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Unsolved problems section?

+ 5 like - 0 dislike
921 views

Recently, this question was asked: http://www.physicsoverflow.org/22034/2d-ising-model-in-cft-and-statistical-mechanics?show=22034#q22034 . The question is basically asking "How do you identify the conformal field theory description of a given lattice model second order phase transition?"

This was a major unsolved problem in conformal field theory in the 2000s, but it might be solved now. On mathoverflow, it is standard to reject problems that are equivalent to famous conjectures (or at least accept any answer that shows the equivalence to the famous conjecture).

But in our case, since we have a review section, I think it might be appropriate to include unsolved problems as "hard research level questions". The answer to these questions would be automatically research level. Certainly answering this question would require a serious research effort.

We could implement this inside the reviews section, but I think it is a separate sort of thing--- it's an "unsolved problems" section. The rating for this can be "difficulty", and when we get an answer, this can modify the score by exp(difficulty^1/3), much as originality does in the review section.

It's an idea. I don't know where to put hard major research level questions like this. They will never get an answer on Q&A, there is no incentive there to do hard things like this.

asked Aug 11, 2014 in Discussion by Ron Maimon (7,535 points) [ no revision ]

I do not care about scores, but I like such a section. I would present some unsolved problems that are forgotten today.

Can we not just make a new "unsolved proplems" subsection in the Q&A part? I would not invent a third rating system for them, but maybe some kind of bounties could be awarded for particularly good answers to them? I think we should by no means reject such great questions.

It's ok, so long as they are separated out, and given a ton more rep for a complete answer, like a permanent bounty of a large number of points.

But perhaps, for these types of things, we can allow users to post an Erdos style money-bounty for a complete correct answer (a complete and correct answer is determined by consensus after posting to reviews, for example, +5 correctness score, positive originality score, upvoted positive reviews with no net-upvoted negative review, and reviewer agreeing that the solution solves the problem).

Then we can aggregate the money bounties, give 12% to polarkernel, and the rest to the answerer. This might demonstrate the economic viability of the site.

I think there are many individuals and organizations who are itching to put money bounties on small unsolved problems, like the Clay institute did in a grandiose way, except much smaller scale. Small scale bounties, unlike large-scale ones attract serious people, not crackpots.

This can work, and it don't think it will interfere at all with ordinary reviews or ordinary Q&A. It can also generate a signficant revenue stream over time.

For unsolved problems, one can also envisage a creativity score, although it is somewhat redundant with originality notion.

Good idea, maybe they could be created as submissions?

@VladimirKalitvianski: The idea is that any proposed complete solution to the problem would not be in an answer, but would get separately posted on reviews, with the associated answer just a link to the review page. The answer to a research level unsolved problem question would then get evaluated by the community as if it were a research paper.

Incomplete solutions, sketches, or incremental steps toward a solution could be posted as ordinary answers to the question and get voted on in the usual way. In this way, we can encourage a communal thing to develop like the mathematics collaborative wikis of recent years.

2 Answers

+ 2 like - 0 dislike

Bump for offtopicarium talk. shouldn't we do this before the talk? That way people who come here can see some research level unsolved problems with some bounties. This section requires no significant coding, it's just a partition of the questions, and one can start with a few unsolved problems on other sites.

answered Aug 27, 2014 by Ron Maimon (7,535 points) [ no revision ]
Most voted comments show all comments

I agree with Dilaton for now, only to save time in coding, normal questions for the time being might be best. The answer, when it is complete, can be a link to a submission, partial answers or steps as normal answers voted in the normal way, but perhaps with a rep multiplier because of the difficulty. A way to do it is to multiply the rep gain per answer by the exp( (number of upvotes on the unsolved problem)^1/3) which is a measure of the difficulty of the problem and the interest in the problem combined.

It is also possible to make it a review type question, where the question has a "importance" (originality) and "difficulty" (accuracy) rating, and this gives the asker rep, while the answers get a rep which is multiplied by the rep for the question--- so a +3 answer to a +21.3 question gets 64.7 rep. Negative vote answers will then cost a lot of rep, keeping the discussion focused. If someone wants to ask something regarding a question, they can comment with a link to a chatroom, and then it won't cost them rep to ask for clarification.

The final answer should be a linked submission that can be voted on normally, and if it is accepted, we should give the points for the submission as rep, and also the points for having solved the unsolved problem--- meaning the vote on the link. That's another possible implementation. But anything will do for now, we're still in beta.

You can guess what problems are unsolved pretty easily. We can put them up tentatively, and if someone says "look, this is solved, see this and this classic reference", then return it to the regular problems section. People generally know what's unsolved, but in some cases, it might be obscure.

A slight and maybe better (?) variation: On MathOverflow they call them Open Problems ...

"Open Problems" sounds just perfect!

@dimension10 The open problems category looks odd at the bottom branch of the category tree away from Q&A and Reviews. At the very least, it should be above Meta, just to stress its status as a category more clearly.

Most recent comments show all comments

@physicsnewbie Good idea, but I don't know how to change the category ordering (or set it at all, by default it's just set as per it's age); maybe @polarkernel or @Dilaton may know?

When you choose the Open Problems category in the admin panel, you can choose its position by a dropdown menu called position. I have now put it below Reviews and above Meta.

+ 1 like - 0 dislike

Isn't it enough to put a tag ''unsolved-problem'' or ''open-problem'' on the question? Then anyone interested can search for them (or a button at the top of the page could do the same, for newcomers).

answered Aug 28, 2014 by Arnold Neumaier (12,385 points) [ revision history ]

It's not enough if you want to score them differently, I think they should be scored much much higher, so that a research level solution gets rewarded properly, as compared to a rehash of earlier work. Also, we can then make Erdos-style money-bounties. I was thinking of attaching a symbolic money bounty of $10 (I'll pay it personally to the solver) to the unsolved problems we have so far. Then others can chip in more, and we'll get attention for sure (and perhaps a small revenue stream). The bounty is awarded for a complete solution, and it can accumulate to a large sum, and then we can take a finder's fee of 12% or 20% to maintain the site, and give the rest of the money to the author.

One of Dimension10's concerns regarding this is that non-money problems will become second-class citizens. If you can only attach money to research level problems, this becomes less of a concern, because ordinary Q&A will be money free and uncorrupted. But then we have to be careful about admitting problems to the unsolved category, to make sure they are really unsolved.

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