The old saying "curiosity killed the cat" is a warning against sticking your nose into business that might get you into trouble. But as a leader, curiosity is one of the most valuable tools you can have.

That's the finding of to a 2015 PwC survey of more than a thousand CEOs, cited in Harvard Business Review. "With curiosity comes learning and new ideas. If you're not doing that, you're going to have a real problem," famed tech entrepreneur Michael Dell said in his response for the survey.

Leaders no longer should give the impression (or believe themselves) that they know it all. "Welcome to the era of the curious leader, where success may be less about having all the answers and more about wondering and questioning," Warren Berger, author of the book A More Beautiful Question: The Power of Inquiry to Spark Breakthrough Ideas, writes in HBR. "As Dell noted, curiosity can inspire leaders to continually seek out the fresh ideas and approaches needed to keep pace with change and stay ahead of competitors."

Admitting you don't know everything can be difficult. But the search for new paths--new products, new revenue streams, new talent, new efficient ways of building, creating, and getting things done--is part of a leader's job. "These days, a leader's primary occupation must be to discover the future," Panera Bread CEO Ron Shaich told Berger. "[It's] a continual search."

While researching his book, Berger says, he found that the most innovative leaders used curiosity "as a starting point to reinventing entire industries." He says Jack Dorsey came up with the idea for payments company Square after seeing a friend lose a big sale because he wasn't able to accept credit cards.

"Dorsey wondered why only established businesses, and not smaller entrepreneurs, were able to conduct credit card transactions; his search for an answer resulted in Square, a more accessible credit card reader," Berger writes.

Curiosity is all about asking questions and wondering why things are a certain way. Berger says leaders can use curiosity not only to explore new and uncharted waters but also to have a breakthrough on old, or overly "familiar confines." 

The "curious leaders tend to try to see things from a fresh perspective. The ones I studied in my research seemed to have a penchant for bringing a 'beginner's mind' approach to old problems and stubborn challenges," he writes. "They continually examined and re-examined their own assumptions and practices, asking deep, penetrating 'Why' questions, as well as speculative 'What if' and 'How' questions."

If you think some people are more naturally curious than others, you're right. But Ian Leslie, author of the book Curious, says that curiosity is "more of a state than a trait." You can attain a curious state by exposing yourself to new information, opinions, and experiences.

"We all have the potential to be curious, given the right conditions," Berger says.