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Following my research interests, I am working out a challenge that is like an infinite tournament or competitive game to find short proofs (includes ongoing potential bounties and a wall of fame). Proofs are in some special Hilbert systems of propositional logic, and I currently call it "The hardest logic puzzle game: Help me reduce my oversized proofs!".

I have so far posted it (partially) on Code Golf Sandbox (Meta) to get some feedback, but I have serious doubts that Code Golf would be the right place, despite there being a "proof-golf" tag. (However, there was no feedback so far.)

After now seeing some fairly sophisticated mathematical challenges and competent people on Puzzling, I wonder if this isn't a much better place.

On why this is a puzzle, I wrote:

Proofs for different theorems are components which can be used to build new components when arranged in a specific (and potentially very difficult to find) way. When it comes to snapping formulas together in order to create another one, things behave the same in all D-systems.

But are my tournament rules viable for this site and do you think many people here would take it? Is there a feedback thread on Puzzling Meta similar to Sandbox for Proposed Challenges?

In case you think this is not the right place, do you have any alternative suggestions?

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    $\begingroup$ From your post and comments, I don't think you're seeking to solve a puzzle in the straightforward sense, so much as perform mathematics research. Stack Exchange is not the ecosystem for that, even on the sites where the audience is research-level professionals and experts in that area. $\endgroup$
    – Nij
    Commented Feb 18 at 23:56
  • $\begingroup$ @Nij You're right that I am trying to perform original mathematical research here, but there are two Stack Exchange sites meant to assist with this kind of research, namely MathOverflow and CSTheory. However, those sites are probably not a good fit for this competition style. $\endgroup$
    – xamid
    Commented Feb 20 at 10:36

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Unfortunately, we here at PSE have a rule against open-ended puzzles, which means anything "infinite" is out of the question. The only way this problem would be on-topic here is if you posted an unoptimized proof - one where you already knew what the most optimized version was - and asked people to find and prove that optimization, but it sounds like that's not at all what you're trying to do with this challenge.

As for where else you could post the question, have you looked into MathOverflow or Math.SE? I'm not familiar with their policies, but if you're not satisfied with posting this to Code Golf, those would be the places I would suggest.

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  • $\begingroup$ This is unfortunate, indeed. Maybe I'll look into those sites to compare with Code Golf. But for those three theorems which have not yet been proven in w2, asking for any such D-proof at all would still be a valid question here, right? $\endgroup$
    – xamid
    Commented Feb 16 at 3:49
  • $\begingroup$ Another issue is that strictly speaking it would be [optimization], not [open-ended], because minimality is technically provable (just not practically, as far as we know now, due to limited resources). $\endgroup$
    – xamid
    Commented Feb 16 at 4:06
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    $\begingroup$ @xamid if it's not provable in an answer, then for the purposes of this site it's not provable. The policy on open-ended puzzles aims to address situations where people would keep posting answer after answer, no one sure whether they were the last. $\endgroup$
    – bobble
    Commented Feb 16 at 5:56

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