Mathematician Richard Hamming used to ask scientists in other fields "What are the most important problems in your field?" partly so he could troll them by asking "Why aren't you working on them?" and partly because getting asked this question is really useful for focusing people's attention on what matters. 

CFAR developed the technique of "Hamming Questions" as different prompts to get your brain to (actually) think about the biggest problems, bottlenecks, and unspoken desires in your life.

(Taken from here)

See also Open Problems