Ab initio calculations of the basic properties of solids have advanced significantly, and it is now possible to simply access a crystal structure database, and from the given constituent atoms and their positions, calculate reasonably accurate values for elastic constants and thermomechanical properties that may be derived from them. However, progress has been impeded by a unique discrepancy involving the sign of one of the elastic constants of an important material: Al₂O₃. In this letter, this longstanding discrepancy is resolved with experimental measurements.