# Give us your suggestions!

### Goldbach & FLT

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

### Just do it!

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 Conjecture

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 ;-)

### Our policy

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.

### Could you please add

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

### More Categories !!

It would be nice to have more categories. For example : A subtopic on "Combinatorial Graph Theory" under "Graph Theory".

### More subjects

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 / Measure (I'm not sure what a good collecting term for these topics would be)

- \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)

### Categories for Logic

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,

TJ

### Re: Categories for Logic

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

RS

### Re: Categories for Logic

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,

RS

### Yes, we definitely plan to add more categories

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).

### Categories for Theoretical CS

I suggest adding the following topics to Theoretical CS: "Complexity", "Coding Theory", "Cryptography"

I also suggest that the "Complexity" topic will have the following subtopics: "Derandomization", "Hardness Amplification", "Interactive Proofs", "Hardness of Approximation", "PCP".

### Yes, Theor. CS needs more categories

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! :-)

### After some more thought

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.

## simple-to-state open problems

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?