I will report the on joint work with Andras Nemethi concerning the topological nature of certain   analytic invariants  of  isolated surface singularities. The geometric genus p_g is such an invariant, and the question is whether one can express it  in terms of topological invariants of the link of the singularity. For this to happen  the link has to be a rational homology sphere (QHS), and the complex structure of the singularity must satisfy some mild  rigidity condition (Gorenstein, or  complete  intersection etc.)  A decade ago  Fintushel-Stern, Neumann-Wahl gave an affirmative answer  for many complete intersection singularities   whose links are  INTEGRAL homology spheres (IHS) by proving a formula  relating the Casson invariant of the link to  the signature of the Milnor fiber. This signature  differs from p_g  by a topological quantity.  The obvious  change Casson ---> Casson-Walker , when going from IHS to  QHS links  leads to  false conclusions. Even worse, most singularities  are not smoothable, and in these cases  there is no Milnor  fiber to speak  of.  In  my talk   I will   explain how to resolve this conundrum by relying on  the  Seiberg-Witten invariants.