October 16. 2025
From antiquity until the late 1800s, geometry was considered a self-evident truth. Non-Euclidean geometries arose precisely from the conviction that if the Fifth Postulate was not accepted, it would lead to a contradiction, which would then prove the postulate.
In fact, it was later discovered that it was possible to create perfectly logical (though not necessarily true) geometries without that postulate. This might have remained a simple intellectual exercise, but it was understood that these geometries could also be applied to reality.
In short, it was discovered that what appears self-evident does not necessarily mean it is true.