I'm sure I'm not the only one with this quandary so hopefully this question is suitable for Mathoverflow. I'm posting anonymously for obvious reasons.
In a couple of my papers I have answered questions which were fairly well known inside my sub-field and posed by well known people. However, the solutions themselves are not hard – they do not involve any substantially new idea, other than perhaps the insight that some well-known techniques in a slightly different field could be of use. In the end I submitted (and published) to journals taking into account more the difficulty of the solution rather than the prestige of the problem. Several people later told me I could/should have aimed higher.
Now I am in a similar situation, with a couple of papers in preparation where the techniques I use are well-known, but they have just not been applied to the type of problems I solve (which again, are questions asked by very good people and open for at least a while. They are not major famous questions). Maybe I just have a good smell for low hanging fruit!
My concrete question is twofold:
- Generally speaking, are papers who answer a respectable open question judged more for the problem solved than for the difficulty/innovation of the solution?
- What are some good journals that welcome this sort of papers? (General journals as well as specialized ones)
Best Answer
I think you already have your answer: if you've been told to aim higher by several people who know your work better than we can, then aim higher :-)
More philosophically, it's a good idea to take an empirical approach to your own career. Don't make too many assumptions about what will or won't get published; instead, try out different strategies. In this case, you know that you can publish your results on lower-ranking journals. Now it's time to do the experiment where you try for higher-ranking ones.
As for which specific journals, why not ask the people who posed the problems to begin with? Or think about where you'd like to read this kind of result. On a more specific level, you might think about your introductory paragraphs, and what is the broadest possible audience to whom you'd be able to explain why your results (the results! not the proofs!) are interesting.