I kid you not, when I say I know of, and have heard, recordings of the following composers themselves conducting their own music-Richard Wagner, Richard Strauss, Sir William Walton, Wilhelm Furtwangler (yes, the famous conductor was also a composer), Sir Edward Elgar, Aaron Copeland, Alexandre Glazunov, Maurice Ravel, Sergei Prokofiev, Igor Stravinsky, Gustav Holst, Ferde Grofe.

              And what an experience it is, to hear the composer's own take on how their music should sound! 

I know of some 20th century/contemporary composers: Hanns Eisler (on the "Historic Recordings/Historische Aufnahmen" series), Pierre Boulez, Bruno Mantovani ( https://www.youtube.com/watch?v=KU70HMUin9A" rel="nofollow - D'un rêve parti ).

I have several discs with Boulez conducting Boulez: Répons, Messagesquisse/Anthèmes 2, Le marteau sans maître and Dérive 1 & 2 (for an example see https://www.youtube.com/watch?v=kUeRfwUU_oE" rel="nofollow - Dérive 2 ...).

Stravinsky! 

In rock music, the only example I can think of is Frank Zappa, who used to get upset when some folks were not listening to the music and only wanted a guitar solo. He would put down the guitar and take up the baton ... and I think he was wielding that as well as any conductor probably could!

Concerto Arena 2002

Here is Palmer's superb adaptation of "War Child" with the London Symphony Orchestra:

That would be world news! But highly unlikely. Although experimentation with sound recordings began in the1850s, as far as I know the first recordings of music that we know of are from 1888 (The Lost Chord played by unknown musicians) and 1889: Brahms playing his Hungarian Dance on piano (see https://www.youtube.com/watch?v=H31q7Qrjjo0" rel="nofollow - here ). So, that would be a couple of years after Wagner's death...

No, the man himself recorded a cylinder in 1880 as is released on this Grammofono cd, along with the later recordings conducted by his son, Siegfried!

This cd set mentions a fragment of a Love Duet from Tristan conducted by Richard Wagner in 1880; it used to be on youtube, but I think it is gone from there, but here is the cd cover, itself.

Well, I sincerely put in doubt the veracity of that claim of Grammofono, who put out this cd. Partly because of Wagner's health conditions in his last years, partly because the performance history of Tristan und Isolde (but I'm not a Wagner specialist), but especially because of the state of recording techniques in 1882, 1883... Nothing is impossible, but it seems really very highly unlikely to me.

I thought it would not be too difficult to find out more about this recording... Apparently, this cylinder was recorded in 1903. You can read more about it in Jonathan Brown's book on Great Wagner Conductors https://books.google.fr/books?id=mNO7AgAAQBAJ&pg=PA753&lpg=PA753&dq=grammofono+wagner+conducts+wagner+recording&source=bl&ots=cjBrZKNGWm&sig=ACfU3U3b8l-_rKfP185F4qUoV6xeYRIbDw&hl=fr&sa=X&ved=2ahUKEwjtx5ixlMPyAhXOzYUKHfZAAdcQ6AF6BAgNEAM#v=onepage&q&f=false" rel="nofollow - here . This Grammofono disc is mentioned here.

Yes, I know. There is some device with which you could record every nuance of someone playing piano.

A side note about Schönberg: What very few people know is that he also did paintings (mostly self-portraits). Jean and I once were at an exhibition of his paintings.

Here is one of his self-portraits:

I had no idea about that aspect of Schoenberg. Lovely.