[bsder]

> What about the idea that parallel lines do not intersect and that there is exactly one line through a point parallel to another given line? These were thousands of years old and well accepted until pretty recently.

Actually, that axiom made even the ancients uncomfortable. There were lots of attempts over the centuries to "prove" or "disprove" it.

The fact that violating it can still produce a self-consistent geometry was what was stunning.