I am looking for examples of recently (last 20 years, say) published math papers such that:
- the results/examples were fairly trivial (by this I mean anyone with the definitions and standard background in the area of research could have thought of them, but never took the time to do it, or it simply never occurred to them); and yet
- the questions posed in the papers, which were motivated by the results, lead to future research and solutions which were non-trivial.
These should not be foundational papers in the sense that they introduced an entirely new field. Assume those papers published long ago, with books written on the subjects, etc.
I guess this question stems from a fear that my papers fit this mold. The questions (often my own) I am unable to answer seem far more intriguing than what's actually in my papers…
Best Answer
I have a paper which may qualify, except that it was published approximately 30 years ago. It contains:
a) a simple definition, which was very natural to make in this area, b) a theorem which any specialist in the area could prove (the level of difficulty of an average MO question), and c) a conjecture.
The paper is published in a conference proceedings. http://www.math.purdue.edu/~eremenko/dvi/banach.pdf
This had a substantial effect over the years. To have an impression of this effect type these keywords on Google: "escaping set", "Eremenko conjecture". The conjecture is still unproved but there are many deep and interesting results related to it. Here is a very beautiful exposition: https://www.impan.pl/~perspectives/Rempe-Gillen.pdf
Remark. There are at least two people who proved the result themselves but did not care to publish it (this was after my paper but they did not know about it.)