Why does the criterion for a good question change with reputation?

Question

If a person asks a question on this site, they are supposed to provide their own attempt at solution, context, possibly even a reference to the problem source.

We seem to remind newer people on this site of these keys to good questions on a frequent basis.

However it seems high rep users fall prey to the very same problems low ranking ones do!

For instance, questions on integrals and series are quite commonly asked here on the site. However only about $1/2$ the questions have provided an attempt at solution and in my opinion only $1/2$ of those provide a satisfactory attempt at solution.

To make things concrete consider this question. No, attempt at solution is made and evidently the Op already has a solution! Another. One more for good measure

I do indeed have a legitimate question. Do I have the criteria for a good question wrong? If so, what are the criteria, perhaps we should update the help pages. If not, why do we allow these questions to persist in their current form?

Response 1: In response to a vague definition, I define a high rep user to be any user over 1,000 in rep. It's arbitrary but is sufficiently high to weed out new users.

Answer 1

I do agree that sometimes higher reputation users are given greater leeway than lower reputation users. This is not just true with questions, but also "answers". This is unfortunate, but also somewhat understandable. If you have achieved, say, 10K reputation on the site, you have likely been active for a considerable amount of time, and have contributed a fair number of good posts: you are known to other users, who have an idea of what you are about. This is certainly not true with 1 reputation users.

But you go astray on one major point: the necessity of a shown attempt. We actually have no requirement that an attempt at a solution be shown. We do want users to provide context to their questions, which can come in many forms:

• Include your work
• You can provide some motivation to your question.
• You can tell us where the question comes from.
• Indicate your own background
• Give full references.
• Give definitions.

So the inclusion of work is one way that context can be provided. Another way is for users to just admit that the question is not originally theirs but is Exercise 5(a) on p.492 of Stewart's Calculus: Early Transcendentals, 8^th ed.

Of the three questions you have linked, I only have some difficulty seeing the context being provided in the first. There is some very vague context provided ("Here is a question that naturally arose in the study of some specific integrals") and a promise of the OP's solution.

The other two questions undeniably have context provided. They both clearly state the motivation for the questions they are asking.

Compare these with

How to calculate the following integral? $$\int_0^1\frac{\ln x}{x^2-x-1} \, \mathrm{d}x=\frac{\pi^2}{5\sqrt{5}}$$

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But, yes, you can find poor questions asked by higher reputation users. A relatively recent one looked like

Calculate in closed form $$\small \int _0^1\int _0^\infty \left(-\frac{9 \sqrt{\frac{3}{\pi }} \Gamma \left(\frac{4}{3}\right) \Gamma \left(\frac{5}{3}\right) \, _2F_2\left(\frac{1}{6},\frac{5}{6};\frac{1}{4},\frac{3}{4};\frac{27 t^4}{256 u^3}\right) \, _3F_3\left(1,\frac{4}{3},\frac{5}{3};\frac{3}{4},\frac{5}{4},\frac{3}{2};-\frac{27 u^4}{256 (t-1)^3}\right) u^{3/2}}{16 (1-t)^3}+ \cdots \right) \, du \, dt$$

where the integrand went on and on and on. That question is currently (rightfully, IMO) closed.

Answer 2

Context is everything.

When one of my students asks me "How can I solve question 1", I know what they are asking, I know what they were taught and what tools they have accessible to solving the question, and I may or may not recognize them personally and be able to size up their ability to approach the problem or their difficulties in doing so.

When someone posts a question on this site "How can I solve question 1", even if they tell me exactly what is the question, I don't know what they were taught and what tools they may or may not have for solving the problem, and I might have no idea how to estimate their understanding of the material. So I need more context in order to provide a helpful answer.

Users who spent enough time on the site may generate enough material so I can infer, if need be, the context and tools they have available. Of course it isn't always the case that other-generated context is enough to help me understand their problem. But it often can be a lot.

That being said, there's also the issue of "show your work". When someone just dumps a problem on the site, I want to see their work and know what they did or didn't do in order to solve the problem. I also know that a lot of people are just "passing by", coming here to ask a few questions and then they are gone for a while until their next assignments. So from these users I expect more effort in solving to be shown. Because I want to know that they are invested in this problem. And when a user posts their solution, it helps giving context and understanding as to where they ran into a problem.

