  We discuss an analytic approach towards the solution of pure Yang-Mills
theory in 3+1 dimensional spacetime. The approach is based on the use of local
gauge invariant variables in the Schr\"odinger representation and the large
$N$, planar limit. In particular, within this approach we point out unexpected
parallels between pure Yang-Mills theory in 2+1 and 3+1 dimensions. The most
important parallel shows up in the analysis of the ground state wave-functional
especially in view of the numerical similarity of the existing large N lattice
simulations of the spectra of 2+1 and 3+1 Yang Mills theories.
