We clarify the relationship between probe analysis of the supergravity dual and the large-N solution of the localization matrix model for the planar N=2 super-Yang-Mills theory. A formalism inspired by supergravity allows us to systematically solve the matrix model at strong coupling. Quite surprisingly, we find that quantum phase transitions, known to occur in the N=2 theory, start to be visible at the third order of the strong-coupling expansion and thus constitute a perturbative phenomenon on the string worldsheet.