Suppose I developed a small theorem in a particular domain of mathematics and I don't know whether it was discovered earlier or not.

The theorem I derived or the result I found on my own may be obvious or significant theorem with a particular name in literature or a variant of a significant theorem.

Can I ask these details regarding my research work by presenting the results I got on either MSE or MO? In concise, is it allowed to ask for identification request for my result by presenting the result?

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    $\begingroup$ Note the blurb that appears when you hover the mouse over the upvote button on main Math.SE: "This question shows research effort; it is useful and clear." It seems to me you have not established the history of results in the area "regarding my research work," which is a bit of a conundrum. No refereed journal would accept a paper (I hope) which lacks a bibliography of prior work. The most charitable interpretation I can make is that you are not an academic and want Readers to make a literature search for you. Is that so? $\endgroup$
    – hardmath
    Jul 31 '18 at 4:56
  • $\begingroup$ Asking for identification or a name of the theorem seems the wrong idea. If you have proven something and you have done a thorough literature search and haven't found it, then it could still be reasonable to ask whether it really is new (since one might have missed something). I have done this myself on MO before. $\endgroup$ Jul 31 '18 at 6:24
  • $\begingroup$ The problem is that what I think new may be so obvious for mathematicians and may not be in literature with the same idea as me. I mean, it (the method i found) may be an obvious alternative way of doing it. In such cases literature survey helps hardly and how to know whether it is an obvious result or considerable for some small research paper? $\endgroup$
    – hanugm
    Jul 31 '18 at 6:33
  • $\begingroup$ In general, if an amateur mathematician or hobbyists develop a theorem, they can find on Internet easily. There are very less chances for novelty. In most of the cases, they may be obvious and hence not discussed in literature. So I hope there will be no issue if such questions are asked. $\endgroup$
    – hanugm
    Jul 31 '18 at 7:17
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    $\begingroup$ Neither MSE or MO are appropriate places to either ask for the correctness or novelty of "new" results. $\endgroup$
    – davidlowryduda Mod
    Jul 31 '18 at 18:50

TL;DR version: Such questions are almost certainly off-topic. However, if enough context is given, it is possible that a question about a potentially new result might be well-received.

The goal of MSE is to produce a repository of questions and answers pertaining to topics within mathematics. Questions that are appropriate for MSE are of broad appeal (i.e. the questions themselves should be interesting to people other than the asker, and should lend themselves to answers that are of broad interest as well). Original research is not really a good fit for that model.

Typically, new ideas are vetted for "interestingness" (among other criteria) through publication. The form of publication may vary, depending on the novelty and generality of the result: you may present your result at a conference, you might write a thesis in partial fulfillment of a degree (e.g. an undergraduate honors thesis or a PhD dissertation), posting to a preprint service like arXiv (though it is kind of expected that this is only a first step towards publication in a journal), or you might publish your result in a peer reviewed journal. With these forms of publication, there are "gatekeepers" there to help vet the result. Alternatively, if you wish to avoid the gatekeepers, you should consider getting a blog and publishing your result there.

So, broadly speaking, you should not ask questions on MSE about new results. It is possible that MO might be more open to such questions (I suspect not), but MSE is definitely not the right place.

With the above in mind, your question isn't quite about asking questions about new results, but rather about literature review. If you think you have a new result, the first step is to familiarize yourself with the literature in that part of mathematics (this is something that you should have been doing while proving your result in the first place, but you might as well look now). It is worth noting that Google has a search engine for academic resources, called Google Scholar, which is a good place to start your literature review. Once you have familiarized yourself with the pertinent body of work (which can take some real time), then it might be appropriate to ask a question on MSE.

Again, such a question might be appropriate for MSE. Even so, if you were to ask such a question, I would be prepared for a fair amount of pushback. The people who answer questions on MSE are donating their time to help build the repository. If it looks like you are asking them to do a literature review for you, or prove a result for you, then your question is likely to get closed very quickly.

Therefore keep in mind that your question needs to provide context. At the very least, I would suggest that it should contain

  • a clear and precise statement of the result that you think is novel,
  • an explanation of why that result should be interesting to an outsider, and
  • a concise survey of the literature, with references.

As a possible example, I (personally) probably would be okay with a question that looked something like the following:

I have been working to show that the Hausdorff dimension of the attractor of an iterated function system can be computed in a relatively straightforward manner if the system is well enough behaved. Specifically, let $\{\varphi_j\}_{j=1}^{J}$ is a finite collection of maps $\varphi_j: [0,1]^d \to [0,1]^d$ of the form $$ \varphi_j(x) = c_j U_{j} x + b_j, $$ where $c_j \in (0,1)$ is a scaling, $U_{j}$ is a $d\times d$ unitary matrix, and $b_j \in \mathbb{R}^d$ is a translation. If $\varphi_j([0,1]^d)\cap \varphi_k([0,1]^d)$ whenever $j\ne k$, then the Hausdorff dimension is the unique real solution to the equation \begin{equation*} \sum_{j=1}^{J} c_j^s = 1. \end{equation*}

This result is of general interest as it gives a simple way of computing the Hausdorff dimension of a relatively large class of subsets of $\mathbb{R}^d$. Moreover, given a positive real number $s$, this result gives guidance on how to construct a set with Hausdorff dimension $s$ (by choosing appropriate contractions on a sufficiently large space). This shows that for any nonnegative number $s$, there exists (an explicitly constructible set) with Hausdorff dimension $s$.

I do not see this result in the literature on measure theory. For example, in [Book $X$] the Hausdorff dimension of the ternary Cantor set is computed "by hand." My result gives the same information, but in a more general setting. I have also read [Books $Y$, $Z$] and [Articles $\alpha$, $\beta$, $\gamma$], which construct the Hausdorff dimension and motivate the question, but don't the same general result.

Question: Is this a known result? If so, can you please provide a reference?

Then tag the question with and (plus any other relevant tags).

  • $\begingroup$ I think it is apples and oranges. Ask a question about references, no need to include a sketch or outline of the proof, or to ask about its correctness. If later it turns out that correctness may be an issue, ask a separate, different question, with the sketch. No need to include in that case the books that were consulted or similar information. Mixing both questions is likely to produce unsatisfactory results. $\endgroup$ Jul 31 '18 at 22:39
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    $\begingroup$ @AndrésE.Caicedo I've edited the example. Though, as I said, I don't think that MSE is really a good place to either publish new results or to offload the task of a literature review. I still think that the question I've written is of pretty marginal quality, but it at least borders on acceptable (maybe?). $\endgroup$
    – Xander Henderson Mod
    Aug 1 '18 at 1:22

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