Whoosh.
OP, I think you’re approaching this from the wrong angle. Beethoven’s music isn’t popular because he was considered a genius; he’s considered a genius because his music was popular. If he woke up from cryogenic suspension tomorrow and announced that he’d written a tenth symphony, people wouldn’t automatically think it was good (well, some would).
However, they would expect it to be good, since his other ones were.
Beethoven forms the bridge between the Classical and Romantic periods in the history of music.
At the beginning of his career, Beethoven was working in the Classical tradition, which emphasized decorum, good taste, pleasant singable melodies, conventional harmonies, and traditional forms (which risked being formulas). Music was polite entertainment, even background noise, and wasn’t supposed to surprise, shock, or upset people.
Beethoven (maybe not quite singlehandedly, but more so than anybody else) changed all that. As he got further into his career, his stuff got wilder and woolier, more expressive, more forceful, more individualistic. Each new symphony or other major work was an individual creation. Beethoven helped usher in the idea of the composer as an Artist, a tortured genius struggling to bring forth the great works that he has within him, to break the molds and forge new paths. It also didn’t hurt the mystique that many of his greatest works were written after he went deaf.
From listening, I can tell you that Beethoven’s music has its own individual character; no one else’s works sound quite like his.
Beethoven is a genius because of 2 things:
Ode to Joy
Moonlight Sonata 3rd Movement
Oh and who else could compose and play the Suicide Symphony? 
FWIW, Schulz has said that his own favorite composer was Brahms, but he made Schroeder a Beethoven fanatic because it was funnier that way.
To say nothing of the movies with the slobbery St. Bernard.
“It’s a sobering thought, for example, that when Mozart was my age, he’d been dead for three years.” – Tom Lehrer
Actually fourteen years for me.
Only one (Fidelio). But it’s a doozy.
No, no! It was P.D.Q Bach, and it was called the Pandemonium!
“the loudest instrument ever created, the pandemonium, but he wisely skipped town before the instrument’s completion, having sensed with uncanny accuracy, that the Pavilion of Glass was perhaps not the most felicitous location for the inaugural concert.” – www.schickle.com
I am a Math Geek and have very little (if any) artisic bones in my body. My musical tastes must be low considering I was a metal head in high school and I like pop40 stuff today.
However, Many moons ago I listened to classical music to see what all the hubbub was about. I had seen Amadeus before and REALLY REALLY wanted to like Mozart.
Mozart was ok…but BEETHOVEN! My God, everything I listened to from him was just great! It’s hard for me to explain…but listening to his stuff was a pleasure. That man knew how to write music.
Might have? The tour he did as a child seemed to show that he already had such a career.
Mozart was the first composer to live off selling his music instead of patronage, which was not by choice. (And he wasn’t poor, unlike what was shown in Amadeus.) When Haydn toured England, and wrote his later symphonies, he seemed excessively interested in the attendance at the concerts and how much money they pulled in. Beethoven staged concerts to raise money, and also got some from the sale of sheet music by his publisher.
This. The first movement of Eroica is longer than the standard symphony of the time. He also broke the structure of the symphony, and got rid of the Minuet movement. The Ninth was the first use of a chorus in a symphony, and the late string quartets could well have been written by someone like Glass - they are not only modern, they’d be revolutionary if written today.
I watched an interesting DVD from the BBC called Eroica, which is about the first performance of it for his patron. Almost the whole thing is the performance. Through the placement of various characters in the room, it shows the reactions of shock to it.
I find Schubert’s symphonies remind me of Beethoven’s, but there is of course a direct influence there.
I’m no musical expert, either. But I note that Beethoven’s music reflected the revolutionary times in which he lived: the French revolution and the rise of Napoleon. His music was also influenced by the grimmess of his childhood (he had an abusive father) and his hearing problems.
We are so familiar with his Symphony No. 5 that we don’t hear it the way his contemporaries did: a ferocious, cutting-edge piece of modernistic music. Beethoven combined the Enlightenment spirit of individuality and the spirit of revolutionary change (characterized by Europe) with his own personality.
But, of course, other composers wrote cutting=edge music. Debussy wrote the first atonal music, and for him timbre was as important as melody, rhythm, and harmony. His Nuages shows his conception of timbre as a thematic element. He rejected major/minor modes in favor of non-traditional pitch collections. In Nuages, we hear undulating winds playing an ostinato motive (a repeated motivic pattern).
