Last month, Jordan Ellenberg wrote about the Proof School, wondering, “ought there be a school just for math kids?” He is not entirely sold on the idea but later notes that there are schools just for music kids. What are the parallels between music education and math education? Are they fundamentally different? Ellenberg thinks that success in mathematics doesn’t require, or necessarily benefit from, the single-minded dedication that many musicians give to their instruments at an early age.
Coincidentally (I assume), around the same time, Conrad Wolfram wrote a post about what mathematicians can learn from music education. He disagrees with the idea that doing calculations by hand is similar to practicing a piece of music, a necessary step towards becoming a mathematician/musician. Unlike practicing music, Wolfram says, “practising hand-calculating doesn’t relate to the real-world outcomes in any direct way. It’s not akin to practising a piece of music because the real-world outcome is disconnected.”
This connection between mathematics education and music education has been made several times, especially in mathematics education circles. Paul Lockhart’s famous Mathematician’s Lament starts with an analogy between math education and music education. We would be appalled if music students weren’t allowed touch their instruments until they had been through years of training in how to write sheet music, but Lockhart and many others fear that this is how we approach math education.
These posts about math and music education got me thinking. Until my junior year of college, I didn’t know whether I wanted to do math or music as my career. I had a viola performance scholarship, but I probably wasn’t cut out for a performance career. I loved music theory as well and considered going to graduate school in that subject before ultimately deciding in favor of mathematics.
Before I went to graduate school, my music education and math education were very different from each other. In math, there was a right answer or a wrong answer, and when I finished all the problems on my math homework, I was done with it for the day. In music, there was never a finish line. There were performances, but even after those, I had more music to learn and more practicing to do. Even if I felt good about my performance, I knew there were things I could improve. I never felt like I had practiced “enough.” More practice was always better. In that way, my music education was a better preparation for graduate school in math than my math education was, at least up until my last two years of college. When I read this interview with biochemist and Nobel Prize winner Thomas Sudhof, I saw the same idea. In response to the question, “What was your most influential teacher, and why?” Sudhof responded: “My bassoon teacher, Herbert Tauscher, who taught me that the only way to do something right is to practice and listen and practice and listen, hours, and hours, and hours, and hours.”
But the ideas about the importance of practice and perseverance I (and Sudhof) got from my music training are not specific to music. If I had been an accomplished athlete, actor, or painter as a young person, I probably would have learned similar lessons from those endeavors. I think there is, however, a real connection between the way I approach music, both in terms of performance and in terms of music theory, and the way I approach mathematics, but I have trouble putting my finger on it. Yes, musical rhythms are connected to fractions. (Malke Rosenfeld of the math/dance education blog Math in Your Feet just wrote about using music to teach fractions.) Yes, musical intervals are related to ratios of frequencies of vibrating strings and therefore to number theory. In fact, rock star math graduate student Robert Schneider of the Apples in Stereo and Emory University has used his mathematics background to develop a new tuning system and microtonal scale. But I think the connection is deeper than that. I can’t pinpoint it precisely, but music and math both deal with structures in ways that feel similar to me.
So where does that leave my thoughts about math education and music education? I do think the mind-body connection in music performance is fundamentally different from mathematics education, which can be done while lying in bed, not moving a muscle. And I think Ellenberg is right that early dedication to music is much more important than early dedication to math. And I am convinced that my music education did influence my mathematical development, even if I can’t pinpoint how. But would a more math-intensive curriculum earlier on have done more for me than my music education ever could? I went to a math and science program for my junior and senior years of high school, but it was important to me that I could take courses outside of math and science and continue taking viola lessons. As commenters to Elllenberg’s posts point out, magnet schools offer courses outside their specialty areas, so students at the “proof school” will not be deprived of literature or history. The school will just emphasize mathematics more than most schools do. I probably wouldn’t have been interested in even that amount of specialization at age 12, but middle-schoolers who already know they are interested in pursuing mathematics professionally probably have a lot to gain from getting a solid foundation before college.
I know there are a lot of musical mathematicians and mathematical musicians out there. Do any of you have more concrete ideas about how your pursuit of one discipline has influenced your pursuit of the other?