Are there any good strategies for conveying the true significance of the results that look obvious post factum?

Question

In nearly any field there is a number of important results which look obvious to experts post factum but somehow are not that easy to come by in the first place (e.g. in mathematics some important definitions look exactly like this). Unfortunately, this apparent post factum simplicity makes conveying the importance of the idea to expert audience (and in particular to the journals' editors and referees) very difficult. To make things worse, sometimes the author is unable to illustrate the application of the idea by sufficiently striking examples.

The question is whether it is possible (and if yes, how) to mitigate this apparent post factum simplicity in the talks and research articles, i.e., what can be done to adequately convey the significance of "post-factum-obvious" results to the audience and, in particular, to get these results to the journals they truly deserve?

I am particularly interested in the advice applicable to mathematics/mathematical physics but the suggestions suitable for other fields are very welcome too, as the situation in question does not seem to be all that field-specific.

Answer 1

The best approach may be to address the issue head-on: include a paragraph in the cover letter, in the introduction or discussion sections of a manuscript, and explicitly in the conclusions section of a talk, that sets up a "straw man" critique. Something like: this result may seem obvious because of (expectations in the field; the beguiling simplicity of the final proof; the incorrect assumption that the problem was already solved; etc). But actually that assumption is flawed (and say or show why). Our result is not obvious because (state reasons).

Answer 2

The OP writes that "experts", "journals' editors" and "referees" will fail to realize the "importance" of a result, if it looks "obvious" after statement.
I note that "importance" should have been somehow defined in the question, or at least be endowed with some operational meaning. But let's pretend we understand roughly the same things by reading the word, and let's assume that, indeed, all these people don't get this "importance". Then who understands it? The author? Namely, the one who "is unable to illustrate the application of the idea by sufficiently striking examples"? In other words, the person who has labored deeply into the case, he, on the one hand cannot come up with "striking examples", but at the same time "knows" that his result is "important"?
How does he know, if he does not know why the result is important? And if he knows why it is important, how can it be that he cannot communicate, however imperfectly, these reasons why? He may be lousy regarding presentation skills, he may be a bad writer. But still, how come nobody of those in the scientific community that know the field and the subject, realizes the importance of the result, in any form of communication, except the author?

Important results are sometimes initially overlooked because they are stated in a very specialized framework and their generality and wider applicability are not immediately, or even easily, evident. But "obvious" results, are, exactly, evident, and so their importance should either be evident, at least to some individuals that are part of the populations of "experts", "journals' editors", and "referees", or chances are, it does not exist. Difficulty of derivation or conceptualization are neither necessary nor sufficient for "importance".

But of course, I may be wrong -so I would really, honestly, appreciate it if someone could provide an actual example of such a situation.

I note that the impression I got from the question is that the OP does not refer to "paradigm shifts" and "revolutionary ideas" that may "fall on deaf ears" for sociological reasons. For such situations, it is a whole different, and largely theoretical, discussion.

Answer 3

In talks, you can use some didactic means. For example: start by presenting the problem. Then, ask the audience to think about it for a minute and suggest some directions for a solution. If somebody suggests a direction which doesn't work, show why it doesn't work. If nobody answers, prepare in advance some apparently useful directions that turn out to be unfruitful.

The disadvantage is that it requires you to spend about half the presentation time on discussion with the audience. The advantage is that, maybe, after the talk, your audience will better appreciate the difficulty of the problem.

I am not sure how to adapt this didactic technique to a paper, though.

Answer 4

To make things worse, sometimes the author is unable to illustrate the application of the idea by sufficiently striking examples.

I think this goes hand in hand with the problem you describe. You cannot expect an audience to evaluate the difficulty of the problem you have solved in a short time and often the same goes for reviewers and editors (unless of course, they are familiar with the problem). But you can show that you are addressing an important problem, which does not yet have a (satisfying) solution.

Now, if the latter is true, others should have thought about it before you. But as they have not come up with a solution, the problem could not actually have been that obvious. (Of course, it could have just been that nobody spotted the problem or the general approach you have taken – but then you can take credit for that.)

^{I have attended some interdisciplinary conferences and observed a general tendency that participants from more theoretical fields failed at motivating what they are doing – which was one of the key issues that made their talks very difficult to sit through or their posters not interesting.}

---

If there are standard approaches to your general type of problem, you could also shortly explain why these do not work. This way you can demonstrate that the problem required some thingking out of the box.

Answer 5

I have first hand experience with this and can say that it depends on how you present and apply the findings. I recently published a paper where I derived from first principles a relation showing how a property of some natural systems varies in some conditions. The corollary of the mathematical relation where just the well known facts from Nature, except one, which was surprising. The relationship itself looks obvious when one sees it written, and this was noted by the reviewers, but they appreciated how it was presented and the fact that it provided some sort of consistency and logical framework for the observed facts.

So, in my opinion, go ahead, make a nice case on why your findings are worth publishing: examples, relations and some sort of harmony.