Can someone clarify Hamming's notion of important problems in relation to modern academia? I was reading the transcripts of a seminar by Dr. Richard W. Hamming. In this, Hamming goes on to say the following statements:

Explaining why one guy was successful while the others weren't as much successful. 


  I have never heard the names of any of the other fellows at that table
  mentioned in science and scientific circles. They were unable to ask
  themselves, "What are the important problems in my field?" If you
  do not work on an important problem, it's unlikely you'll do important
  work. But the average scientist does routine safe work almost all
  the time and so he (or she) doesn't produce much. It's that simple. If
  you want to do great work, you clearly must work on important
  problems, and you should have an idea. Most great scientists know
  many important problems. They have something between 10 and 20
  important problems for which they are looking for an attack. And when
  they see a new idea come up, one hears them say "Well that bears on
  this problem."


Now my question is:  If I ask myself the question, 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 am sorry but I am unable to get myself a clear picture of what exactly is meant here. Will anyone please help me out with ideas.

Many thanks.
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.