There's a great post about this here

Basically, everyone back then already knew the world was round; mathematicians in Europe knew how long the voyage west to Asia would take, assuming there was no continent in between, that is, they were sure he would die because his ship couldn't carry enough supplies for such a voyage; when Columbus did find land, people realised it was a new continent. So it's not like everyone went, omg, the world is round! More like: aha, a new place to find gold in, and even better: without large, modern-equipped Chinese armies. Let's go.