Using the theory of standard Artinian Gorenstein $\mathbb{K}$-algebras we give a new proof of Gordan-Noether’s Theorem. This classical theorem, stating that an hypersurface $V(F)$ in $\mathbb{P}^n$ with $n\leq 3$ is a cone if and only the hessian of $F$ is zero, was first stated by Hesse and then proved by Gordan and Noether. They also proved that for $n\geq 4$ the theorem is false by constructing explicit counterexamples.