I recently asked the following question, and within 3 minutes it got 2 downvotes:
(Some minutes later it then received an upvote, but then it received another downvote.)
Also, someone else shortly afterwards posted a question asking whether equivalence of two norms on the same vector space can be determined just from whether they share the same collection of compact sets. Again, this question almost immediately received several downvotes. After one person (of very high reputation) posted a comment to say that they didn't understand the downvotes, someone else responded that the text over the downvote button says "This question does not show any research effort...".
(Similarly also, in my question, the first comment posted was "what are your thoughts?")
So my question:
It seems to me that there are essentially three types of question that one can ask on MathSE:
- I'm a student (or researcher in a different field who is "functionally" a maths student here), and as part of my learning I would like help trying to work out the answer to this problem...
- I'm a researcher, and I would like help trying to solve this particular problem that's relevant for my research... [although this is probably more appropriate for MathOverflow]
- I'm a researcher, and I have the following interesting/useful question that is simple enough that there is clearly a known answer somewhere, but it's difficult to find the answer using Google...
Obviously in category 1, the student should give an indication of what they've tried, as this will best help the person answering to benefit the student effectively. Obviously in category 2, the researcher should offer his thoughts or commentary.
But in category 3, is it not an active waste of everyone's time to have to read your "initial thoughts" on how to answer the question? Isn't the most important thing that if the question gets answered, then vast numbers of people who might in the future be interested in the question (or just find it cool) are much more likely to see the answer to the question (whether by a Google search or by just browsing interesting questions on MathSE)?
And in category 3, isn't the statement "This question does not show any research effort" only true if the answer (or information that immediately yields the answer) is fairly easy to search and find on Google?
Now I understand that MathOverflow is often the place to ask questions of category 3, but I think the attitude of many professional mathematicians is that if the question is sufficiently basic - but not directly within the researcher's particular field of expertise - then the question is well-suited for Math Stack Exchange.
As for my own "initial thoughts" on this question:
MathOverflow also has exactly the same text over the downvote button as MathSE, and one of the central purposes of MathOverflow is that professional mathematicians can ask questions of category 3.