Definitions are invented, theorems are discovered. The Pythagorean theorem is a discovery about Euclidean geometry. But in order for that discovery to be meani

Definitions are invented, theorems are discovered. The Pythagorean theorem is a discovery about Euclidean geometry. But in order for that discovery to be meaningful, one must first invent Euclidean geometry, or at least something sufficiently similar to Euclidean geometry.