I just made a Mozart Pandora station and I know his teacher was Hayden, but I don't know Hayden's teacher. Who is the oldest composer we know, what music of his do we know of, and do we know of anyone who played it?
Well the oldest known music is the Hurrian Hymes written in 1400 bce by Puẖiya(na), Urẖiya and Ammiya. Here is a recording of one of them
http://youtube.com/watch?v=DBhB9gRnIHE
The oldest song that has lyrics is the Seikilos epitaph which was written in around 100bce and here is a recording of that song. As Hank Green said recently this song amusingly enough can be summed up as YOLO.
http://youtube.com/watch?v=xERitvFYpAk
There is some conjecture that various Chinese songs are older based on tails that certain ceremonies have remained unchanged for thousands of years but if you are looking at hard evidence the two I just mentioned are the oldest known songs.
I just wanted to point out that there is little evidence that Haydn was Mozart's teacher. Mozart was mostly taught by his father. Furthermore, he was in his late twenties and already fully educated by the time he first met Haydn. Haydn's music, however, greatly influenced Mozart (Haydn was, after all, one of the most recognised composers at the time), and Haydn appears to have acted as some kind of mentor for Mozart on occasion (lending him a book on counterpoint is the only thing I am aware of)