Teachers and Grandteachers

I was fascinated to learn recently that mathematicians keep track of their "genealogies", tracing teacher-student relationships for several generations. (To make the genealogical analogy even stronger, in German, the advisor for a dissertation is actually referred to as a Doktorvater (0r Doktormutter).*

Composers and other musicians (especially pianists and violinists) often like to keep track of their teacher-student lineages, too. It's not unusual for a pianist to be able to trace their teachers and grandteachers back to Liszt, Busoni, Schnabel, or Cortot or a violinist back to Joachim or Auer. Compositional lines are often like divisions on a battlefield; the Skriabinistes here, the Second Viennese there, and the Boulangerie, like a fortress, over there. Even someone as self-assured as John Cage was always clear about his teachers: Weiss, Cowell, Schoenberg. Placing the teaching of composition into institutional settings within which young composers come into contact with teachers from a variety of backgrounds has watered this all down a bit, so that I'm not unusual in being able to claim parallel lines to Schoenberg, Cowell, Copland, and even Stravinsky**. (Although this may seem like an awfully broad swathe of music history, other prominent teaching lineages are quite alien for me -- Hanson, Piston, Hindemith, Sessions, Babbitt, Messiaen, or Milhaud.)

For mathematicians, these teacher-student lines can have import for the history of mathematics as many senior mathematicians work "through" their students, in that they use their students to fill in or carry out their own larger research programs and teacher-student paths can be useful in tracing the development of mathematical ideas and mathematicians talk, not unreasonably, about having "styles" of working which may be carried down these paths. A similar "carrying on" may hold for some music teaching situations (more so for performers than for composers, but I can imagine that this was the case for some students of Babbitt or or Stockhausen or Brün), but musical teaching, being ultimately an aesthetic concern, tends to invite elements of conflict or rebellion, often accompanied by complex motives, frequently psychological, even oedipal, in character. And that's where things get interesting, where the the history of that which we mysteriously call "style" is written. But, having had very little in the way of oedipal conflict with my own teachers, I'll spare you any further analysis.
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* I think it's cool to be able to call Alvin Lucier my Doktorvater.
** Stravinsky rarely taught. However: Stravinsky -> Robert Stevenson -> La Monte Young -> me.