By the famous Mather-Yau theorem,a complex hypersur-face germ V with isolated singularity is completely determined by its moduli algebra A(V).The proof of the theorem does not provide an explicit procedure for recovering V from A(V),and finding such a pro-cedure is a long-standing open problem.In this talk,I will present an explicit way (discovered jointly with N.Kruzhilin) for reconstructing V from A(V) up to biholomorphic equivalence under the assumption that the singularity of V is homogeneous,in which case A(V) coincides with the Milnor algebra of V.Furthermore,I will discuss a characterization of the Milnor algebras of homogeneous singularities in the class of all complex commutative associative algebras.