Consider the field from its inception and how it has changed over time. We move into higher abstractions and release ourselves from having to worry about details such as memory management. Even so, as an embedded software engineer I find myself wrestling with memory usage and throughput budgets. As AI becomes reality, it would be ideal to mold (evolve?) an AI to help me address specific weaknesses in my capabilities to allow me to focus on "the problem at hand". If you're curious about that sort of AI development as it relates to embedded software, check out "hyper-heuristics".

You can really answer your question according to the observable trends of the field. The role of the "programmer" will shift, that's all.

Regarding what a programmer needs to know, I think you'd be hard pressed to find something that wouldn't be useful in some way. Personally, I am trying to read as much of the "Old Masters" as I can. I've started with Claude Shannon and have tried to hit all the big names along the way. Bernard Widrow's work (http://www-isl.stanford.edu/people/widrow/publications.html most articles are free) got me started.