Influenced by Debussy, Stravinsky avoided the traditional pitch collections, but his music is most characterized by asymmetrical rhythms. When the Rite of Spring was first heard, most critics were very critical and many of the attendees at the concert booed the performance. Now, it is recognized as a masterpiece. His asymmetrical rhythms was the basis for much of the new music genres.
So, Beethoven, Debussy and Stravinsky were innovators. They broke the mold that existed. I don’t see how Beethoven was more a genius than those two, or others before who broke existing molds. After all, isn’t that part of the definition of a genius: one who is able to step out of the box and envision stuff never even thought of before?
Yeah, but that’s only part of it—you also have to be good. 
Crap doesn’t cease to be crap just because no one’s ever crapped that particular crap before. Beethoven didn’t just break new ground; he did so by writing really good music.
For more on Beethoven’s symphonies, I liked this podcast.
An excellent analogy 
Replace ‘guitar’ with ‘orchestra and string quartets’ and you’ve got a description of Beethoven.
I was going to mention the fifth, in the same way - just as with the RIte of Spring, not matter how intimately you know the piece, it does not in any way relent in its ability to grab you by the neck and shout 'you are going to LISTEN to what I need to say!!
That’s not the definition of musical genius, but it’s what kind of genius is present in Beethoven’s music.
(A tangential point: the controversy of the Rite at its premiere was at least as much dues to the choreography as the music.)
The 19th century music critic Eduard Hanslick once said of listening to the first movement of Brahms’ 4th Symphony that “I had the feeling that I was being given a beating by two incredibly intelligent people.” This is something that Beethoven really excelled at and it is as much a cornerstone of his genius as something that can, and has, be held against him.
A few months ago, I did a Beethoven marathon. Over the course of a few days, I listened to all his piano sonatas, symphonies, piano concertos and string quartets in chronological order. That left me (and my wife) quite exhausted, and a very unexpected result of my binge was a new-found appreciation of… Haydn! Yes, he’s often trite, but he knew humility and restraint in a way that Beethoven couldn’t have conceived.
All of these posts, and nobody has mentioned that in later years Beethoven was deaf. Sure, by then he was already the world’s most accomplished composer, but he kept churning out masterpiece after masterpiece . . . that he himself could never hear. (After conducting the premiere of his Ninth Symphony, they had to turn him around so he could see the audience wildly applauding.) Imagine a painter continuing to create masterpieces after going blind. This is beyond mere genius.
And a measure of his true greatness: You could eliminate all of his “Greatest Hits,” and he still would be considered a Giant.
See post #22 by Thudlow Boink.
I have heard Beethoven got really radical with his final string quartets, but now I’m really intrigued. Anything in terms of pieces or recordings you guys might recommend?
I was blown away by Arvo Part last year and am interested in broadening my musical horizons. Also considering some Philip Glass.
The ultimate radical string quartet is the Grosse Fuge I mentioned above.
This piece is radical in how he takes a very well established form that was considered at the time a bit out of date, and he takes it to its unfathomable extreme. Most Bach fugues are a few minutes long at most. This is 16 minutes, and it’s 16 really, really dense minutes. And, he gets this out of a very simple musical subject.
The link above is by the Alban Berg Quartet. They have a very good box set of Beethoven’s quartets.
Another example of a really radical mindfuck is his last piano sonata. For those who can read music, it’s worth taking a look at the score for the second movement:
http://imslp.info/files/imglnks/usimg/0/07/IMSLP00032-Beethoven__L.v._-_Piano_Sonata_32.pdf (scroll down to page 603 and pay attention to the time signatures.)
I read someone comment about that score to the effect that it’s like zooming into time itself.
Here’s Claudia Arrau playing it:
Wow. At 5:10 it sounds a little like he’s playing ragtime in a western saloon. Bizzare.
ETA: WTF?!?!?!?! 6:57 TOO!!! Jesus, you weren’t kidding.
I think here we’re getting into matters of taste though. I would judge that Mozart is held in the same esteem as Beethoven, or close to it, but his music absolutely leaves me cold. OTOH Beethoven’s and Wagner’s music is a delight to me. So is Bach, just to demonstrate that my taste is not based on a fixation on the Romantic era in German arts.
Edit: I complained about page numbers but I now see that you didn’t mean PDF pages, you meant those numbers in the upper left corner.