Mathematics. No problems there because the wisdom of the ancients is still true.

Actually, a surprisingly large amount isn't. For example, the entire use of infintesimals had to be rethought during the mid nineteenth century and replaced with rigorous constructions over the real numbers. It wasn't until a century later that a rigorous use of infitesimals was constructed and it looked pretty different from the version used by Newton and the people after him.

Similarly, the question of how polyhedra's Euler characteristic behaved advanced through a series of proofs followed by counterexamples to the "proofs." (Although my understanding is that it wasn't quite as extreme as what occurs in Lakatos's "Proofs and Refutations.")

Nicomachus in his treatise on perfect numbers (from around 100 CE) made a number of incorrect statements that took almost a thousand years to be shown to be wrong.