"If aliens visit us, the outcome would be much as when Columbus landed in America, which didn't turn out well for the Native Americans," he said. "We only have to look at ourselves to see how intelligent life might develop into something we wouldn't want to meet."
He also speculated that aliens' capabilities "would be only limited by how much power they could harness and control, and that could be far more than we might first imagine."
It might even be possible for aliens to harvest the energy from an entire star, he added.
"Such advanced aliens would perhaps become nomads, looking to conquer and colonize whatever planets they can reach," Hawking said.
But though Hawking may think that looking for aliens is not a wise choice, his daughter Lucy, with whom he has written a children's book, told Sawyer that she disagrees.
"We have a fundamental disagreement on that one," she said good-naturedly. " Because I think if they're so smart that they could destroy us, then it doesn't matter if we look for them or not. Because if they're that clever, they know we're here. They can find us whether we look for them or not."
But Lucy said she and her father agree on many other things.
"We like the bustle, we like the excitement, we like the lights, we like the company," she said. "We like all the complicated things that human civilization has created."
As Hawking's children navigate the many complexities of human life, he told Sawyer that he's offered up three pieces of advice.
"One, remember to look up at the stars and not down at your feet. Two, never give up work. Work gives you meaning and purpose and life is empty without it," he said. "Three, if you are lucky enough to find love, remember it is there and don't throw it away."
If you want to learn more about the 5-day World Science Festival, click here.