While he obviously has some intelligence, he's still very much an idiot. One just has to look at his immature and mostly incoherent public relations and business decisions to see that. Further, as smart as he thinks he is, he's not designing rockets. He pays much smarter people than him to do that for him.

People will often say that very rich people MUST be extremely intelligent, after all - they have more money than you!

I would counter that sociopathy and the ability to work with a complete lack of morals is what allows people to truly become wealthy. There's no such thing as an ethical billionaire.