Lessons in learning from a piano master class

Today I went to some master class in the Shaw Auditorium (mainly to satisfy some requirement). At the end, some guy asked in the Q&A session about what piano students who are disadvantaged resource-wise and cannot attend master classes such as this should do. The master’s main point was that teachers should equip these students, and perhaps not just these students, with the ability to self-learn. But something that I really took away, and that I have thought about and agreed with for quite some time, was when he said that many students sometimes lack motivation to practice a specific piece as they dislike this composer. He pointed out that, very often, this is caused by a lack of knowledge on the composer and if the student learned more, it is likely that he/she will come to like that composer. It is thus the teacher’s responsibility to impart this knowledge on the student for them to gain motivation.

You may know what I’m getting at. I like application-inspired mathematics, partly because there is a motivation. There is an easy-to-understand abstraction which arose from some real-life phenomenon, which is also easy to understand. I am neutral towards something like higher topos theory and homotopy type theory precisely because I see no point in these theories. In other words, I don’t have prerequisite^M, where M is a very large number. Thus, it is natural to remain neutral on these topics.

But the problem is: how do you find something that you are most interested in? It is unreasonable to understand the prerequisites to every topic before you choose a topic. That would take more than a human lifetime as of 2023, probably even for the greatest mathematician in all of history. I don’t have a solution to this. But I use what my friend Toby Lam told me as a temporary measure: do something that requires learning what you are going to learn anyway. In my case, that would be anything related to some fundamental courses for many areas (Lie theory, for example), and some of my ‘current topics of interest’.