One of C.Taubes' theorems says that for a symplectic 4-manifold $X$ with $b^2_+>1$ (where $b^2_+$ denotes the dimension of a maximal positive-definite subspace of $H^2(X;\mathbb R)$ under the intersection form), $\mathrm{Gr}(e)=0$ if $c_1(K)\cdot e-e\cdot e\neq0$. Here $Gr(e)\in\mathbb Z$ is a particular count of $J$-holomorphic curves in $X$ which represent the class $e\in H_2(X;\mathbb Z)$, and $K^{-1}$ denotes the canonical bundle. This theorem is proved using Seiberg-Witten theory. **Can one prove this gauge-theory-freely?**