Questions which are research level but where the OP is unlikely to have the background to follow the research

Question

There is a type of question which gets closed a lot which I find frustrating. An example is How to compute the volume of a region transformed by a matrix? , which I recently took the liberty of rewriting. If I understood the OP's question correctly, it is definitely a topic of current research. For example, Alex Barvinok and Michael Joswig think about the sort of polytope questions I raise. I am less familiar with the semidefinite programming literature, but Pablo Parrilo and Cynthia Vinzant are two people who think about variable elimination in nonpolyhedral convex geometry. It strikes me as unlikely that this question would get a good answer on math.SE ; it is not a textbook topic.

At the same time, there are a lot of clues in the OP's phrasing that suggests they are not at a level to understand this literature. Most substantively, they don't understand that the answer to a question about algorithms should be clear as to how the input data is specified and which parameters are growing and which are fixed. On a more superficial level, they don't emphasize the key point that $r < n$ and they don't use buzzwords like "linear programming" and/or "semidefinite programming" and "variable elimination".

I want us to help people in this situation. Is there a good way to help OP's in this situation connect with experts who can help them?

Answer 1

I agree that it is good to help people who have research-level questions on their hands but lack the language to work well with the current literature. This situation appears often when people doing research encounter problems that require tools outside their areas of expertise.

I have seen two ways you can use MathOverflow to connect people with experts. The easy way is for you to leave a comment or answer citing the relevant work - then the questioner has some names to look up. A more direct method is for you to contact an expert you know, and inform them that there is a question close to their subject. At some point, however, it is the questioner's responsibility to run with the leads they are given.

As far as site norms are concerned, I suggest we be more charitable about leaving questions of this nature open. Unfortunately, it can be hard to separate these questions from those that are not research-relevant, and we have an interest in keeping the site on-topic. One possible rule is that if a known specialist says that a question has research interest, then perhaps we should give that question the benefit of the doubt.

I encourage experts to revise questions that touch on research-level mathematics to make the on-topic part more visible, and to give answers that address research-level aspects of a question where it is not obvious (Joel David Hamkins has been particularly good at this). Naturally, these edits and answers take time and effort that we may not have, but I encourage the people of MathOverflow to keep the possibility in our minds.

Answer 2

I think it is good to have MathOverflow as a helpful resource for many people. In order to maintain such a resource, it needs to be helpful to the maintainers foremost. That means providing "MathOverflow quality " responses.

Remember that being helpful on this forum is primarily to give succinct answers to questions. We are not a help desk, or a Wikipedia extension, or a replacement for someone doing a web search; we provide a service that allows other researchers to make further progress in their work, with the side benefit that other readers can also benefit from such answers. Often this service is "Yeah, it's been done before: use this search term and check these links.", which is essentially literature orientation that most others can't do without spending substantial time learning the subject.

Sometimes the service is to sketch the idea of solution, and hope the reader has enough chops to fill out the sketch. Even among MathOverflow regulars, the filling out can be substantial work, but there is still time saved because a helpful idea is presented.

If a poster does not have the experience to appreciate the given answer, there is not much we can do on the forum itself. You don't want to write a tutorial or attempt to spoonfeed the poster in your answer, as that is beyond the scope of the mission of this forum. However, you can write brief comments and provide links. I and other members of long standing should have no issue with you providing a link in your answer to ancillary material (tutorials, filled out sketches, reading lists with commentary) that you develop. The researchers can choose to ignore or follow the link, and the other forum members can choose to ignore it understanding that such material is meant for someone who is still learning how to learn.

Gerhard "Is Learning How To Write" Paseman, 2020.01.03.