Mathematics and Music

Pierre de Fermat was born in in the first decade of the 17th century. He was an amateur mathematician, but one who became very famous for his “Last Theorem”: no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. This deceptively simple theorem, eluded a formal proof from the most gifted mathematical geniuses for over three centuries. The theorem was not proven until September 1994, when Andrew Wiles finally achieved his lifelong ambition and proved it.

Once a mathematical theorem is proved, it becomes like a law of nature. Plants are green, the sun is yellow, the square of the hypotenuse of a right-angled triangle is the sum of the squares of its two sides, and so on. There is no mystery about it, it doesn’t engage our minds any longer because there is nothing to engage, only to learn. Once you study it sufficiently to learn it, there is nothing else left to learn. Fermat’s challenge to humanity lasted over three centuries, but it is a challenge no longer.

Wolfgang Amadeus Mozart was born in January 1756. He is world famous for many of his compositions. Over 250 years later, his compositions still continue to baffle listeners. We can study a composition and learn it, but it will continue to engage us and we will find there is yet more to learn. Our learning of great compositions is never complete.

Mathematical truths are eternal and timeless. But the genius mathematicians who discover them for the first time are distanced from that truth. The beauty of the truth does not belong to the discoverer, it belongs to the universe.

Musical compositions are eternal and timeless too. But the genius composer who creates them remains an integral part of them. The beauty of the truth in great compositions belongs as much to the composer as to the universe.

Mathematical beauty is innate to the Universe and gifted to mankind. Musical beauty is created by man and gifted to the Universe.

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  • Brijesh Kartha

    interesting. Something is not sitting right though. Got to ruminate on this. Will get back if the point strikes me.

    • OK. Thanks for reading! 🙂

      • Brijesh Kartha

        unluckily I have not been able to delve deeper into this Mahendra, I know what I want to convey is just there beyond the horizon of my thoughtspace but alas it looks like I am not able to concentrate on it. Dave has given me an interesting tidbit which might help me with that quest.

  • Dave MacLeod

    It is an interesting premise, and I particularly like the insight about something being engaging only whilst it remains unsolved. Unfortunately I think your analogy misses one important fact; mathematics is fact. All else is subjective opinion. Musical compositions are not eternal and timeless – no more than a painting or an episode of American Idol. Time will pass, they will disappear, but 1 + 1 will ALWAYS = 2.

    • Agreed. Musical compositions as being eternal was a romanticism!

    • Brijesh Kartha

      Dave, I kinda get your point. But then again even Mathematics is relevant only within a given context, right? There is nothing sacrosanct about it if we move the contextual mileposts.

  • In a sense, I agree – mathematics is self-contained. Music, like poetry, has esthetics of form which might well be appreciated and emulated by a completely alien life form. But for humans, much of their meaning stems not from the pattern of words and notes themselves, but the references and emotions they evoke in a wellspring of shared human structure and experience.

    But in another sense, all creative work is a search through bitspace for “interesting” numbers and patterns. I once tried teaching myself to play the keyboard (failed) but one thing which struck me vividly was how “inevitable” simple pieces of music seemed to be, discrete mathematical functions unrolling like a beautiful Turkish carpet. And you start wondering if you can actually generate simple tunes by some nosing around with an algorithm.

    The real fun starts when someone like David Cope takes that feeling forward and creates a program like EMI, an “alien life form” which can parse an existing body of work and create new pieces of music in that style. Imagine a future generation of EMI, which generates music that most experts and enthusiasts agree, sounds and feels absolutely like Mozart, and moves them to tears. But then they are told it was produced by a program searching through bitspace, rather than a human – what would they feel about it?

    To some extent, EMI itself has produced this reaction:
    http://www.internetarchaeology.org/www.geocities.com/Templarser/requiem.html

    • Thank you, as always, well-said. I had heard of algorithmically composed music, but was unaware about EMI specifically. Fascinating! Thanks for sharing.