It's the converse that tends to be true, but many people have trouble distinguishing between converse and contrapositive. Rich people tend to be smart.
There are lots of bright ideas. The few that turn into successful companies are the ones that, at a few critical points, didn't fail. A good way to fail is to make mistakes and do nothing. So, to avoid failure, one must learn from mistakes, which tends to make people smart and is something smart people tend to do.
The extra axiom necessary for showing smart->rich is risk taking. Smart people who don't take a chance and do something drastic are no more likely than anybody else to get rich. There are people who pay others to be smart, but they generally don't pay much more than a normal salary.