Eugene's posting in the Siegel thread on one of Siegel's next to impossible pieces prompts this thread.
For some time I have collected extremely difficult works for classical guitar, and I have started a similar collection for solo mandolin. I look at these from time to time, mainly as a source of amusement, but occasionally, of inspiration. To be clear I am speaking of pieces that are:
--extremely difficult for people who have professional level techniques. The rest of us may find some piece difficult, but what I am talking about is virtuouso level for virtuosi.
--the piece actually has to be performable as evidenced by an actual performance, or failing evidence of this, a published (not mss) score. For example, as Neil Gladd has pointed out, Aubrey Stauffer made many arrangements for solo mandolin for which no one knows if he actually gave a performance -- but he did publish the arrangements and some of these are truly (truly) difficult.
--the piece is for SOLO mandolin ORIGINALLY. This rules out extremely difficult parts for mandolin in chamber works (e.g. Zappa, the Ranieri concerto) or arrangements (various Paganini caprices).
So, to get the ball rolling, a piece that I consider nearly impossible, or at least extremely (extremely) difficult is Ernesto Rocco's "Serenade". We know it is performable because Rocco (and one or two others) played it, and it certainly was published. In his book Paul Sparks singles out the Serenade as an example of an extremely difficult piece of solo mandolin music. It certainly is for me -- I can get through the first page or so, but after a while, it is too much.
I would be interested in other examples. Among people who post here I am sure that Michael Hooper, Joe Brent, Chris Aquavella, Richard Walz have their favorite impossible pieces. I'd also love to know which pieces that Gertrud (or any number of Germans) finds difficult, ditto Alex and his students, ditto Carlo.