I was chatting with a Ukrainian friend the other day when she asked me, “Do you play any musical instruments?” I admitted that I could, by certain not terribly high standards, be called a piano player. “A-ha! I knew it. Math people are always music people,” she responded triumphantly, and started to list off all the people she knew who had a combined love of math and classical music.
Of course, we in the United States are bound to take all utterances from Ukrainians on the subjects of music, math, and ballet as unquestionably true. But there’s a lot of supplementary evidence as well, from great mathematicians and physicists who either played an instrument or had a deep and profound love of music, to the necessary connections between what is great about math and what is great about music that attract one and the same mind.
It’s the structural similarities that get me. Mathematics is the art of saying a universe while bound by formalist fetters of the toughest stuff. Every word, every turn, has to bear the scrutiny of an epoch of rigor. When you find something new to say within those confines, you’ve pulled off an unparalleled act of creation. A stunning proof can get me positively teary-eyed, and it’s that exact same structure of finding creativity in the face of impossible restriction that touches me in classical music.
I’m going to take an extreme example because, hey, it’s the Holidays. Consider the last movement of Beethoven’s Appassionata Sonata. It is from his stormy middle period and is often used in film when they need a piece of piano literature for an unhinged virtuosic criminal mastermind to thrash out in the solitude of his mountain fortress. Or maybe I just feel like it should be. In any case, the restrictions are profound. Leave out a note, and you’ve ruined it. Ignore a dynamic marking, and you will be dropped from all men’s esteem. Considering the freedom that you have as a pop star when covering a song to do pretty much whatever you damn well please as long as something like the melody of the chorus creeps through, it seems like there would be nothing left to individual human creativity when playing this piece of music. We should have a hundred recordings, each a metronomical copy of the other, the only difference being the quality of the sound equipment employed.
And we do have a hundred recordings, but the amount of variation that the performers have squeezed out over the years within the constraints set by Beethoven is astounding. Here is Wilhelm Kempff, one of the greats, performing it with his immaculate attention to the possibility for dynamic change within each measure (fast forward to 15:43 to get the third movement):
Now, compare that to Sviatoslav Richter’s performance, which basically conceives of the movement as an exercise in titanic thrash metal. He is about speed and ferocity. All the notes are the same, but the philosophical center of the piece is wildly different.
As I said, these are two extremes of an already extreme piece of music. Part of the endless joy of classical music for my math-snuggling mind is sniffing out moments where performers do something unspeakably subtle that is entirely within the rules but that changes utterly the flavor of a piece, savoring that human ability to express individuality in the most seemingly unpromising situations. Those moments have all the thrill of finding buried treasure, precisely because they are so hard to accomplish. Further, once that new variation is discovered, it is added to our total experience of the piece, always there in the background, defining what comes after, so that each new performance is really a communication with all those that have come before. Just as a mathematical proof is a conversation with Euler and Lagrange and Hilbert, so is each new Appassionata recording a piece of art that bears with it the decisions made by Kempff and Richter and thousands of others, and the more records you listen to, the better and richer each new record becomes.
So, get listening!