Have you ever been to see somebody you hadn't seen for about twenty years and they joyfully proclaim, "you haven't changed a bit!"
That's probably bull-hockey, but we seem to be wired to want to recognize personality traits and hang onto those despite any conflicting evidence. You and I have probably changed a great deal in twenty years, but there may, in fairness, be some things that have remained more or less the same.
When it comes to a composer, one can often observe similar ideas across the board in their works, too. This is a bit harder, given so much musical information over such a wide swath of time. But it can still hold, and, even it it oversimplifies things, making a list of those frequently encountered traits in a composer's music might give us some insights into the way they communicate musically. Here's the start of one for Beethoven:
Beethoven likes to work with short musical ideas (except when he doesn't). These can be subject to endless manipulation, and by changing a single note, can send the composition spinning off in a completely different direction.
Beethoven enjoys exploring harmonies by full, rich, arpeggiated passages, usually in the development section and/or codas, making active, hair-raisingly virtuoso moments out of what could otherwise be simple chord progressions. Although, for a definition of simple, see the last paragraph.
Beethoven can work within predictably classical phrase structures. But often he willfully stretches a passage out, or transitions suddenly from one thing to another. Ideas or keys can also collide roughly. Sometimes Beethoven does this to play with our expectations, even tease us, amuse us, or annoy us. These can be experienced as transgressions against all things good (as his contemporaries often felt) but there is no reason to imagine that Beethoven wasn't trying to let us in on the humor or the exploration, so long as we are willing to come along.
Beethoven is a great musical architect. Little details often become major plot points later on. No transitional passage lasts longer than the material wants it to. Even his endings can, far from the conventional image of the repeated blasts, simply evaporate. In fact,
Beethoven's music shows enormous variety. It hardly fits in the popular image of him. And if you have time to really listen to his music, you'll notice that. There is little that can be said of him that would apply to everything he wrote; in fact, some of his music will show the opposite quality. It suggests he was always interested in trying new things, not repeating himself, and willing to go where the material led him, rather than coming at a piece with a set of assumptions about the genre or style he was supposed to be working in. A symphony does not have to be grand, or a sonata small. Each piece is its own creature.
This is only the start. Given a whole semester to think about his music has challenged some of the things I and my teachers thought about Beethoven in years past. Some ideas hold, others are being "updated." For example, the way he uses the sforzando mark. But I'll save that for later.
The man did put an enormous number of marks on paper. And it is amazing what we can do with all of that.
Douglas Adams once remarked (trying to express admiration for Bach) that "Beethoven's music shows us what it was like to be Beethoven" (before suggesting that Bach's music "shows us what it is like to be the universe"). I don't know, though. It might seem small by comparison, but that fellow had a lot to say. And being Beethoven must have been quite something.
He can have it, though. Along with my admiration. And my attention.