He didn’t actually write one, of course — but he did write sketches, and Beethoven scholar used them to flesh out a conception of what the first movement would have sounded like:
I have always enjoyed this, just as I enjoy the attempts to realize the fourth movement of Bruckner’s Ninth Symphony.
This is not Beethoven, exactly — but if you have never heard it, you might be surprised. It’s neat.
[Cross-posted at The Jury Talks Back.]