I was talking to a classical pianist the other day, and told her I'm three generations removed from Bela Bartok. She replied that she's 6th generation Beethoven. My link to Bela Bartok stems from having studied piano with Michele Cooker, who studied with Gyorgy Sandor, who was a student of Bartok's. Though Michele taught me piano rather than composition, maybe some quality of Bartok rubbed off, because I went on to write many short piano pieces for my students, in the spirit of Bartok's Mikrokosmos.
Similar lineages are traced in the world of mathematics. Jon Johnson, who's on the board of Friends of Herrontown Woods, sent me this link documenting Oswald Veblen's mathematical descendants. By this count, Veblen had 16 students and 10,126 descendants. The second number will steadily increase as descendants advise each new generation of mathematicians. The majority of Veblen's mathematical descendants can be attributed to three of his students, Alonzo Church, R.L. Moore, and John Whitehead. That Veblen played the advisor role for just 16 students must owe in part to his having left Princeton University to join the Institute for Advanced Study, which did not have the traditional advisory relationship between faculty and graduate students.
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