What does really make a question good?

Actually, this website is one of the good areas to discuss math problems from almost every branch. while looking for something, I can encounter many interesting things.

The thing which is weird for me is that while there are many beautiful question ranked at most 4 and 5, there are some useless questions ranked in the 50s. Of course this is my opinion; what do you think about that? What is a really good question? When a question cannot be solved, does it really mean that it is a good question? For example, it is known that when the degree of a polynomial is bigger than 5 then it has no general solution so, if I ask roots of a polynomial degree 6 with appropriate coefficients, probably nobody can solve this. Does that make this question good? I guess some people think so. As a result what should be criterion for evaluating the questions?

• – Git Gud Nov 15 '13 at 21:06
• It may be instructive to read this article by Randal Monroe or this article by Eval Miller that it links to. In short, {upvotes}-{downvotes} is not very well correlated with quality. – user14972 Nov 17 '13 at 10:57
• Yes,this article is very useful and gives the statistical formula for evaluating average rank,In my opinion, this website should also use the formula.Is there any way to suggest it to the admin? – mesel Nov 18 '13 at 6:24
• The answer to your title question depends on who’s answering it. We don’t all have the same notion of what constitutes a good question in the abstract or in what constitutes a good question for MSE, and for many of us those are two different notions as well. – Brian M. Scott Nov 18 '13 at 6:39
• I recently asked what turned out to be excellent questions for the sake of my own learning. They were not problems from a book. They were questions which arose from my attempt to align my previous experience with the new material. I provided my answers to those questions, but that doesn't represent the extent of my growth in understanding resulting from considering the situations. I have very little "need" for help. I rarely get so stuck that I can't eventually figure something out. Much of my reason for posting questions to math.SE is just to be able to communicate with others. But alas – Steven Thomas Hatton Jun 14 '17 at 19:17

Since you mention votes and quality in the same paragraph, I'd like to emphasize that these are not synonymous. The answers to

1. What makes a good question?
2. What makes a highly upvoted question?

are different.

A good question usually arises from a person's desire to understand mathematics better, followed by focused consideration of a particular problem or concept, followed by careful writing (see How to ask a good question? for the last part).

A highly upvoted question is usually something accessible to a wide population, something that's easy enough to trigger the "ooh! ooh! I know!" response of several Math.SE users, and consequently place the question in the "Hot List" network-wide. Once the "hot" status is attained, additional votes are given by users from StackOverflow who click on random links because their work day is slow.

• Highly voted can be those who appear on reddit/ycombinator/other forums as well. – Asaf Karagila Nov 17 '13 at 9:07

Good spelling and grammar for one.

• I think that this was intended as a comment on (the original version of) this question. So this should not be posted as an answer. – Martin Sleziak Nov 16 '13 at 11:48
• @MartinSleziak Maybe, maybe not. I think it is a perfectly good answer to the question. – user940 Nov 16 '13 at 16:22
• I concur with the answer and with @Byron's comment. Actually the fit between "good spelling and grammar" and "good question in the mathematical sense" is probably quite high. – Did Nov 17 '13 at 10:36