>a (previously considered) unattainable goal.

I've got a PhD. Personally, I'd say "unrealized" instead of "unattainable." Unattainable makes it seem like a dissertation topic is always some magical effort.

Lots of PhD work is a investigating some mundane area that somebody else hasn't (due to lack of time or interest) investigated yet. I wonder how many dissertations come from a random comment by a professor saying like "Well here is some minor tangential topic I/somebody should look into."