It is well-known that the geometric genus and multiplicity are two important invariants for isolated singularities. In this project we give a sharp lower estimate of the geometric genus in terms of the multiplicity for isolated hypersurface singularities. In 1971, Zariski asked whether the multiplicity of an isolated hypersurface singularity depends only on its embedded topological type. This problem remains unsettled. Recently, we answer positively Zariski's multiplicity question for isolated hypersurface singularity if the Milnor number or geometric genus is small. This is a joint work with S. S.-T. Yau.