I didn't mean that humans can't do things that haven't been conceptually solved. I agree that humans can do humor and that humor isn't conceptually solved, so I'll assume that you mean to say that we can make computers do humor, even though it isn't conceptually solved.

I disagree that we can make computers do humor. Kobeya linked to a paper that shows unsupervised joke generation, but it's a stretch to call this humor. I haven't explored beyond what's in that article, but the examples of jokes produced do little to convince me that this program is doing humor:

I like my relationships like I like my source, open

I like my coffee like I like my war, cold

I like my boys like I like my sectors, bad

Show me an AI that can produce original joke forms and I'll reevaluate.

Go was not conceptually solved decades ago if it required the development of new tree-pruning algorithms to work. Improving an algorithm is conceptual innovation. If it could have worked with only a few orders of magnitude difference in performance, or with only marginally inferior results without new algorithms then maybe it was conceptually solved decades ago, else no.

You study these things on fixed forms because it is easier to analyze and understand what is going on. But the extension to general joke-making is straight forward, provided you have working NLP (a big if!): data-mine the concept graph for thoughts/memes which have similar structural content but surprisingly (in the technical sense) different meanings, then construct a sentence that maximizes probability during reading of the first interpretation but ends with the second. This captures basically all humor from puns to "I like my X like I like Y: Z" to most forms of stand-up comedy.