Work in an area or work on problems?

Question

I have a question about two possible career paths, for which I was unable to come up a better title. Let me explain what I mean:

Path 1, Working in an area: By this I mean, making a career by adding to the knowledge of a field of study. This may include sorting out open questions in that field or identifying new issues or pushing the boundaries of existing knowledge. This typically involves having a larger perspective and understanding of the field and its relevance to the world.

Path 2, Working on problems: By this I mean making a career by solving a series of specific challenging problems not necessarily belonging to a common field of study. Here one only attempts to understand enough about the problem at hand to solve the problem, but does not show an interest in developing the area as such.

Working in an area requires one to have a broader vision, scholarship and commitment to the development of the area. Working on problems does not involve commitment, but requires one to repeated invest oneself in learning about a new area. By working in an area one can encounter a degree of monotony. By working on problems, one can potentially find new challenges at every juncture.

So my question is: career wise, what is a better option? Specifically, which of these kind of academics are more valued by the community? What, if any, are pitfalls of these paths? Meta question: is path 2 a path at all or do all academics eventually settle into path 1 after spending some time on path 2?

Edit: I guess the key difference between the two paths is that path 1 leads one to become an "expert" with extensive knowledge in a particular area. Path 2 exposes one to a variety of problem situations and makes one a better problem solver, though it may not make one an expert in any field. For the purpose of this question, you may take the area to be a well studied field such as, say integer programming, which has some long-standing open problems, but is not necessarily so young that it allows for a variety of research opportunities.

Answer 1

Without knowing anything about the specific area, I'd say that you've set up a false dichotomy. I don't know if anyone ever consciously does one or the other exclusively. Sometimes you work bottom up (i.e path 2 -> path 1), and sometimes you work top down (path 1 -> path 2). Both these "paths" should be dimensions of your research.

Answer 2

I am reading the paths 1 and 2 as follows

Path 1 : The culmination of working on one problem (either success or failure) leads to another which leads to yet another and it goes on and on.

Path 2 : Number of problems on a field that are not related to each other and are stand alone; do not depend on or influence the other.

As @Suresh has already pointed out the answer might heavily depend on the field. But trying to answer in general, it is better to follow the Path 1, as it is mentioned in the question itself, it is focussed on a long term goal and elevated vision. Academia always long for broader vision and greater commitments. An employer would love to hire some one who has a concrete long term goal and enthusiasm.

While Path 2 is not a way that does not involve commitment, it is more focussed on short term goals and narrowed vision, such as getting a degree, finishing a project etc. This also involve commitment, but not on a large scale.

Thus brings up the question, "Why we want to learn or explore?" Irrespective of the field, this seems to be the essence of the question.

Answer 3

Areas are not well-defined, they change over time and even if a dean know when the boarder between some fields, Nature does not (as they are mostly communities emerging from common scientific interests).

Moreover, confining oneself to a given area may end up into working in a exhausted subfield that people no longer care about (and missing new opportunities).

However, when it comes to your visibility and prestige, other researchers will care only about your skills and achievements in a given field. But again, there is also a question of how much the disciplines overlap, both in terms of communities and methodology.

So here there is a trade-off between being recognized (and prepared) well in one field vs less but in more.

When it comes "is it better to focus on solving particular problems or learning general stuff", the question is a bit different from your career-related one. Opinions may vary (and it may be a matter of one's personal philosophy), but for research_ output (not e.g. teaching skills) the first one is the only the one that counts. And if someone is skilled and committed, the later comes anyway (and the converse is not true).

(Anyway, it's the reason why during PhD it is (arguably) advisable to focus on solving problems (and learning stuff needed to solve them), not on spending hours on general courses.)

Answer 4

A classic interview question (paraphrased) comes to mind:

1. What do you think is the most important problem in your area?
2. What have you done to solve this problem?

Perhaps, these questions might be worth thinking about when choosing a career path.

Although this might look more like a comment than an answer, what I mean is you need to think about your question from several perspectives: what do you think is essential for your field and how you can contribute there, and what are your personal talents or virtues, such as working on technical problems in depth, or administrative skills in managing resources for problem solving in a broad sense, or something else. These are your assets. List them and do analysis on how would they be better applied, what combination of them would yield bigger impact or bigger rewards, depending on what you favor.