Can someone clarify Hamming's notion of important problems in relation to modern academia?
What are the important problems in my field?, how should I expect to get an answer to this. Is it by deeply diving into literature and finding loopholes that exist. And even if I do find something worth working upon, how do I know it's an important problem of the field or a trivial subset of some other large problem?


I would interpret this statement not so much as trying to look for "loopholes" in the literature, more as trying to identify what the core problems are that are holding back further advancement in your field, and what would need to change in order for them to become tractable. This requires you to deeply understand the existing work, so as to learn what exactly needs to change for your field to really jump forward.

However, I should warn you - Hamming’s approach is certainly a high-risk-high-reward one. If you implement this, you will almost certainly have to invest quite some work detailling and understanding a large number of difficult problems that you will in all likelihood make no progress on during your lifetime. Really important problems invariably don't have a straight-forward solution (or, in many cases, no solution at all), so even if you bring yourself into the best position to attack them in the right circumstances, there is little guarantee that these circumstances ever come to pass (or that you are the first to recognize if some recent development in the field makes one of "your" open problems tractable). That said, if you manage to address even one really big, important problem, your impact will indeed be higher than what you can achieve in decades of incremental research.