Euclid's parallel postulate looked less self-evident than his other four, and mathematicians spent two thousand years trying to derive it. Why is the failure one of the most productive in the subject's history?

C. Because denying it produced consistent geometries, not contradictions

Assuming the negation produced no contradiction but a coherent geometry, spherical and hyperbolic, so the postulate was independent rather than derivable. Axioms became choices with consequences instead of self-evident truths, and the non-Euclidean cases turned out to describe the Earth's surface and curved spacetime.