@jmorris I think the main problem is that "solved" there is a pretty fuzzy concept, unless we take it to mean "all non-spam is delivered, all spam is filtered", but then the question morphs rapidly into "what is spam, anyway?"
And softer goals seem to turn into moving targets. Bayesian filtering/etc. definitely makes the problem more tractable, but I feel like the "solution" always ends up with a small army of personnel minding the filtering machinery and keeping it well-oiled.