Despite there once being widespread belief in a spherical world, most of the advanced understanding of the universe, conducted by the scholars at Unseen University and its contemporaries in Fourecks, the Agatean Empire, and Krull, actually confirms this hypothesis. Krullian chelonauts have descended below the Rim and confirmed this to be the case. It is also well-known that Rincewind and Twoflower were sent over the edge in an unfortunate accident, which set the Turtle Gender Project back by about a decade (see chapter 42 in "What I Did On My Holidays").
Belief in a round world never occurred around the Rim, where the Rimfall was part of everyday life. However, in some of the isolated islands and towards the Hub, the uneducated were often of the understanding that the world was spherical, no doubt deceived by the motion of the sun around the disc appearing to be the world moving around the sun rather than, as is now understood, the sun moving around the Disc, a belief widely spread by the religion of Omnianism. Due to the militant proselytization and their rigid adherence to their religious texts, Omnians held tightly to their beliefs and attempted to spread them despite scientific facts proving otherwise.
I don't even understand how this is a question. One only has to go to the end of the rim to verify the truth of the matter. We indeed are carried on the back of a giant turtle. Now obviously, his (or her) name as Great A'Tuin is completely subjective, but yes, we do stand on the back of a giant turtle.