Will I get bashed for that?]]>

In particular, Noah Snyder's comment that "open problem" means "question which people have thought about for a while but everyone is stumped on" does not match my personal experience. It sometimes means that, but in my experience, it just means, "problem to which the answer is not known." If I give a talk on my research, I frequently will mention that certain problems remain open. By no means am I asserting that anybody other than me has thought about them, let alone thought about them for a while and gotten stumped. In fact, I myself might not be stumped; I might just not have gotten around to thinking about them.

The intent of the statement would be greatly clarified by just inserting a single adjective.

]]>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.

(There is a link to this thread after this paragraph)

]]>this thread has been dormant for more than a year. Perhaps you could remind everyone what you're referring to?

]]>Given a rectangular array of symbols over a finite alphabet, how many other arrays share its multiplicities of rectangular subarrays?

The "problem" here is that some natural-appearing classes of multiplicities are not known (versus known not) to exist. I think that questions such as this or TImothy's should be considered kosher, whereas "is the abc conjecture true" should obviously not be.]]>

I would like clarification on this point. It seems to me that the intent of the prohibition on open problems is to stop people from posting open problems *that they know are hard*. If this is the intent then I think the guidelines should be stated that way.

Let me give some examples. The paradigmatic example of a good MO question is a missing lemma. As far as I'm concerned, my missing lemma is an "open problem." I might not be sure that it is open, but I might suspect that it is. On the other hand I might also suspect that the right person would make short work of it. So I post to MO. Technically, I have violated MO's prohibition on posting "open problems." Clearly, we don't want to forbid that.

Another example is my question on rational equivalence of quadratic forms. Skip Garibaldi derived an elementary result as an "accidental corollary" and wanted to know if there was an elementary proof. He asked some experts and none of them recognized it or saw an immediate proof. Nonetheless, there was still a good chance that someone would be able to solve it without too much effort. Not knowing the MO rules, I posted this "open problem" to MO. Within a couple of days, two responders had solved the problem between the two of them. This is surely an MO success story. Had I known about the prohibition on open problems and been scrupulous about abiding by them, this never would have happened.

A final example is my question on k-trail-ordered graphs. This is definitely an open problem and it has even been published in an open problems section of a journal. However, I am sure that not many people have looked at it and that there is a good chance that someone might find a simple proof. Of all my examples so far this is the clearest example of an "open problem." Nevertheless, I still feel it is within the spirit of MO (given what I've seen of MO so far) to post it to MO. The important thing in my mind is that this problem is not well known and not known to be hard. While we don't want to clutter MO with open questions that are known to be hard, I don't see the harm in asking questions that are appealing but that have received very little attention. In fact I would think that this is the kind of question that we *want* to see on MO. Therefore I suggest that the guidelines be rewritten accordingly.

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")

]]>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.

]]>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?

]]>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.

another site, that is meant just for open problems:

Open problem garden (garden.irmacs.sfu.ca).

It is most developed in the direction of discrete math, but

we welcome contributions from any research area in mathematics.]]>

Questions which are generally known 'open-problems' should be tagged as such, and community-wikified. Hopefully the contributed answers will become a summary of what is known about the problem, major approaches that have been tried, and a brief description of why they've fallen short.]]>

It can still be useful to have a repository of what is known about an open question and what approaches people have tried. On the other hand, we don't want people fishing for reputation by posting open problems. Making open problems a community wiki seems like a good solution to me.]]>

I would also say that I posted the 6-sphere question, because I'm not in close touch with people who might be working on that and I was curious about whether any progress had been made on it. The response from Joel Fine was quite nice and exactly what I was looking for.

I will monitor the discussion and promise to try to abide by the spirit and rules you all decide on. Thanks!]]>

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.

]]>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.

Personally, I'm undecided on whether or not MO would be a good place to ask open problems. Supposing I had an answer to a long-standing conjecture -- presumably it would be many pages long, and I'd prefer to put it up on my personal webpage rather than make a massive posting to an online forum.]]>

But isn't there room here for a more open-ended site? All of the questions I've asked so far are ones that I believe are unanswered. Two of them are definitely hard open problems, but one ("Point singularity of Riemannian manifold") is one that, as I say in my description, I suspect could be answered by a smart Riemannian geometer. So it's fun to throw the question out there and see if anyone can do it.

Or maybe I should just rephrase my questions differently? Instead of "Is there a complex structure on the 6-sphere?", maybe I should have asked "What is currently known about the existence of a complex structure on the 6-sphere?" But do you really want to enforce this kind of restriction on the wording of the questions?]]>

For now, I've edited that post to include the tag "open-problem", and invited the commenters over here.]]>