The shape of the earth was one of the first theories verified using the modern scientific process. Europeans screwed the math up pretty badly and grossly underestimated the size of the planet, but Greek and eastern mathematicians pretty much nailed it.
No scholar of any real note or relevance believed that the earth was flat as far back as 500 BC.
But everyone else did.
Like climate change deniers of today the resistance to the concept of a spherical earth was not led by scholars. It was led by interests invested in the concept of a flat earth in very much the same way climate change denial is being promoted by special interests now. The "round earth" theory was denied mostly by religious leaders invested in discrediting the scientific process, and climate change theory is being denied mostly by oil and gas companies who stand to lose a great deal of money if it gains popular acceptance. In both cases denier factions used very similar strategies to hold up the advance of these theories.
The concept of a round earth was mathematically proven more than two and a half thousand years ago using Pythagorean mathematics, but until a couple centuries ago very few common folk could even add, much less understand what at the time was considered advanced mathematics. Round earth deniers were able to play on that lack of understanding in exactly the same way climate change deniers are playing the complexity of climatology against the general public now. After all... how could the earth POSSIBLY be anything but flat? It just stands to reason all the oceans would drain off the edge.
Round earth deniers used "common sense" to debunk the mathematics that most people didn't understand. The contrast in messages between scholars and layman was profound. While scholars were insisting that the universe was something complex and outside most people's understanding, deniers were able to mock that contention as pompous and arrogant.
Given the choice between...
"I know you don't understand it, but you must believe me the world is round," a message which made people feel small and ignorant...
OR...
"Bah... those guys are jerks who think you're stupid, OF COURSE the world is flat," a message which allowed them to keep their sense of understanding and control...
...Most people quite naturally chose to believe the latter. Flat earth believers formed the overwhelming majority of the public, in open contempt of scholarly understanding, pretty much right up until Magellan proved the earth was round by circumnavigating it in the early 16th century, about two millennia after mathematicians had first proven the theory.
The problem, of course, being that we don't have two thousand years to realize that maybe the scientific process works this time, and if it's going to take a practical demonstration to prove it the way Magellan did we're completely fucked because we don't have a spare earth lying around to destroy.
