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Hello rodya_mirov,
welcome to the site!
Let me try to give a (preliminary) answer to some of your questions/suggestions. [I am in no way an'insider', but around here since a while.]
A main thing to know is that MathOverflow is much more loosely linke to the stackexchange universe than other sites. It runs on an old version of the same software, and there used to be a link from there to here; but I believe even this is, since or following the creation of math stackexchange, now not so anymore. Basically, this site is completely independent.
So, to really move questions in the way you suggest is impossible on technical grounds. [And for various reasons, which I am not qualified to explain, this rather will not or cannot change.] ADDED: By latest news in another thread, this is/might not be true anymore.
I am not sure what you mean by the main site; but if it is the one where math stackexchange lives: it is not surprising that you are not recognized here, while having an account there. The sites are essentially independent. You should however be able to login using OpenID; if this does not work for you, perhaps additional details will allow somebody to give a better response. If you mean that you cannot login to this meta board using OpenID; this is not surprising, as far as I know, this meta board is technically completely indepedent and does not support OpenID.
Continuing on the 'moving': what is now standard procedure for questions suitable for another site (but not here) is to suggest to the questioner this other venue (and to close the question here). So, basically moving the question; but via a detour as the direct way is technically impossible. Some questioners appreciate this information, some not and react annoyed to the information that their question is unsuitable here. It is true, at least IMO, that sometimes the way in which people are told their question is unsuitable is suboptimal. There are occassionally discussions on this here, and it is my impression that things regarding this get rather better than worse over time, but i think it is good to be reminded of this problem periodically. Sometimes it is my impression that questioners that ask a clearly off-topic question and are being told about it in a neutral form, still react in an angry way. For these I honestly have no good solution.
Reagrding the subjects on this site: the representation of different mathematical subjects is certainly uneven. However, this is merely due to the personal interest of the current users. Questions on any mathematical subject are on-topic (provided they meet the general criteria as per the FAQs, of course); what I mean is, the fact that there is less activity in, say, PDEs than Algebraic Topology does not mean that the former would not be appreciated. It is just that it (at present) comes up less regularly.
Only one caveat: for more 'exotic' (for MO) mathematical subjects it is particullarly important to write a good question; in the sense of giving background and motivation.
Ok you can essentially scrap my original reply -- in light of the second post, it does not address rodya_mirov's actual question.
@rodya_mirov: there are a lot of reasons for the site to stay somewhat away from stackexchange. But one of the moderators should explain the reasons.
EDIT Ah, bad timing. quids' reply is much better.
rodya_mirov, I did not take your question as a complaint. Sorry, in case my answer caused this impression; it was unintentional.
Regarding the 'disconnected': just an hour ago Anton Geraschenko, who is the key-person regarding this, created a thread essentially on this (which prompted my 'ADDED'). In it he also links to some earlier discussion. In case you are curios and/or wish to voice an opinion on this subject, this other thread seems the perfect place and this the perfect time.
I probably should have replied here as well as posting the other thread. quid is exactly right. MO is disconnected from the rest of the SE network first because of history, and then because of politics. If we migrated, one of the benefits would be that we could migrate questions to math.SE as rodya_mirov suggests. I think it's still a bit uncomfortable when somebody posts a question on the wrong site, but if it's easy to move the question to the right place, it does mitigate the discomfort.
I think that it is much preferable to point to concrete examples of 'rudeness', so that we can discuss ways of dealing with the issue in better ways. I honestly have not seen any instance of what I would call rudeness in dealing with off-topic questions...
Mariano, could you give made-up examples of what you would consider rude in this context? (This is meant seriously.)
@quid: I don't think it's completely accurate to say that MO is independent. My understanding (and I may have misunderstood this) is that MO is still hosted on SO/SE servers, and that they therefore have the power to pull the plug on the entire operation if they so choose (which they won't, at least not in the near future, but it could happen). A few diligent souls are working to find a way to host MO independently with our own software, but I don't know what progress has been made on that recently.
Mariano, one type of pre-closure comment that verges on rudeness is, "we're not here to do your homework". Well, that's very true, we don't provide such a service. But the accusation itself is presumptuous; it doesn't matter how much it smells like homework. [By the way, I don't guarantee that I haven't said the same thing on occasion.] And in cases where it is demonstrably not HW at all, this can lead to very uncomfortable situations, and leave a bad taste in people's mouths.
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