Gustav Mahler was a conducting composer, probably the most famous in history. Or was he a composing conductor? The poor guy worked very hard as a conductor, reserving only summer weeks to compose. He gave us nine symphonies, among a relative few other things (including a completed movement of a tenth).

Esa-Pekka Salonen has worked very hard as a conductor. Indeed, the fabulous Finn was the music director of the Los Angeles Philharmonic from 1992 to 2009. I interviewed him in 2011, and he said he had a strong desire to spend more time composing. It had always been a battle with him: conducting versus composing, or conducting in conjunction with composing. He still logs his time on the podium. He is, for example, the principal conductor of the Philharmonia Orchestra (London). But he is also putting his pen to paper, or however composers do it these days.