The Mayas can and did think the world was flat, and not only that, they thought it was a straight plane in all directions. In what is now modern day Brazil, they attempted to prove this by constructing tall pyramids as high as modern technology would allow. They did this all over the country.
The theory was: if the world was flat, then the tops of pyramids built long distances from one another would still be visible to one another through binoculars. When these experiments failed, the Mayans realized they were wrong. Around this time, the Spaniards had come over across the Atlantic with proof that the world was in fact round, and Mayans started practicing European science.