minimal surfaces (critical points of the area functional) have a rich and successful history in the study of the interaction between geometry and topology that goes back to the 1960s. in practice, the presence and properties of minimal surfaces inside a riemannian manifold profoundly influences the ambient geometry. in this talk, we will discuss how one can use the allen--cahn equation to guarantee the existence of a rich class of geometrically and topologically distinct minimal surfaces inside a generic riemannian 3-manifold. as a byproduct, one obtains a pure pde resolution of a number of previously unapproachable questions in minimal surface theory, which parallels recent simultaneous advances that instead use geometric measure theory.