Many had tried in vain to prove Euclid's parallel postulate using the existing axioms and theorems. But my question is that what is it about the parallel postulate that made it seem so much like a theorem that mathematicians just felt uncomfortable to accept it as an unprovable assumption?
Because it was considerd (probably well before Euclid) as not as "intuitive" as the other postulates.
See e.g. :
- Boris Rosenfeld, A history of non-euclidean geometry (1988; original ed.,1976)
as well as the introduction to :
- Gerolamo Saccheri, Euclid Vindicated (1733) : Edited and Annotated by Vincenzo De Risi (2014) :
We know of early attempts to prove this postulate in Classical Antiquity. In fact, these attempts probably preceded the composition of the Elements, suggesting that Euclid perhaps assumed his Fifth Postulate unwillingly, because he could not devise the proof for it that he sought.