He is immature, obstinate, rude, socially retarded (Possibly mentally so. Not 'crazy'. He's not. His mother had him tested). He is not nearly as intelligent as he thinks he is and there would be no show without him.
The only glimpse of reality concerning his character is the flashback to when he and Leonard met. The ex-roommate spray painted "Die Sheldon Die" on his bedroom wall. In reality, someone would have put Sheldon's lights out long ago...or flat out killed him. In fact, it is good that he associates with inherently non-violent 'friends' and exists within an academic environment in California. He is thus insulated from different segments of our culture who would take pleasure in doing him harm.
But I love the show. Seen all the episodes.
You bring up something that reminds me of something else I like about the show….they are refreshingly honest about the fact that Big Education is about only one thing….MONEY. The Deans and administrators are all about the money, the characters admit at times their research is a money scam…..all of this is of course true about big eductation….and here’s a show with 6 well paid academics, and rarely do any of them teach anyone anything….
There's no show without him, as played by Jim Parsons. I've heard that the actor playing Leonard was the original cast for Sheldon, and that he insisted they hire Parsons. I think that actor Johnnie Gilecki is the weak link in the show, but give him credit for that suggestion! Also, FWIW, I think the best comedic timing by far goes to Wolowicz….
Mrs. Rightsmart works with young adults like Sheldon. She says this show portrays the character perfectly. She has even used clips of the show to show her students how not to behave in social situations.