:

Herein I think one clearly discerns the internal grounds of the coincidence or parallelism, which observation has long made familiar, between the mathematical and musical ἔθος. May not Music be described as the Mathematic of sense, Mathematic as Music of the reason? the soul of each the same! Thus the musician feels Mathematic, the mathematician thinks Music,-Music the dream, Mathematic the working life-each to receive its consummation from the other when the human intelligence, elevated to its perfect type, shall shine forth glorified in some future MOZART-DIRICHLET or BEETHOVEN-GAUSS -a union already not indistinctly foreshadowed in the genius and labours of a HELMHOLTZ!

[JJ Sylvester, Algebraical Researches, Containing a Disquisition on Newton's Rule for the Discovery of Imaginary Roots, and an Allied Rule Applicable to a Particular Class of Equations, Together with a Complete Invariantive Determination of the Character of the Roots of the General Equation of the Fifth Degree, Philosophical Transactions of the Royal Society of London, Vol. 154 (1864), pp. 579-666 (footnote on p.613).]

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  1. From the ancient Greeks until the European Enlightenment, music and mathematics were considered the same type of human activity, very distinct from the arts. Only from the late 18th century has music been considered an art in western culture.



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