Why did mathematicians find Euclid’s parallel postulate difficult to accept?

Mathematicians found Euclid’s fifth postulate difficult to accept because, unlike his other four postulates, it did not seem entirely self-evident. For centuries, geometers attempted to prove that it was not a necessary postulate but could instead be deduced from the other axioms of Euclidean geometry.12

The reluctance to accept the postulate was also rooted in deep philosophical beliefs. Many mathematicians, influenced by Immanuel Kant’s view that geometric statements were necessarily true with empirical content, believed that concepts like the existence of similar figures of different sizes were self-evident. Furthermore, researchers like Johann Heinrich Lambert demonstrated that rejecting the postulate implied the existence of an absolute unit of length, which contradicted the prevailing view that units of length were conventional.2

It was not until the 19th century that the discovery of non-Euclidean geometries by mathematicians such as Nikolay Lobachevsky and János Bolyai proved that consistent mathematical systems could exist without this postulate.1