Below is a question I would like to ask on math.SE, but as it is a soft question I want to check first that it would not be considered too vague (or otherwise inappropriate). Here it is:

Title: "Lonely theorems"

What are some instances of theorems which are especially unique in mathematics, i.e. for which there are not many other theorems of a similar character? An example I have in mind is Pick's theorem, since it is the only theorem I have ever seen concerning geometry of polygons with vertices on a lattice.

There are three reasons I am interested in "lonely theorems" like this:

  1. It's hard to find these results. By virtue of their uniqueness, they tend to not fall within the scope of most traditional math classes. The only reason I found out about Pick's theorem was through math competitions.

  2. Related to the last remark, lonely theorems allow those who know of them to solve problems which other people cannot (which is presumably why they tend to arise on math comps), because there are generally not alternative approaches to fall back on.

  3. Sometimes, what begins life as a lonely theorem later becomes the centerpiece of an entire new branch of mathematics. An example that comes to mind here is Mobius inversion, which was initially a trick applying to arithmetic functions, but is now of great importance for lattices & incidence algebras.

So my question for meta is: Is the above question appropriate for math.SE?

EDIT: The proposed question is now posted at Lonely theorems

  • 1
    $\begingroup$ I dunno, are we still taking in big-list questions? $\endgroup$ Jun 16, 2016 at 2:50
  • $\begingroup$ @J.M., why would we have stopped taking in big-list questions? $\endgroup$ Jun 16, 2016 at 3:28
  • $\begingroup$ @Gerry, I'm not that "current" anymore, that was why I was asking. $\endgroup$ Jun 16, 2016 at 3:32
  • $\begingroup$ @J.M., OK, so far as I know, there's no ban on big-list questions. $\endgroup$ Jun 16, 2016 at 5:24
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    $\begingroup$ As soft questions go, you've done enough to motivate the Question by my "standards". In many cases it is more expeditious just to go ahead and ask, rather than to ask if you can ask. $\endgroup$
    – hardmath
    Jun 16, 2016 at 6:08
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    $\begingroup$ It's not too vague, but in my opinion too broad. $\endgroup$
    – mrf
    Jun 16, 2016 at 9:10
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    $\begingroup$ Most big lists questions are too broad. (This is not an endorsement of this question but rather a criticism of big list questions.) $\endgroup$ Jun 16, 2016 at 9:44
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    $\begingroup$ Kudos for phrasing the question ("would this question") as a self-referential sentence on a math forum. You just made a whole bunch of set theorists extremely anxious. $\endgroup$
    – Mark
    Jun 16, 2016 at 10:07
  • $\begingroup$ i would test it by posting it in SE, you have my +1 :P , once you post it on SE ping me in comments $\endgroup$
    – avz2611
    Jun 16, 2016 at 10:13
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    $\begingroup$ (That's offtopic here, really — but I can't resist) (Re: «An example I have in mind is Pick's theorem, since it is the only theorem I have ever seen concerning geometry of polygons with vertices on a lattice.») Pick's theorem is the simplest manifestation of Ehrhart theory. $\endgroup$
    – Grigory M
    Jun 16, 2016 at 11:07
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    $\begingroup$ IMO there are no «lonely theorems» — there is only ignorance. And as for a poll «for which theorem you don't understand its mathematical context» — I don't see the point. (But of course if there are some theorems that look like something completely isolated («lonely») to you — feel free to ask questions about them.) $\endgroup$
    – Grigory M
    Jun 16, 2016 at 11:17
  • $\begingroup$ The main message I'm getting from this discussion is "try it on SE and find out". I'll do that. $\endgroup$
    – Yly
    Jun 16, 2016 at 15:06
  • $\begingroup$ @avz2611 I posted this question at math.stackexchange.com/questions/1828623/lonely-theorems $\endgroup$
    – Yly
    Jun 16, 2016 at 15:08
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    $\begingroup$ @GrigoryM Thanks for the pointer to Ehrhart theory! That's sort of like my point 3 about how lonely theorems later become part of extensive theories. $\endgroup$
    – Yly
    Jun 16, 2016 at 15:12
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    $\begingroup$ @AndreaDiBiagio Already did :) It's posted at math.stackexchange.com/questions/1828623/lonely-theorems $\endgroup$
    – Yly
    Jun 23, 2016 at 1:06


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