Why was Wittgenstein great?

I am not looking for subjective opinions here, ie “was Wittgenstein right or wrong in his beliefs?” I am looking for the sort of straightforward answer an encyclopedia might give: why is Wittgenstein considered such a great philosopher?

I ask because I have been able to digest brief descriptions of most other philosophers with ease, yet I have never heard a clear description of why Wittgenstein is considered one of the most important philosophers of all time.

Basically, he’s considered a great philosopher because his work influenced a lot of modern philosophy.

I think it had more to do with his personal influence than his writings. Apparently he was a very charismatic teacher, and most of the next generation of British philosophers were former students of his, still under his spell.

… because he was a beery swine, who was just a sloshed as Schlegel.

Aw, now you see? I’ve been waiting for more replies since there were no replies, before I posted that! And then I’m beaten to the punch!

He argues quite well that some questions don’t actually involve problematic concepts but problematic language. Hume had a somewhat similar approach, and gets his share of esteem – and anyone who got their first “there’s simply no ‘there’ there” head-smack by way of Wittgenstein on one of the Big Questions might well feel he’s THE go-to exemplar of philosophy as practical clarification.