# May I know why is my question on hold when it is clearly research-level?

This is my question

https://mathoverflow.net/questions/262039/central-properties-of-the-integers-mathbbz-over-other-structures-with-sum

I think the question is clear enough and it is easy to understand what I'm asking. The question is not easy, it is difficult, but this is not a good excuse to closed it or put in on-hold. It should be open because someone could answer it. I could be agreed on put it as community-wiki, but why have they closed it?

• It was closed for the reasons stated, mainly insufficient clarity. I have studied logic and some model theory, and I know what wording I would use for a question like this. However that would reflect my experience and understanding, not yours, so it would not be the same question. There is the chance of reopening the question after you revised it. I suggest not using anabelian geometry as an example until you can make its relevance clear. You might also respond to the comments already made: do they answer your intent? Gerhard "This Needs More Community Understanding" Paseman, 2017.02.12. – Gerhard Paseman Feb 12 '17 at 21:17
• @GerhardPaseman Excuse me, what do you think it is bad in the redaction exactly? What is not clear about what Z is and what Z is not? – Chronos Feb 12 '17 at 21:26
• For starters, your sentences run on, making them hard to parse. At this writing, I give up on sentence 2 paragraph 1, sentence 1 paragraph 2. I am unsure that paragraph 3 is relevant to your intent; an explanation for those ignorant of anabelian geometry might help. Finally, the basic answer you seek is simple but impossible to justify using equational logic: The sum of two like powers of high potency are also not powers of the same potency. But this is just a restatement. I think just looking at structures is not enough. Gerhard "FLT Is Not An Equation" Paseman, 2017.02.12. – Gerhard Paseman Feb 12 '17 at 21:35

It would be good if closers see this thread and could amplify further, but my guess is that the truth of the specific FLT statement is, according to current understanding, more like an epiphenomenon of deeper truths such as the modularity conjecture. Meaning that asking what ring-theoretic properties of $\mathbb{Z}$ are responsible probably doesn't reflect, to the minds of the closers, a research-level acquaintance with what is truly at stake; to put it another way, it's very likely unclear what sort of response to the question as asked could be really satisfactory to people who really understand this stuff.