Parallel postulate
Mathematicians found that when they replaced Euclid's fifth postulate with this axiom, they were still able to prove many of Euclid's other theorems. One way to imagine elliptic geometry is by thinking of the surface of a globe. On a globe, lines of longitude appear to be parallel at the equator, but they all meet at the poles. Late in the 19th century, elliptic geometry was shown to be consistent. This proved that Euclid's fifth postulate was not independent of the other postulates. After this, mathematicians mostly stopped trying to prove the fifth postulate from the other four postulates. Instead, many mathematicians began studying other geometries that do not follow Euclid's fifth postulate.