I'd like to understand intelligence. I think there are several areas of research that are especially interesting: conjecture, criticism, realism, problem-solving, and universality.
We're faced with a constant stream of problems, and we're quite good at finding solutions. How do we quickly and efficiently navigate the space of all possible solutions?
A new problem might be solved with an old solution, or some variant of it, with some ideas added, removed, or tweaked. Analogies or random combinations may help.