This question already has an answer here:

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?


marked as duplicate by Conifold, Community Nov 10 '16 at 4:11

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.


Because it was considerd (probably well before Euclid) as not as "intuitive" as the other postulates.

See e.g. :

as well as the introduction to :

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.


Not the answer you're looking for? Browse other questions tagged or ask your own question.