Fryderyk Chopin, a brilliant mathematician?

That’s the title, in Polish, of what appears to be a 4th-6th grade lesson plan developed for the composer’s bicentennial in 2010.  Another plan invites the student, in the words of Google translate,  “In the footsteps of Frederic Chopin [to] improve math skills“.   Five years have gone by, the 17th International Fryderyk Chopin Piano Competition is taking place at this very minute in Warsaw (the Impromptu in A flat major Op. 29, to be precise), and it may be the moment to ask ourselves:   what did Chopin think about mathematics?

The answer is:  apparently, not very much one way or the other.  But there is this entry in the painter Delacroix’s journal for April 7, 1848 (my rough translation):

I asked [Chopin] what established logic in music.  He helped me to understand the nature of harmony and counterpoint; so that the fugue is like pure logic in music, and to be a scientist in the fugue is to know the element of all reason and all consequence in music.… I thought how happy I would be to learn all these matters that so depress vulgar musicians.  This feeling gave me an idea of the pleasure that those who deserve to be called scientists find in science.  The true science is not what one ordinarily understands by this word, that is to say a part of knowledge distinct from art; no!  Science viewed in this way, demonstrated by a man like Chopin, is art itself, and on the other hand art is then no longer what the vulgar believe, that is to say a sort of inspiration that comes from who knows where, that works by chance and only presents the picturesque exterior of things.  It’s reason itself, ornamented by genius, but following a necessary path and governed by higher laws.

The poet Alphonse de Lamartine was effectively dominating the newly proclaimed Second Republic at the time of this conversation, and it was perhaps the time for the musician and the painter to talk about big questions like the relation between art and science.  Here’s a more contemporary big question in the same vein, which is the real motivation for this post.  During a break a Chopin specialist, talking about interpretation, claimed that a musical score is only an indication and  determines a performance only in the most general way.  If the Chopin competition means anything at all it could hardly be otherwise; after all, hundreds of contestants are asked to perform basically the same pieces, but the computer on which you are reading this can play the notes without ever making a mistake.

Now the big question is whether it can also be said that a written proof is only an indication and determines the presentation (“performance”) of the proof only in the most general way.  If we were to admit this as a possibility, then, while the developers of automated theorem provers may not exactly be seeking a chimera, it could well be argued that formalized mathematics is meaningless in the absence of the — presumably human — performer.

(But maybe fifteen years from now the 20th International Fryderyk Chopin Piano Competition will be won by a descendent of Deep Blue equipped with fingers and feet — having these appendages must be somewhere in the ground rules — and what will the contemporary Delacroix have to say about that?)

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