Who wrote the best music is a far more subjective matter. I am interested in of the most famous composers of the Classical and Romantic periods, which ones wrote the most technically difficult pieces to play. For instance the third movement of Beethoven’s Moonlight Sonata sounds difficult to play (the version I’ve been listening to is around 15 mins so I am not sure if it is the complete version or not). I don’t play piano so I am not always sure what music is more difficult to play and has the more demanding time signatures and such.
I’ve always heard that Rachmaninoff is tough (yes, I’ve seen Shine!) - but his Piano Concerto #3 is supposed to be very technically challenging. It’s also a damn fine piece of composing.
I second Rachmaninoff. Some of his solo piano works are so complex, you’d swear you were hearing two pianos, or at least one piano, four hands.
cool thread.
You might get more responses in Cafe Society.
Well if a mod agrees they can move it.
John Cage did a few pieces where the two hands are not playing in the same key. I have to imagine that’s extremely difficult to play.
I don’t play piano, but I’ve always heard Sorabji wrote some of the most difficult piano pieces, Opus Clavicembalisticum in particular.
Agreed, provided we’re allowed to call it “music.” 
Also these:
Prokofiev, 2nd Concerto
Rach Second
Rach Third
Aloysiuos Bertrand, Gaspard de la Nuit
Beethoven, Hammarklavier Sonata
Chopin, Prelude in G minor
Liszt Etudes, Transcriptions
Scriabin, Sonatas 5 - 10
Charles-Valentin Alken, Concerto for Solo Piano, op 39 or 76
Mily Balakirev, Islamey
Ravel’s Gaspard de la Nuit is considered to be one of the harder pieces in the solo piano repertoire (it’s possibly a bit more modern than you’re looking for, though).
Ah, yes, Ravel. Most embarrassing.
Not exactly a “technical demand”, but I seem to remember my daughter complaining that Lizst must have had huge hands.
There’s the story – I have no idea if it is true or not – that in order to show up a bragging pianist, Mozart once wrote a short peice that was literally impossible to play with only two hands, having one hand playing high, the other low, with a single note in the center of the keyboard at the same time.
(When the frustrated pianist claimed that it was impossible to play, Mozart sat down, playing the piece with two hands, then leaned down and playing the offending single note with his nose.)
If you don’t know the trick, this must be one of the hardest piano peices every written.
According to a factoid I once read in USA Today, the hardest piano piece was something by Paderweski (I’m sure that’s misspelled), as no one but him could figure out how to play the piece for 20 years. Interestingly enough, one of the people he taught how to play the piece was a fellow by the name of Harry S. Truman.
How about Conlon Nancarrow? From what I’ve read, he composed for the player piano, as puny humans were incapable of playing his compositions. His music influenced Frank Zappa’s compositions for the Synclavier.
Beaten to the punch by this much 
!
I should say, the bulk of Nancarrow’s work doesn’t count, as it was specifically written for the player piano, and not human pianists. Most of his late studies wouldn’t be difficult for a human to play, they’re simply impossible. However, his “Three Canons for Ursula” must be pretty damn hard. Apparently the second was thought to be impossible, though some pianists have tackled it. I have a recording and it sounds insane.
Oh and ultrafilter, ISTM that a piano piece in two keys would not be especially hard to learn - I used to play the piano, learned a bit of Bartok, I’m pretty sure some of it was bitonal. Much more challenging would be playing with the two hands at different tempos. Which brings us back to those Three Canons.
Liszt transcriptions of portions of Wagner’s operas (such as the overture to Tannhauser and the fire music from Gotterdammerung) are supposed to be very hard to play because of the difficulty in translating the orchestral texture into a piano piece. I heard a recording of these once, and I was pretty amazed at the sheer athleticism required to get through one of these pieces.
Richard Strauss also tended to think orchestrally, even when writing piano accompaniments to his songs, so they tend to be difficult as well.
According to my accompanist, though, the trickiest thing he ever attempted to play was the piano part in Saint-Saens’ Organ Symphony.
I once read that Brahms’ transcription for piano left hand of the Bach Chaconne from the Partita #2 for Unaccompanied Violin, BWV 1004, is not only supremely difficult but was intentionally done that way to make it difficult for pianists with a left hand of merely human proportions.
Apparently Brahms had enormous hands. He would have made one hell of a baseball catcher, and made more money besides. 
I’ve seen Liszt’s hands (actually, plaster casts thereof) in a Budapest museum. They were long and thin, but nothing like the chick’s with the “man hands” on Seinfeld.
That said, they must have been gigantic for his day. Liszt simply had an incredible finger spread that allowed him to play tenths (a spread of ten notes) on the keyboard.
Check out the photos halfway down on this site, comparing the hands of Beethoven, Liszt, and Chopin.
I seem to recall reading the same thing about Carl Maria von Weber.