What is a simple way to prove that for any compact two-dimensional surface $S$ and an element $g$ in $\mathbb \pi\_1(S)$ there exists a finite index normal subgroup $\Gamma\subset \pi\_1(S)$ such that $g\notin \Gamma$? 


In fact, who was first to prove this statement?



Residual finiteness of fundamental groups of surfaces.
See  [this text.](http://www.math.umbc.edu/~campbell/CombGpThy/RF_Thesis/3_Knot_Manifold_Groups.html)  The proof is just a few lines. 


