Recognizing important problems
An anonymous commenter makes some insightful remarks in the comments section on an earlier post about doing worthwhile research:
how about: most people don’t fail because they simply don’t work on important
problems, but they don’t RECOGNIZE an important problem when they see one? Most scientists aren’t taught by anyone how to recognize it, either.
I agree wholeheartedly. The stereotype, of course, is that scientists win kudos by solving well-known problems that are agreed to be important. (I’m thinking, e.g., of Andrew Wiles.) But a substantial amount of great science is done by people who recognize important problems that no one else yet fully recognizes.
This process of recognition is very different skill than problem-solving per se. It’s not taught in any systematic way, at either the graduate or undergraduate level. I have some thoughts about teaching it, but they’re not fully formed, and would take some time to unravel.
Somewhere near the core of those thoughts is Abel’s advice on mathematics, which I think applies to other fields equally as well: read deeply in the masters, not their followers. This advice, however, needs to be combined with the suggestion made elsewhere in the same comments – don’t just read the masters, but try to solve from scratch the same problems they faced.