Open Problem Garden - Give us your suggestions! - Comments

simple-to-state open problems (re: Give us your suggestions!)

Anonymous — Sat, 27 Oct 2012 06:14:24 +0200

why not take an open problem that is hard to explain and find an equivalent simple-to-state question so an amateur might find something about the problem?

More subjects (re: Give us your suggestions!)

cwenner — Sat, 04 Apr 2009 17:58:43 +0200

I am curious, is it easy to move all problems of a subtopic to another subtopic and is it easy to move from a subtopic to a topic? Might I push for the ability to place a problem in up to three topics and subtopics? Many current and potential are categories are overlapping and rightly so.

I believe we need the following

\item Probability Theory \item Measure Theory \item [Mathematical) Statistics \item Stochastic Processes

\item Applied Mathematics

\item [Theoretical/Mathematical) Physics (it could be given its own subject if enough problems are added)

Our policy (re: Give us your suggestions!)

md — Fri, 23 Nov 2007 08:43:51 +0100

As we (the Gardeners: R. Samal and M. DeVos) have discussed with Benschop, our policy toward claimed, but unrefereed proofs of conjectures such as this will be to have the claim appear as a comment to the stated conjecture.

Goldbach Conjecture (re: Give us your suggestions!)

Benschop — Wed, 21 Nov 2007 13:38:26 +0100

I saw that you removed & changed the text that I provided. For the conjecture that's OK. But I protest the removal of my suggestion of a proof (using semigroup theory and carry extension). I put it back, in shorter form, and I hope you have the decency to leave it there for interested readers, who can of course comment on it. I understand that you don't want contamination with trash, but the residue-and-carry method that is used in the proof is also used for a short FLT proof (mod p^k + carry extension), which was published nov.2005 by the Acta Mathematica of Univ. Bratislava ( http://pc2.iam.fmph.uniba.sk/amuc/_vol74n2.html pp169-184), so this approach can be taken seriously. My Goldbach proof is already several months in review at another Acta Mathematica which can take years, in view of the 2 years it took Bratislava to collect enough courage to place the short FLT proof (a theorem that in 10x longer and indirect fashion was already published by A.Wiles in 1995 ;-)

Just do it! (re: Give us your suggestions!)

md — Thu, 06 Sep 2007 19:48:53 +0200

While Robert and I (M. DeVos) have posted many of our favorite conjectures, we do not view it as our responsibility to post the Goldbach Conjecture, or any other particular unsolved problem. The Garden is a community resource, and it will be what people make of it. If you would like to see a page about the Goldbach Conjecture here, you can create one yourself with ease.. as the slogan goes - just do it!

Goldbach & FLT (re: Give us your suggestions!)

Anonymous — Wed, 05 Sep 2007 15:26:00 +0200

Why does the known Goldbach problem (each 2n > 4 is the sum of two odd primes) not appear as unsolved problem in the subsection Additive NrTh of section Number Theory?

A short & direct proof of FLT would also be a challenge (much shorter and more direct than Andrew Wiles proof of 1995, which is an indirect proof via the Tanyama-Shimura conjecture about modular forms and elliptic curves) -- dr. Nico F. Benschop

Re: Comp. N.T. (re: Give us your suggestions!)

rs — Sat, 04 Aug 2007 12:00:17 +0200

Done.

Could you please add (re: Give us your suggestions!)

maxal — Sat, 04 Aug 2007 01:49:22 +0200

Could you please add "Computational Number Theory" subcategory?

Also, is not that better to implement categories and subcategories as tags, making it possible for one problem be in several different categories at the same time? It seems to be much more flexible and useful than the current strict tree-like categorization.

Thanks, Max

Labeling (re: Give us your suggestions!)

kintali — Thu, 19 Jul 2007 22:57:34 +0200

right ! "Labeling" under "Graph Theory" would be more appropriate for my entry. Please create this subcategory.

Thanks -Shiva

After some more thought (re: Give us your suggestions!)

ormeir — Thu, 19 Jul 2007 21:42:56 +0200

Maybe the categories "PCP" and "Hardness of Approximation" should be united.

Also, I think that "Hardness Amplification" should be renamed to "Average Case Complexity", so it will be able to contain more problems.

Re: Categories for Logic (re: Give us your suggestions!)

Robert Samal — Thu, 19 Jul 2007 07:46:28 +0200

It's added now. Looking forward for contributions to this brand new category :-)

Re: Categories for Logic (re: Give us your suggestions!)

Robert Samal — Tue, 17 Jul 2007 02:13:24 +0200

Sure. I'm only not sure: should be Logic under Th. Comp. Sci.? Or vice versa, or both at the top-level?

Any more sub-topics for Logic?

The list of problems you pointed to is a nice one -- looking forward to someone putting it to our site :-) (please, check with the original maintainers of the list, though). If you'll be doing this: try to make it readable for someone, who does not actively work in logic (frequently wikipedia has all the definition, and it is easy to link to it, as is pointed in the "Guide").

Best,

Categories for Logic (re: Give us your suggestions!)

tjgreen — Sat, 14 Jul 2007 18:25:35 +0200

If someone could add a Logic -> Finite Model Theory category, the list of open problems maintained by Dietmar Berwanger and Erich Gradel at

http://www-mgi.informatik.rwth-aachen.de/FMT/problems.pdf

is crying out for Web 2.0-ification.

Thanks,

Yes, Theor. CS needs more categories (re: Give us your suggestions!)

Robert Samal — Sat, 14 Jul 2007 01:53:00 +0200

And yours are good suggestions -- they are added by now. Any more subtopics? Where should a question "Is this in P?" go?

I'm looking forward to some problems that will go to the new categories! :-)

Yes, we definitely plan to add more categories (re: Give us your suggestions!)

Robert Samal — Sat, 14 Jul 2007 01:33:54 +0200

I'm not sure however, what problems should be classified under Combinatorial Graph Theory. For your contribution about Graceful labeling I'd rather create a category Labeling (may be under Graph Theory -> Coloring ?). But if you have some content for the category, we can add it.

Anyway, thanks for the suggestion (and for the Graceful contribution).

Give us your suggestions!

md — Fri, 13 Apr 2007 02:12:10 +0200

This is a forum created for the purpose of having an open discussion about this website. Please post any bugs or errors you find, and tell us if you have any ideas for features you would like to see.