What they didn't know is that the New World was in the middle of the ocean between Europe and Asia. Columbus wasn't worried about sailing over the edge, but his crewmen were worried about running out of water. But Chris did have a map, even if he didn't realize what exactly the map showed. He thought it was India, and thought the world was more pear shaped than round.
Just as good - the consensus today is that people back then believed the world was flat, even thought the evidence clearly shows that they knew better back then. Clearly a modern consensus can be wrong.