A growing body of research tells us that success is not so much a function of raw intelligence, but of work, circumstances and time applied to a specific skill.

It's a theme that helps power the American meritocracy and drive the dream that anyone can make it if they just try hard enough – even in the knowledge economy.

But it may not be entirely true.

A new study from Jonathan Wai, research scientist at Duke University, finds a strong correlation between brainpower and success – especially wealth. As the study states: "the top one percent in wealth highly overlaps with the top one percent in brains."

(Read more: Top Universities for Billionaire Alumni)

About 45 percent of billionaires are in the top one percent of cognitive ability, the study states. Billionaires were generally smarter than Fortune 500 CEOs, where 38.6 percent were in the top 1 percent of brains. Senators ranked just below that, with 41 percent, along with federal judges 41 percent. Members of the House were less smart, with 21 percent. (The smartest sub group of the American rich and powerful are male Senate Democrats).

Even among billionaires, however, there are wide variations in brainpower. Billionaires who made their fortunes from investments and technology were far more likely to be in the top one percent of brains; 69 percent and 63 percent of them were brain-one-percenters. Billionaires who made their money in fashion and retail, as well as food and beverage, were less brainy: with 25 percent and 23 percent of them in the brain elite, respectively.

So higher brainpower is not just concentrated at the top: it's concentrated among certain segments of the top.

There is one caveat to the theory. The study measures cognitive ability by attendance at 29 selected "elite colleges," which, it says, typically requires high test scores and therefore indicates high intelligence and high IQ. "Elite college attendance indicates a high general ability level," the study says.

(Read more: Who Says Money Doesn't Buy Happiness?)

But not always. As the study concedes, factors other than test scores and IQ can play a role in admission to elite colleges, like legacy preferences, wealth, sports scholarships and other attributes. And some very smart people don't go to the elite schools for financial or other reasons.

An earlier study from a research scientist finds that "IQ really has no relationship to your wealth."

Still, the Duke study found that fully 88 percent of the Forbes billionaires graduated from college. I guess Bill Gates and Mark Zuckerberg are more exceptions than the rule.