All of us have moments from our past that make us cringe in embarrassment and memories for which we'd like to go back and give our younger selves either a stern talking-to or an encouraging hug. That's even true, apparently, if you spent your 20s founding a billion-dollar company that would one day make you one of the world's richest people.

This week, Bill and Melinda Gates participated in a live event hosted by Hamilton creator Lin-Manuel Miranda. When it came time for the question-and-answer section of the evening, the billionaire philanthropists fielded a query from a very special fan. Speaking via Facebook Live, a young leader by the name of Mark Zuckerberg asked, "If you could go back and give your younger self one piece of advice, what would it be? Asking for a friend."

Bill Gates didn't have to scratch his head long to come up with an answer. According to Business Insider, his response was to express regret that he once thought traditional smartness, in the sense of a high IQ, was all you need to succeed in life:

I was so naive about different skill sets. I thought if somebody had a high IQ, they could be good at everything. And that idea that you had to blend different skills together, that still surprises me. This notion that there was just this simple idea of smartness, and it could solve everything -- I wish I had known better than to think that.

The smartest people in the world know IQ isn't enough.

There are several reasons why that's a great answer, and one that people who fancy themselves blessed in the brains department would do well to listen to.

First off, because it's simply scientifically true. While we tend to think that smarts equals IQ, Harvard research shows there are actually six other types of intelligence, including everything from the "bodily kinesthetic intelligence" of gifted athletes and dancers to the "intrapersonal intelligence" that gives us the self-knowledge to understand and manage our own feelings, preferences, and quirks.

Traditional intelligence is certainly handy to have, but it's also possible to achieve great things with less raw computational horsepower and higher levels of these other skills. And if you really want to get to the very top, as Gates suggests, it's probably essential not just to hone your IQ but to work on complementary intelligences like EQ as well. (Alibaba billionaire Jack Ma insists the key to greatness is actually something he terms "LQ.")

Want some more evidence? Scientists recently found that leaders with super high intelligence are often actually rated lower by their teams, who struggle to communicate with the egghead boss. Being an excellent leader isn't just about having the biggest brain then. It also requires the complementary emotional and communication intelligence to convey the amazing ideas in your head and inspire others to help you make them a reality.

So smart aspiring leaders, listen up! Gates has been in your shoes and certainly knows what he's talking about. Don't rest on your laurels or get cocky about your high IQ. And certainly don't think the big brain you were gifted with is enough to allow you to coast your way to greatness. Being smart is a fabulous head start in life, but it's only a start. We all need to appreciate and cultivate other types of intelligence as well.

Curious about Melinda Gates's answer? Check out the complete BI post.