There is a prevailing dispute on methods to determine surface energies of surfaces involving a solid. The most widely used methods are the surface component (STC) theory and the equation of state (EQS) approach. Several versions of these basic theories have been developed, and their predictions for various systems differ but are of the same order of magnitude. However, the solid/liquid surface energies determined by the methods based on the effect of interface curvature on the equilibrium phase change temperature, as described by the Gibbs-Thomson (G-T) equation, are 2 orders of magnitude higher than those determined by the STC and the EQS. This controversy is addressed here by critically analyzing both the thermodynamic and mechanical derivations of the G-T equation. It is concluded that none of the arguments recently presented against the use of the G-T equation, to explain the discrepancy, appear to be valid. Consequently, it appears that both the STC theory and the EQS approach may be incorrect.