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I think a low density of open problems is acceptable, but I don't like want people to straight-out post problems they know to be open. What do people think of the following protocol?
If it turns out that a problem is equivalent to a known open problem, then the [open-problem] tag is added, and the question is converted to community wiki. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?" That way, the MO thread for the problem becomes a repository of resources related to the problem. Perhaps the answers could be organized by approach, with an outline of the basic approach, followed by a horizontal rule and a summary of what is promising about the approach and why it doesn't give a complete solution.
Rather than posting problems you know to be open, I'd rather you ask questions you're actually seriously thinking about. If you're thinking about a well-known open problem, provide some background and ask about something specific related to the problem, like "Such and such is a well-known open problem. So-and-so proposed this and that approach in the 80s. Does anybody know if this aspect of their proposal can be made to work under these circumstances?" If you know a problem is open and hard, but you post it as though I'm going to produce a solution without reading any of the literature, then I'm likely to resent it when I learn that you've tricked me into wasting my time.
The FAQ says "this is a place for questions that can be answered!", which seems to imply that you only want questions where the person asking knows that there is an answer but forgot both the answer and where to find it.
My interpretation of that is that MO is for questions of the sort where I think "Someone must have thought about this before.". Sometimes, that's because the thing feels like such an obvious idea that you can be pretty sure that someone else has done it, but tracking it down in the literature can be tricky if you don't know where to start. Critch's question on group objects is a good example of this. However, it can be hard to know when a question is that sort, and sometimes the answer is "No, no-one has".
It's classic Rumsfeld: MO is for the unknown knowns. However, knowing that something is an unknown known is quite tricky so we have to let through some known knowns and unknown unknowns. However, what, maybe, we really want to guard against is the known knowns, aka homework problems.
Strangely, I have been thinking about roughly the same question about the same week ago.
One of aspects of MathOverflow, I think, is that by definition questions that are good should have an answer. Another nice aspect is that questions can be edited.
Therefore my feelings are that Anton's After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?" is close to nailing the most beneficial policy with perhaps the small addendum: one could also edit the original post itself so that it formally becomes a new, answerable, question. Once we have this established as a good policy, moderators can be encouraged to do this automatically.
@ilyani: I absolutely agree that the original post should be edited to reflect the fact that it's been discovered that the question is equivalent to a known open problem. One advantage of a moderator hitting the post with the "wiki hammer" (converting the question and all answers to community wiki) is that the post and all answers become editable by anybody with at least 100 reputation. Of course, it also has the benefit of discouraging "reputation whoring" (the term used on Stack Overflow for trying to game the system to gain reputation).
The question Is the set of primes translation finite? is equivalent to well-known open problems. However it seems inappropriate to me to wiki-hammer this. In some sense it's "finished". It has a good answer, summarising the equivalence.
Also -- a side question: does wiki-hammering retroactively affect reputation from votes on questions and answers (i.e. treat them as if they've been wiki all along)? What about posts that become wiki from multiple edits?
@Scott: converting to wiki does not retroactively affect reputation. If you feel like it's not appropriate to convert to wiki, I don't have a problem with that.
In my mind, there are two main points of converting open problems to wiki: (1) to prevent people from trying to gain reputation by posting open problems, and (2) to make it easy to gather a body of knowledge about the problem in one place. If it doesn't look like anybody is being a "reputation whore", and MO is clearly not going to become a place to gather information about the problem, I think it's fine to just leave the question alone.
I think the idea is that every question has an answer. So, if somebody posts a question "Is P = NP?" this should receive an immediate answer.
I think the problem "(1) to prevent people from... " is not related to one particular class of questions (full disclosure: I was a center of controversy here recently about a different class of questions) -- should people who post a trivial question that happens to answerable be rewarded compared to people who happened to think about hard question independently?
To me it would be mostly about the amount of work somebody does. If a person invents the classes P and NP and posts a question about them, let her/him get all the rep they deserve. Conversely, if somebody copied from a book a simple answerable well-known question, even an interesting one, and purposefully did it only to gain some reputation, I would personally think that person tries to use Math Overflow in less ethical ways.
(I won't be interested in discussing whether one should label these people "community whores")
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