Users with reputation aplenty are already invested in this site, to some extent. I'm not worried that they are fleeting faceless foam on the waves of the data ocean called "the internet". Or at least, I'm less worried that they are. I expect a well written question from high rep users, in the sense that the relevant definitions will be there, and that they will try and pinpoint their problem with as much precision as possible. This can be done without showing your work.

Let me finish with pointing out that it's not unheard of that experienced users do post badly written questions, or questions that lack context. And the above is not by any means a comment glorifying high reputation users or absolving them from blame for posting crap.

Answer 3

I answer questions on math.se for several reasons. In roughly decreasing order of priority:

1. To help researchers with problems they run into (especially those from fields outside pure math, whose mathematical problems have a chance of being at the level I can understand!)

2. To teach the general public and curious independent learner.

3. To help students who are confused by their professor/textbook and need additional explanation, or are stuck on homework problems and need a nudge.

4. To think about interesting problems strictly for the intellectual pleasure.

I refuse to answer questions whose goals seem to be

5. To cheat on a contest, exam, or problem set.

6. To treat math.se as a "Wolfram Alpha++" for answering questions the asker is too lazy to spend even a token amount of time thinking about.

Asking a user for context is helpful for establishing the mathematical level at which an answer will be useful, determining what tools the user knows or doesn't know, etc. But it also serves the purpose of establishing which category above the question is in. Now when a high-reputation user posts a question, my presumption will be that the question is in category 1 or 4. On the other hand, a low-reputation user needs to show evidence to convince me that they are not in category 5 or 6 -- this might be obvious from the type of question asked, but if not, needs to come from additional statement like an initial attempt at the problem, a statement about where the problem came from, etc.

Perhaps this is unfair, but on the other hand I don't see too much of an ethical problem with giving more slack to the unpaid volunteers who have a track record (in the form of reputation) of helping others.

Answer 4

In each of the three you linked, the OP knew the material they were asking quite well and the kinds of questions they were asking were rather deep questions about integration and special function theory. Yes not much work was shown, but some integration questions are just damn impossible to show any work for if you don't have the right answer come to you. This site tends to be very lenient (and actually quite favorable) to these really complicated integration questions because the techniques used therein are deep, difficult and usually elegant. There usually isn't much motivation beyond simple curiosity or having seen it in G&R or a similar compendium of integrals.

High reputation users almost never ask bad questions on this site. (Which isn't to say that they never have somewhat trivial questions that they're stuck on - we're only human after all!) For instance, out of general curiosity, I posted a question some months ago asking about whether or not involutions on a Hilbert space must be bounded. Seemingly if an operator squares to the identity, you'd think it would have to be bounded. I tried for a few days to answer the question, but I came to the conclusion that it was one of those questions for which the proof is probably highly non-trivial or the example is fairly straightforward but it was eluding me. You can't really show any work in that sort of situation since there is none. Turned out that I came up with a counter example about half an hour after posting the question.

Based upon the general tone of a question, you can more or less gauge how long someone has thought about a question. Great care is put into it and even though it may be the case that no work has been shown, sufficient background and/or general thoughts are put into the post. Again, the integral posts tend to be an exception to this rule since they are incredibly hard to motivate.

Answer 5

This business of showing your attempt to answer the question is appropriate when the question looks like something that could be assigned as a routine homework exercise in a lower-level course, where the student could copy the question into math (dot) stackexchange (dot) com perhaps without even understanding what the question says.

It appears that in some other situations just coming up with a reasonable question, is considered sufficient without showing your attempt to answer it. Perhaps this question is an example of that. Or this one.

Sometimes intelligent and insightful questions get deleted for failure to show work or other reasons appearing in a standard list of grounds for deletion. Some who frequently delete questions feel very strongly about adhering closely to the letter of those standard lists of grounds for deletion.

PS: Sometimes people around here say that it is rude to post a question phrased like a homework problem, e.g. "Solve this differential equation." or "Prove that this sample mean is independent of this sample variance." I don't think it is rude, but I think it's clueless, because it looks like a case of stenographically copying a homework problem when no mathematical question was in the mind of the poster.