Have you ever watched a “master class” in music on television or in real-life? This is an event where there is a “maestro”, (mostly) to be called “master” in the sequel (man or woman), who is listening to the performance of a student, often exhibiting acute physical discomfort in doing so, and who is subsequently telling the student something like: “You are playing (singing) this in such and such way…, but you should play (sing) it….”.
Nowadays there are also “master classes” in mathematics (the name may have a different origin, but the identity of the names is probably not entirely unintentional). Now suppose that in the latter case the “master” is talking, and a student interrupts the master and says: “Wouldn’t it be much easier (more elegant,..) to use the following line of argument…” Well, if the student is right, the master would say something like: “You’re absolutely right, your argument is much better (more beautiful, or whatever the correct expression may be), it changes my view on the whole matter”. Of course the conditional statement “if the student is right” is harder to interpret in the context of musical performance; you might say, “there is no absolutely right or wrong interpretation of a musical piece” (some musicians seem to think otherwise, though), but this would even allow more freedom for different interpretations. But never have I heard a master in a music master class say anything like “the way you play -sing- this is completely new to me, and it changes my view on the piece” (I may have watched a biased selection of master classes, but I’ve seen a lot of them, so I think that I have a feeling for the general tendency here).
Why is there this big difference? The mathematical world having a kind of anarchy (recent movies on mathematics and mathematicians, although mostly nonsense, rightly point to this aspect), in contrast with the very hierarchical world of (classical) musicians. Both groups are ultimately after the same thing, which I will call “beauty” for the moment, but in the world of musicians there seems to be very little tolerance for differences in interpretation. A notable exception to this rule was Cesar Franck who heard Ysaye play his sonata in a way he did not have in mind when he composed the piece. But he said something like “The first movement is played faster than I had in mind, but it is played so beautifully that I changed my mind”.
Another notable exception to rigid views on interpretation was provided by Glenn Gould (that might be a reason that many mathematicians like him so much). There are the famous two completely different recordings of the Goldberg variations by Glenn Gould that even inspired a nice theatre play for four men, representing different aspects of Glenn Gould’s views on all kinds of things. Of course, Glenn Gould was not the “typical maestro” (the typical maestro is represented in the play by von Karajan). The two different recordings are at the beginning and the end of the play. Glenn Gould also tried (very courageously, but I think somewhat unsuccessfully) to play Mozart in such a way that it would become clear to everybody that Mozart was a bad composer. Still, how original and courageous to try to do a thing like that! Glenn Gould was a real anarchist of the mathematical type! And now please don’t say something like “Glenn Gould played Mozart in this way because he just couldn’t play Mozart”. This is like the critic who suggested that Glenn Gould took such a “scandalously slow” tempo in the performance of the Brahms concerto with Bernstein, because his technical abilities didn’t allow him to play it faster. A more ridiculous statement has never been made about Glenn Gould (and it seems to have been one of the decisive things to make him withdraw from public performances). Of course Glenn Gould could have introduced more “finesse” in his Mozart playing, but he just wanted to make a point.
I recently noticed another sign that things may be changing for the better, reading the booklet with the recording of the first and ninth (Kreutzer) Beethoven sonatas for violin and piano by Pamela Frank (another violinist I have in high esteem) and her father. Pamela Frank is saying: “For me the particular technical challenge of the Beethoven sonatas is that the violin should always strive to sound like a piano”. Very interesting remark! At first sight this seems to be a hopeless goal for a violinist. But what she probably means to say is that the violin and the piano should “blend” in such a way that one forgets that there is a violin and a piano; the “non-instrumental” aspect of Beethoven’s works. The world of musical interpretation might be opening up!