I was watching the said movie the other night, and I started thinking about the equation posed by Nash in the movie. More specifically, the one he said would take some students a lifetime to solve (obviously, an exaggeration). Nonetheless, one can't say it's a simple problem.
Anyway, here it is
$$V = \{F:\mathbb{R^3}\setminus X\rightarrow \mathbb{R^3} \text{ so } \hspace{1mm}\nabla \times F=0\}$$ $$W = \{F = \nabla g\}$$ $$\dim(V/W) = \; 8$$
I haven't actually attempted a solution myself to be honest, but I thought it would be an interesting question to pose. I have done a quick search on this site and Google, but there were surprisingly few results.
In any case, I was curious if anyone knew the answer aside from the trivial.