Using a combined and consistently analysed GAMA, G10-COSMOS, and 3D-HST data set, we explore the evolution of the galaxy stellar mass function over lookback times t(L)is an element of [0.2, 12.5] h(70)(-1) Gyr. We use a series of volume-limited samples to fit Schechter functions in bins of similar to constant lookback time and explore the evolution of the best-fitting parameters in both single and two-component cases. In all cases, we employ a fitting procedure that is robust to the effects of Eddington bias and sample variance. Surprisingly, when fitting a two-component Schechter function, we find essentially no evidence of temporal evolution in M*, the two alpha slope parameters, or the normalization of the low-mass component. Instead, our fits suggest that the various shape parameters have been exceptionally stable over cosmic time, as has the normalization of the low-mass component, and that the evolution of the stellar mass function is well described by a simple build-up of the high-mass component over time. When fitting a single component Schechter function, there is an observed evolution in both M* and alpha; however, this is interpreted as being an artefact. Finally, we find that the evolution of the stellar mass function, and the observed stellar mass density, can be well described by a simple model of constant growth in the high-mass source density over the last 11 h(70)(-1) Gyr.